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croissant.json

@@ -0,0 +1,231 @@
+{
+  "@context": {
+    "@language": "en",
+    "@vocab": "https://schema.org/",
+    "citeAs": "cr:citeAs",
+    "column": "cr:column",
+    "conformsTo": "dct:conformsTo",
+    "cr": "http://mlcommons.org/croissant/",
+    "rai": "http://mlcommons.org/croissant/RAI/",
+    "data": {"@id": "cr:data", "@type": "@json"},
+    "dataType": {"@id": "cr:dataType", "@type": "@vocab"},
+    "dct": "http://purl.org/dc/terms/",
+    "examples": {"@id": "cr:examples", "@type": "@json"},
+    "extract": "cr:extract",
+    "field": "cr:field",
+    "fileProperty": "cr:fileProperty",
+    "fileObject": "cr:fileObject",
+    "fileSet": "cr:fileSet",
+    "format": "cr:format",
+    "includes": "cr:includes",
+    "isLiveDataset": "cr:isLiveDataset",
+    "jsonPath": "cr:jsonPath",
+    "key": "cr:key",
+    "md5": "cr:md5",
+    "parentField": "cr:parentField",
+    "path": "cr:path",
+    "recordSet": "cr:recordSet",
+    "references": "cr:references",
+    "regex": "cr:regex",
+    "repeated": "cr:repeated",
+    "replace": "cr:replace",
+    "sc": "https://schema.org/",
+    "separator": "cr:separator",
+    "source": "cr:source",
+    "subField": "cr:subField",
+    "transform": "cr:transform"
+  },
+  "@type": "sc:Dataset",
+  "conformsTo": "http://mlcommons.org/croissant/1.0",
+  "name": "SimVerse",
+  "description": "A multi-task benchmark for evaluating multimodal LLMs on interactive simulation puzzles. Five independent tasks (Text-VOI placements, cube reconstruction, cube goal-roll, mechanical-arm lamp targeting, Cut the Rope video-to-command) share a uniform 9-section prompt skeleton and a uniform FINAL_JSON output contract for cross-task comparability. Each per-level record carries the literal prompt text the benchmark presents to models, so reproductions need no auxiliary code. Anonymized for double-blind review; author and citation fields contain placeholder values until the review concludes.",
+  "license": "https://opensource.org/licenses/MIT",
+  "url": "https://huggingface.co/datasets/Sayaka123/simverse2026",
+  "version": "1.0.0",
+  "datePublished": "2026",
+  "keywords": [
+    "benchmark",
+    "multimodal",
+    "spatial-reasoning",
+    "video-understanding",
+    "tool-use",
+    "evaluation"
+  ],
+
+  "rai:dataCollection": "All five tasks were programmatically generated. VOI uses a polygon-rasterization XOR generator. cube1 and cube2 use a pure-Python cube-state simulator that records roll sequences and bottom-face imprints. lamp uses a forward-kinematics generator with axis-aligned obstacle placement. cutRope is built on top of the open-source yell0wsuit/cuttherope-h5dx HTML5 port (MIT-licensed) by recording deterministic gameplay clips and authoring matching command scripts. No human subjects or real-world data were involved.",
+  "rai:dataAnnotationProtocol": "Reference solutions are produced by the same generators that create each puzzle (programmatic ground truth). For closed-form tasks (VOI, cube1, lamp), the answer is uniquely determined and machine-verifiable. For open-ended tasks (cube2 goal-roll, cutRope), the dataset's `answer` field carries one known-valid reference solution; validators run the underlying engine against the model's actual output rather than performing string equality, so multiple correct answers earn full credit.",
+  "rai:dataAnnotationAnalysis": "Each generator's output was post-validated by the same engine the eval validator uses, so every shipped record is provably solvable. Sentinel '?' values appear in cube1 records when puzzle constraints leave a face under-determined; this is intentional and follows the documented sentinel-pair rule (rotation forced to 0 when patternId is '?').",
+  "rai:dataPreprocessingProtocol": "All per-level JSON files conform to a v1 schema documented in PROMPT_SKELETON.md (locked schemas per task). A migration step lifts legacy task-native answer formats into the unified `answer` envelope and a separate populate_prompts step embeds the literal system+user prompt strings into each record. Both transformations are idempotent and reproducible from the accompanying code.",
+  "rai:dataLimitations": "Synthetic puzzles in fixed visual styles per task — models may learn render-style shortcuts rather than the underlying reasoning skill. All prompts are English-only. Difficulty distribution is hand-tuned per generator and not necessarily uniform. cube1 includes '?' sentinel patterns when faces are under-determined; downstream uses outside the SimVerse evaluation flow may need to filter these. Because reference solutions for open-ended tasks are non-unique, simple string-match scoring is inappropriate and the bundled engine-based validator should be used.",
+  "rai:dataBiases": "Each task's visual style is uniform across all of its records, which can bias evaluations toward render-style recognition rather than the reasoning skill the task is intended to probe. Reference solutions for open-ended tasks favor specific solution paths even when other paths are equally valid; validators are designed to score by simulation outcome rather than reference matching, but downstream comparisons that ignore this design will systematically under-credit divergent strategies. Object-count distributions in cutRope reflect the original yell0wsuit corpus and are not balanced across gameplay-element categories.",
+  "rai:personalSensitiveInformation": "None. Fully synthetic; the dataset contains no personally identifiable information, no human-subject data, and no sensitive content. cutRope videos are gameplay recordings of an open-source physics-puzzle game with no real-world imagery.",
+  "rai:dataUseCases": "Evaluating multimodal large language models on (a) spatial-pattern reconstruction (VOI, cube1, cube2), (b) multi-step planning under physical constraints (lamp, cube2, cutRope), and (c) short-horizon video-to-program inference (cutRope). The dataset is designed strictly for held-out benchmarking — there is no train split. It is NOT intended as a held-out training set, NOT a real-world capability predictor, and NOT a substitute for application-specific evaluation.",
+  "rai:dataSocialImpact": "Low. Synthetic abstract puzzles are unlikely to encode harmful content or to enable misuse beyond benchmark gaming. Primary risk: if widely adopted, models tuned specifically on these visual styles may show inflated capability claims that do not transfer to real-world spatial reasoning tasks. The dataset is purely for evaluation and contains no instructions toward harmful behaviors.",
+  "rai:dataReleaseMaintenancePlan": "All levels are deterministically regenerable from the generators in the accompanying code repository (linked from the dataset card under the post-acceptance camera-ready URL). Schema and prompt-template changes are released as new versioned snapshots; per-record `legacy_*` fields preserve pre-migration values for one release cycle to ease comparisons across versions.",
+
+  "distribution": [
+    {
+      "@type": "cr:FileObject",
+      "@id": "voi-test-jsonl",
+      "name": "voi/test.jsonl",
+      "description": "Per-record JSON-Lines for the VOI (Text-VOI placements) task, one level per line.",
+      "contentUrl": "voi/test.jsonl",
+      "encodingFormat": "application/jsonlines"
+    },
+    {
+      "@type": "cr:FileSet",
+      "@id": "voi-images",
+      "name": "voi/images",
+      "description": "Per-level rendered images (target pattern + base-shape pieces) for VOI.",
+      "encodingFormat": "image/png",
+      "includes": "voi/images/**/*.png"
+    },
+    {
+      "@type": "cr:FileObject",
+      "@id": "cube1-test-jsonl",
+      "name": "cube1/test.jsonl",
+      "description": "Per-record JSON-Lines for the cube reconstruction task.",
+      "contentUrl": "cube1/test.jsonl",
+      "encodingFormat": "application/jsonlines"
+    },
+    {
+      "@type": "cr:FileSet",
+      "@id": "cube1-images",
+      "name": "cube1/images",
+      "description": "Blank-cross-net and path-imprint images for cube reconstruction.",
+      "encodingFormat": "image/png",
+      "includes": "cube1/images/**/*.png"
+    },
+    {
+      "@type": "cr:FileObject",
+      "@id": "cube2-test-jsonl",
+      "name": "cube2/test.jsonl",
+      "description": "Per-record JSON-Lines for the cube goal-roll task.",
+      "contentUrl": "cube2/test.jsonl",
+      "encodingFormat": "application/jsonlines"
+    },
+    {
+      "@type": "cr:FileSet",
+      "@id": "cube2-images",
+      "name": "cube2/images",
+      "description": "Initial-net and target-top-face images for cube goal-roll.",
+      "encodingFormat": "image/png",
+      "includes": "cube2/images/**/*.png"
+    },
+    {
+      "@type": "cr:FileObject",
+      "@id": "lamp-test-jsonl",
+      "name": "lamp/test.jsonl",
+      "description": "Per-record JSON-Lines for the mechanical-lamp targeting task.",
+      "contentUrl": "lamp/test.jsonl",
+      "encodingFormat": "application/jsonlines"
+    },
+    {
+      "@type": "cr:FileSet",
+      "@id": "lamp-images",
+      "name": "lamp/images",
+      "description": "Workspace images (arm, target, obstacles) for the mechanical-lamp task.",
+      "encodingFormat": "image/png",
+      "includes": "lamp/images/**/*.png"
+    },
+    {
+      "@type": "cr:FileObject",
+      "@id": "cutrope-test-jsonl",
+      "name": "cutrope/test.jsonl",
+      "description": "Per-record JSON-Lines for the Cut the Rope video-to-command task.",
+      "contentUrl": "cutrope/test.jsonl",
+      "encodingFormat": "application/jsonlines"
+    },
+    {
+      "@type": "cr:FileSet",
+      "@id": "cutrope-videos",
+      "name": "cutrope/videos",
+      "description": "Short MP4 gameplay clips (~3s each, 1920x1080) for cutRope.",
+      "encodingFormat": "video/mp4",
+      "includes": "cutrope/videos/*.mp4"
+    }
+  ],
+
+  "recordSet": [
+    {
+      "@type": "cr:RecordSet",
+      "@id": "voi",
+      "name": "voi",
+      "description": "Text-VOI placements task: 600 records.",
+      "field": [
+        {"@type": "cr:Field", "@id": "voi/sample_id", "name": "sample_id", "description": "Stable level id, e.g. voi-000.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "voi-test-jsonl"}, "extract": {"jsonPath": "$.__sample_id__"}}},
+        {"@type": "cr:Field", "@id": "voi/prompt_system", "name": "prompt_system", "description": "Verbatim system-prompt text the benchmark presents.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "voi-test-jsonl"}, "extract": {"jsonPath": "$.prompt.system"}}},
+        {"@type": "cr:Field", "@id": "voi/prompt_user", "name": "prompt_user", "description": "Verbatim user-prompt text (9-section skeleton, instance-filled).", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "voi-test-jsonl"}, "extract": {"jsonPath": "$.prompt.user"}}},
+        {"@type": "cr:Field", "@id": "voi/answer", "name": "answer", "description": "Reference placements list. Schema: {placements:[{shape,angle,vertex,grid}]}.", "dataType": "cr:Json",
+          "source": {"fileObject": {"@id": "voi-test-jsonl"}, "extract": {"jsonPath": "$.answer"}}}
+      ]
+    },
+    {
+      "@type": "cr:RecordSet",
+      "@id": "cube1",
+      "name": "cube1",
+      "description": "Cube reconstruction task: 502 records.",
+      "field": [
+        {"@type": "cr:Field", "@id": "cube1/sample_id", "name": "sample_id", "description": "Stable level id, e.g. C001.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube1-test-jsonl"}, "extract": {"jsonPath": "$.__sample_id__"}}},
+        {"@type": "cr:Field", "@id": "cube1/prompt_system", "name": "prompt_system", "description": "Verbatim system-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube1-test-jsonl"}, "extract": {"jsonPath": "$.prompt.system"}}},
+        {"@type": "cr:Field", "@id": "cube1/prompt_user", "name": "prompt_user", "description": "Verbatim user-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube1-test-jsonl"}, "extract": {"jsonPath": "$.prompt.user"}}},
+        {"@type": "cr:Field", "@id": "cube1/answer", "name": "answer", "description": "Reference six-face map. Schema: {faces:{TOP:{patternId,rotation},...}}.", "dataType": "cr:Json",
+          "source": {"fileObject": {"@id": "cube1-test-jsonl"}, "extract": {"jsonPath": "$.answer"}}}
+      ]
+    },
+    {
+      "@type": "cr:RecordSet",
+      "@id": "cube2",
+      "name": "cube2",
+      "description": "Cube goal-roll task: 502 records.",
+      "field": [
+        {"@type": "cr:Field", "@id": "cube2/sample_id", "name": "sample_id", "description": "Stable level id, e.g. C001.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube2-test-jsonl"}, "extract": {"jsonPath": "$.__sample_id__"}}},
+        {"@type": "cr:Field", "@id": "cube2/prompt_system", "name": "prompt_system", "description": "Verbatim system-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube2-test-jsonl"}, "extract": {"jsonPath": "$.prompt.system"}}},
+        {"@type": "cr:Field", "@id": "cube2/prompt_user", "name": "prompt_user", "description": "Verbatim user-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cube2-test-jsonl"}, "extract": {"jsonPath": "$.prompt.user"}}},
+        {"@type": "cr:Field", "@id": "cube2/answer", "name": "answer", "description": "One known-valid roll sequence. Schema: {directions:['N'|'S'|'E'|'W',...]}.", "dataType": "cr:Json",
+          "source": {"fileObject": {"@id": "cube2-test-jsonl"}, "extract": {"jsonPath": "$.answer"}}}
+      ]
+    },
+    {
+      "@type": "cr:RecordSet",
+      "@id": "lamp",
+      "name": "lamp",
+      "description": "Mechanical-lamp targeting task: 610 records.",
+      "field": [
+        {"@type": "cr:Field", "@id": "lamp/sample_id", "name": "sample_id", "description": "Stable level id, e.g. lamp-000.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "lamp-test-jsonl"}, "extract": {"jsonPath": "$.__sample_id__"}}},
+        {"@type": "cr:Field", "@id": "lamp/prompt_system", "name": "prompt_system", "description": "Verbatim system-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "lamp-test-jsonl"}, "extract": {"jsonPath": "$.prompt.system"}}},
+        {"@type": "cr:Field", "@id": "lamp/prompt_user", "name": "prompt_user", "description": "Verbatim user-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "lamp-test-jsonl"}, "extract": {"jsonPath": "$.prompt.user"}}},
+        {"@type": "cr:Field", "@id": "lamp/answer", "name": "answer", "description": "Reference per-joint angles. Schema: {actions:[{joint,angle},...]}.", "dataType": "cr:Json",
+          "source": {"fileObject": {"@id": "lamp-test-jsonl"}, "extract": {"jsonPath": "$.answer"}}}
+      ]
+    },
+    {
+      "@type": "cr:RecordSet",
+      "@id": "cutrope",
+      "name": "cutrope",
+      "description": "Cut the Rope video-to-command task: 272 records.",
+      "field": [
+        {"@type": "cr:Field", "@id": "cutrope/sample_id", "name": "sample_id", "description": "Stable level id, e.g. rope-000.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cutrope-test-jsonl"}, "extract": {"jsonPath": "$.__sample_id__"}}},
+        {"@type": "cr:Field", "@id": "cutrope/prompt_system", "name": "prompt_system", "description": "Verbatim system-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cutrope-test-jsonl"}, "extract": {"jsonPath": "$.prompt.system"}}},
+        {"@type": "cr:Field", "@id": "cutrope/prompt_user", "name": "prompt_user", "description": "Verbatim user-prompt text.", "dataType": "sc:Text",
+          "source": {"fileObject": {"@id": "cutrope-test-jsonl"}, "extract": {"jsonPath": "$.prompt.user"}}},
+        {"@type": "cr:Field", "@id": "cutrope/answer", "name": "answer", "description": "Reference 3-star command script. Schema: {commands,reason,confidence}.", "dataType": "cr:Json",
+          "source": {"fileObject": {"@id": "cutrope-test-jsonl"}, "extract": {"jsonPath": "$.answer"}}}
+      ]
+    }
+  ]
+}

cube1/data/C084.json

@@ -0,0 +1,215 @@
+{
+  "sample_id": "C084",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C084_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 84,
+    "name": "Reconstruct 084",
+    "difficulty": 1,
+    "move_count": 3,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-084.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "3-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "9",
+    "heart",
+    "V",
+    "2",
+    "3",
+    "Y"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "3",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "LEFT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "LEFT"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "heart",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "3",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "V",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "3",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C084\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=180, flipVertical=true\n- step 2: patternId=heart, rotation=270, flipVertical=true\n- step 3: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: V, heart, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C085.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C085",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C085_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 85,
+    "name": "Reconstruct 085",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-085.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "C",
+    "7",
+    "2",
+    "heart",
+    "square",
+    "arrow_up"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "C",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "heart",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "7",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "square",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C085\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=square, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C086.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C086",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C086_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 86,
+    "name": "Reconstruct 086",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-086.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "2",
+    "7",
+    "circle",
+    "K",
+    "U",
+    "I"
+  ],
+  "start_x": 2,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "2",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "BACK",
+    "LEFT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "K",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "U",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "K",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C086\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=270, flipVertical=true\n- step 2: patternId=U, rotation=90, flipVertical=true\n- allowed patternId values for this task: K, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C088.json

@@ -0,0 +1,215 @@
+{
+  "sample_id": "C088",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C088_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 88,
+    "name": "Reconstruct 088",
+    "difficulty": 1,
+    "move_count": 3,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-088.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "3-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "1",
+    "star",
+    "V",
+    "G",
+    "1",
+    "plus"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "1",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "plus",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "star",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "1",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C088\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=1, rotation=0, flipVertical=true\n- step 3: patternId=plus, rotation=270, flipVertical=true\n- allowed patternId values for this task: star, 1, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C089.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C089",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C089_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 89,
+    "name": "Reconstruct 089",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-089.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "W",
+    "7",
+    "Y",
+    "4",
+    "2",
+    "heart"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "heart",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "Y",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "Y",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "Y",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Y",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C089\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=0, flipVertical=true\n- step 2: patternId=Y, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, Y, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C090.json

@@ -0,0 +1,215 @@
+{
+  "sample_id": "C090",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C090_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 90,
+    "name": "Reconstruct 090",
+    "difficulty": 1,
+    "move_count": 3,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-090.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "3-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "A",
+    "I",
+    "circle",
+    "arrow_right",
+    "O"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 5,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "BACK"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "BACK"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "I",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C090\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=90, flipVertical=true\n- step 3: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: I, S, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C091.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C091",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "P",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C091_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 91,
+    "name": "Reconstruct 091",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-091.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "smile",
+    "smile",
+    "P",
+    "arrow_up",
+    "arrow_down",
+    "D"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 3,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "P",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "P",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "smile",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "P",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "P",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C091\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=90, flipVertical=true\n- allowed patternId values for this task: P, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C092.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C092",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C092_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 92,
+    "name": "Reconstruct 092",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-092.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "plus",
+    "H",
+    "D",
+    "6",
+    "W",
+    "7"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "7",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "H",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "D",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "H",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "W",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "H",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C092\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=90, flipVertical=true\n- step 2: patternId=H, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C093.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C093",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C093_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 93,
+    "name": "Reconstruct 093",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-093.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "6",
+    "7",
+    "5",
+    "heart",
+    "3",
+    "square"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 3,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "square",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "3",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "BACK",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "6",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "heart",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "heart",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C093\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C094.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C094",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C094_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 94,
+    "name": "Reconstruct 094",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-094.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "plus",
+    "heart",
+    "M",
+    "smile",
+    "3",
+    "Z"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 3,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "3",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "M",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "Z",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "3",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "3",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C094\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=3, rotation=270, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: 3, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C095.json

@@ -0,0 +1,214 @@
+{
+  "sample_id": "C095",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "W",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C095_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 95,
+    "name": "Reconstruct 095",
+    "difficulty": 1,
+    "move_count": 3,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-095.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "3-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "E",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "U",
+    "7",
+    "plus",
+    "arrow_right",
+    "E",
+    "U"
+  ],
+  "start_x": 2,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "U",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "7",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "LEFT",
+    "BACK"
+  ],
+  "required_slots": [
+    "BACK",
+    "LEFT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "E",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "E",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C095\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 3\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_right, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=270, flipVertical=true\n- step 3: patternId=arrow_right, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_right, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C096.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C096",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C096_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 96,
+    "name": "Reconstruct 096",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-096.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "L",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "L",
+    "triangle",
+    "V",
+    "square",
+    "4",
+    "A"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 3,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "L",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "triangle",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "A",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "L",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "V",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "L",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C096\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C097.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C097",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C097_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 97,
+    "name": "Reconstruct 097",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-097.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "3",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "3",
+    "arrow_down",
+    "Q",
+    "X",
+    "I",
+    "K"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 3,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "3",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "3",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "I",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "3",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C097\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=0, flipVertical=true\n- step 2: patternId=3, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C098.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C098",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C098_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 98,
+    "name": "Reconstruct 098",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-098.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "circle",
+    "I",
+    "S",
+    "triangle",
+    "heart",
+    "A"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 3,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "I",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "triangle",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "heart",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "S",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C098\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=0, flipVertical=true\n- step 2: patternId=circle, rotation=270, flipVertical=true\n- allowed patternId values for this task: S, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C099.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C099",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C099_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 99,
+    "name": "Reconstruct 099",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-099.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "6",
+    "G",
+    "2",
+    "arrow_down",
+    "arrow_left",
+    "Z"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 3,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "6",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "G",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C099\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=6, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C100.json

@@ -0,0 +1,200 @@
+{
+  "sample_id": "C100",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C100_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 100,
+    "name": "Reconstruct 100",
+    "difficulty": 1,
+    "move_count": 2,
+    "tier": 1,
+    "source_level_path": "levels/reconstruct/generated-100.json",
+    "tier_label": "Difficulty 1"
+  },
+  "description": "2-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "W",
+    "1",
+    "arrow_right",
+    "star",
+    "D",
+    "star"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "D",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "star",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C100\n- net_layout: standard_cross\n- difficulty: 1\n- move_count: 2\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=star, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- allowed patternId values for this task: star, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C101.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C101",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C101_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 101,
+    "name": "Reconstruct 101",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-101.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "arrow_left",
+    "W",
+    "W",
+    "circle",
+    "U",
+    "Z"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "W",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "Z",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "U",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "W",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "W",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C101\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=270, flipVertical=true\n- step 2: patternId=circle, rotation=0, flipVertical=true\n- step 3: patternId=Z, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: U, circle, Z, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C102.json

@@ -0,0 +1,243 @@
+{
+  "sample_id": "C102",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> S -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "W",
+    "S",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C102_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 102,
+    "name": "Reconstruct 102",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-102.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "H",
+    "V",
+    "arrow_right",
+    "7",
+    "8",
+    "5"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "5",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "5",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "7",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "5",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C102\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> S -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- step 3: patternId=7, rotation=270, flipVertical=true\n- step 4: patternId=5, rotation=180, flipVertical=true\n- step 5: patternId=7, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, arrow_right, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C103.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C103",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "W",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C103_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 103,
+    "name": "Reconstruct 103",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-103.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "R",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "R",
+    "T",
+    "R",
+    "X",
+    "V",
+    "H"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "R",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "H",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "R",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "X",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "V",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "R",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "R",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C103\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=R, rotation=180, flipVertical=true\n- step 3: patternId=X, rotation=180, flipVertical=true\n- step 4: patternId=R, rotation=180, flipVertical=true\n- step 5: patternId=V, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, R, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C104.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C104",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "W",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "R",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C104_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 104,
+    "name": "Reconstruct 104",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-104.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "M",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "R",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "M",
+    "C",
+    "5",
+    "R",
+    "S",
+    "A"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "R",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "R",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "LEFT",
+    "TOP",
+    "BACK"
+  ],
+  "required_slots": [
+    "BACK",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "M",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "R",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "S",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "R",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C104\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=R, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=270, flipVertical=true\n- step 3: patternId=M, rotation=0, flipVertical=true\n- step 4: patternId=R, rotation=180, flipVertical=true\n- allowed patternId values for this task: R, S, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C105.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C105",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "W",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C105_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 105,
+    "name": "Reconstruct 105",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-105.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "V",
+    "L",
+    "arrow_left",
+    "Y",
+    "8",
+    "4"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "4",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "FRONT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "TOP"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "V",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "8",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C105\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=180, flipVertical=true\n- step 4: patternId=L, rotation=0, flipVertical=true\n- allowed patternId values for this task: 8, L, V, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C106.json

@@ -0,0 +1,245 @@
+{
+  "sample_id": "C106",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "W",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C106_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 106,
+    "name": "Reconstruct 106",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-106.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "M",
+    "5",
+    "L",
+    "star",
+    "diamond",
+    "U"
+  ],
+  "start_x": 1,
+  "start_y": 4,
+  "grid_width": 4,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "5",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "L",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "M",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "U",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "star",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "diamond",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "L",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "L",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C106\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=L, rotation=0, flipVertical=true\n- step 2: patternId=star, rotation=0, flipVertical=true\n- step 3: patternId=U, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=0, flipVertical=true\n- step 5: patternId=M, rotation=180, flipVertical=true\n- allowed patternId values for this task: L, star, U, diamond, M, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C107.json

@@ -0,0 +1,245 @@
+{
+  "sample_id": "C107",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "E",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C107_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 107,
+    "name": "Reconstruct 107",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-107.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "O",
+    "H",
+    "6",
+    "Z",
+    "X",
+    "8"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "Z",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "8",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "H",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "Z",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "6",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "Z",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C107\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=180, flipVertical=true\n- step 2: patternId=Z, rotation=180, flipVertical=true\n- step 3: patternId=8, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=0, flipVertical=true\n- allowed patternId values for this task: X, Z, 8, 6, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C108.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C108",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "W",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C108_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 108,
+    "name": "Reconstruct 108",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-108.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "square",
+    "I",
+    "smile",
+    "arrow_left",
+    "U",
+    "B"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "B",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "I",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "smile",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "TOP"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "square",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "B",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_left",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "smile",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "B",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_left",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "smile",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C108\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=180, flipVertical=true\n- step 3: patternId=arrow_left, rotation=180, flipVertical=true\n- step 4: patternId=square, rotation=270, flipVertical=true\n- allowed patternId values for this task: smile, B, arrow_left, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C109.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C109",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "9",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C109_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 109,
+    "name": "Reconstruct 109",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-109.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "9",
+    "B",
+    "1",
+    "2",
+    "N",
+    "5"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "5",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "B",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "N",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "1",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "9",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "9",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "5",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "B",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "1",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "5",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "B",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "1",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C109\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=90, flipVertical=true\n- step 2: patternId=9, rotation=180, flipVertical=true\n- step 3: patternId=B, rotation=0, flipVertical=true\n- step 4: patternId=5, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, 9, B, 5, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C110.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C110",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "W",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C110_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 110,
+    "name": "Reconstruct 110",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-110.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "T",
+    "arrow_right",
+    "T",
+    "W",
+    "smile",
+    "J"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "T",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "J",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "J",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "arrow_right",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "T",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "T",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C110\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=arrow_right, rotation=90, flipVertical=true\n- step 3: patternId=J, rotation=180, flipVertical=true\n- step 4: patternId=arrow_right, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, arrow_right, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C111.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C111",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C111_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 111,
+    "name": "Reconstruct 111",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-111.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "M",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "M",
+    "Y",
+    "diamond",
+    "diamond",
+    "H",
+    "H"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "H",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "H",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "diamond",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "H",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "Y",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "diamond",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "H",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "diamond",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C111\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=180, flipVertical=true\n- step 2: patternId=Y, rotation=90, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, Y, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C112.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C112",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C112_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 112,
+    "name": "Reconstruct 112",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-112.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "P",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "P",
+    "L",
+    "S",
+    "Q",
+    "arrow_down",
+    "arrow_down"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "P",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "Q",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_down",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "arrow_down",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C112\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=L, rotation=0, flipVertical=true\n- step 3: patternId=arrow_down, rotation=90, flipVertical=true\n- step 4: patternId=arrow_down, rotation=0, flipVertical=true\n- allowed patternId values for this task: arrow_down, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C113.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C113",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "N",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C113_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 113,
+    "name": "Reconstruct 113",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-113.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "W",
+    "smile",
+    "Q",
+    "arrow_down",
+    "circle",
+    "W"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_down",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C113\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=circle, rotation=270, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=Q, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=arrow_down, rotation=90, flipVertical=true\n- allowed patternId values for this task: circle, arrow_down, Q, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C114.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C114",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> E -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "E",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C114_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 114,
+    "name": "Reconstruct 114",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-114.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "W",
+    "Q",
+    "smile",
+    "D",
+    "T",
+    "C"
+  ],
+  "start_x": 2,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "C",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "Q",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "smile",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "BOTTOM",
+    "TOP"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "W",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "C",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "Q",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "T",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "C",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "Q",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C114\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> E -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=180, flipVertical=true\n- step 2: patternId=Q, rotation=270, flipVertical=true\n- step 3: patternId=C, rotation=180, flipVertical=true\n- step 4: patternId=T, rotation=90, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, Q, C, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C115.json

@@ -0,0 +1,228 @@
+{
+  "sample_id": "C115",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "N",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C115_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 115,
+    "name": "Reconstruct 115",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-115.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "heart",
+    "circle",
+    "plus",
+    "V",
+    "W",
+    "R"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "heart",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "R",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_count": 2,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "plus",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C115\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=plus, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=180, flipVertical=true\n- step 3: patternId=plus, rotation=180, flipVertical=true\n- step 4: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: plus, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C116.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C116",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "E",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C116_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 116,
+    "name": "Reconstruct 116",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-116.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "D",
+    "Z",
+    "L",
+    "2",
+    "U"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Z",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "U",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "L",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "BACK"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "L",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "2",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "Z",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "2",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "Z",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C116\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Z, rotation=270, flipVertical=true\n- step 2: patternId=L, rotation=270, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=L, rotation=180, flipVertical=true\n- allowed patternId values for this task: Z, L, S, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C117.json

@@ -0,0 +1,245 @@
+{
+  "sample_id": "C117",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "N",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C117_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 117,
+    "name": "Reconstruct 117",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-117.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "8",
+    "O",
+    "Z",
+    "W",
+    "L",
+    "1"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Z",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "8",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "1",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "O",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "Z",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Z",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C117\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=0, flipVertical=true\n- step 4: patternId=L, rotation=180, flipVertical=true\n- step 5: patternId=8, rotation=180, flipVertical=true\n- allowed patternId values for this task: O, Z, 1, L, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C118.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C118",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "W",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C118_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 118,
+    "name": "Reconstruct 118",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-118.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "F",
+    "W",
+    "4",
+    "L",
+    "A",
+    "D"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "F",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "A",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "4",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "TOP"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "F",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "D",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "W",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "4",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "F",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "4",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C118\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=D, rotation=90, flipVertical=true\n- step 4: patternId=4, rotation=0, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- allowed patternId values for this task: 4, W, D, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C119.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C119",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C119_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 119,
+    "name": "Reconstruct 119",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-119.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "8",
+    "G",
+    "N",
+    "W",
+    "I",
+    "G"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "8",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "N",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BACK"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BACK"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "8",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "G",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "W",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "N",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "8",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "N",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C119\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=270, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- allowed patternId values for this task: N, G, 8, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C120.json

@@ -0,0 +1,243 @@
+{
+  "sample_id": "C120",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "N",
+    "W",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C120_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 120,
+    "name": "Reconstruct 120",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-120.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "plus",
+    "6",
+    "P",
+    "V",
+    "O",
+    "K"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "P",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "TOP",
+    "LEFT",
+    "TOP",
+    "BACK"
+  ],
+  "required_slots": [
+    "BACK",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "plus",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "V",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "O",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C120\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=plus, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=90, flipVertical=true\n- step 4: patternId=plus, rotation=90, flipVertical=true\n- step 5: patternId=V, rotation=270, flipVertical=true\n- allowed patternId values for this task: V, plus, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C121.json

@@ -0,0 +1,245 @@
+{
+  "sample_id": "C121",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "N",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C121_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 121,
+    "name": "Reconstruct 121",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-121.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "A",
+    "diamond",
+    "S",
+    "G",
+    "V",
+    "9"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 7,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "A",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "x": 5,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "LEFT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "LEFT",
+    "FRONT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "A",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "diamond",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "G",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "V",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "S",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "A",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "G",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C121\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=S, rotation=180, flipVertical=true\n- step 2: patternId=A, rotation=270, flipVertical=true\n- step 3: patternId=G, rotation=0, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- step 5: patternId=diamond, rotation=180, flipVertical=true\n- allowed patternId values for this task: S, A, G, V, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C122.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C122",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "E",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C122_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 122,
+    "name": "Reconstruct 122",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-122.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "T",
+    "3",
+    "8",
+    "1",
+    "A",
+    "V"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "3",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "1",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "A",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "8",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "A",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "1",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "LEFT",
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "LEFT",
+    "BACK"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "T",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "1",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "A",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "8",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "1",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "8",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C122\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=270, flipVertical=true\n- step 2: patternId=T, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=0, flipVertical=true\n- step 4: patternId=1, rotation=270, flipVertical=true\n- step 5: patternId=T, rotation=90, flipVertical=true\n- allowed patternId values for this task: 8, T, A, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C123.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C123",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C123_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 123,
+    "name": "Reconstruct 123",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-123.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "6",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "6",
+    "V",
+    "S",
+    "arrow_up",
+    "diamond",
+    "2"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_up",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "2",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_up",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "diamond",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "S",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_up",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "S",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C123\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_up, rotation=90, flipVertical=true\n- step 2: patternId=S, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=180, flipVertical=true\n- step 4: patternId=diamond, rotation=90, flipVertical=true\n- allowed patternId values for this task: arrow_up, S, 2, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C124.json

@@ -0,0 +1,245 @@
+{
+  "sample_id": "C124",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "W",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C124_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 124,
+    "name": "Reconstruct 124",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-124.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "Y",
+    "P",
+    "O",
+    "circle",
+    "arrow_left",
+    "arrow_left"
+  ],
+  "start_x": 4,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "P",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "O",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C124\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=P, rotation=90, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=circle, rotation=0, flipVertical=true\n- step 4: patternId=O, rotation=0, flipVertical=true\n- step 5: patternId=arrow_left, rotation=270, flipVertical=true\n- allowed patternId values for this task: P, arrow_left, circle, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C125.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C125",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> W -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "W",
+    "W",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C125_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 125,
+    "name": "Reconstruct 125",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-125.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "square",
+    "K",
+    "D",
+    "circle",
+    "O",
+    "arrow_right"
+  ],
+  "start_x": 4,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "K",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "D",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "BACK"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "square",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "K",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "O",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "K",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C125\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> W -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=270, flipVertical=true\n- step 2: patternId=K, rotation=270, flipVertical=true\n- step 3: patternId=square, rotation=0, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- step 5: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: O, K, square, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C126.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C126",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "S",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C126_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 126,
+    "name": "Reconstruct 126",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-126.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "D",
+    "D",
+    "R",
+    "arrow_down",
+    "diamond",
+    "2"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "2",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "2",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "D",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "diamond",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "R",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "2",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "R",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C126\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=90, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=180, flipVertical=true\n- step 4: patternId=2, rotation=180, flipVertical=true\n- step 5: patternId=diamond, rotation=270, flipVertical=true\n- allowed patternId values for this task: diamond, D, R, 2, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C127.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C127",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "N",
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C127_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 127,
+    "name": "Reconstruct 127",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-127.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "9",
+    "Q",
+    "6",
+    "7",
+    "X",
+    "J"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "Q",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "X",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "TOP",
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "BACK",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "9",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "7",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C127\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=9, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=180, flipVertical=true\n- step 4: patternId=X, rotation=90, flipVertical=true\n- allowed patternId values for this task: 7, 9, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C128.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C128",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C128_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 128,
+    "name": "Reconstruct 128",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-128.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "square",
+    "circle",
+    "N",
+    "C",
+    "circle",
+    "M"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "C",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "N",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "M",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "square",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "N",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "N",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C128\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=0, flipVertical=true\n- step 3: patternId=square, rotation=270, flipVertical=true\n- step 4: patternId=circle, rotation=0, flipVertical=true\n- allowed patternId values for this task: N, circle, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C129.json

@@ -0,0 +1,229 @@
+{
+  "sample_id": "C129",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C129_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 129,
+    "name": "Reconstruct 129",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-129.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "K",
+    "X",
+    "D",
+    "T",
+    "J",
+    "F"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "K",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "J",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "D",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 3,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "F",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "X",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "D",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "D",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C129\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=270, flipVertical=true\n- step 2: patternId=X, rotation=270, flipVertical=true\n- step 3: patternId=F, rotation=270, flipVertical=true\n- step 4: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: D, X, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C130.json

@@ -0,0 +1,244 @@
+{
+  "sample_id": "C130",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "N",
+    "W",
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C130_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 130,
+    "name": "Reconstruct 130",
+    "difficulty": 2,
+    "move_count": 5,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-130.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "5-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "M",
+    "arrow_right",
+    "diamond",
+    "V",
+    "Z",
+    "plus"
+  ],
+  "start_x": 3,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "Z",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "diamond",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "TOP",
+    "LEFT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "BACK",
+    "TOP",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "M",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "plus",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "V",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "Z",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C130\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 5\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=90, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=Z, rotation=270, flipVertical=true\n- step 4: patternId=V, rotation=0, flipVertical=true\n- step 5: patternId=plus, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, M, Z, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C131.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C131",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C131_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 131,
+    "name": "Reconstruct 131",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-131.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "arrow_left",
+    "E",
+    "G",
+    "F",
+    "J",
+    "I"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "J",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "arrow_left",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "I",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "E",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "J",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "J",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C131\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=0, flipVertical=true\n- step 2: patternId=arrow_left, rotation=270, flipVertical=true\n- step 3: patternId=E, rotation=270, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, arrow_left, E, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C132.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C132",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> N -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "N",
+    "N",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C132_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 132,
+    "name": "Reconstruct 132",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-132.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "W",
+    "I",
+    "triangle",
+    "H",
+    "S",
+    "smile"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 3,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "I",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "triangle",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "BOTTOM",
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "FRONT",
+    "BOTTOM",
+    "BACK",
+    "TOP"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "W",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "smile",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "I",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "H",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "I",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C132\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> N -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=0, flipVertical=true\n- step 4: patternId=W, rotation=180, flipVertical=true\n- allowed patternId values for this task: I, smile, H, W, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C135.json

@@ -0,0 +1,230 @@
+{
+  "sample_id": "C135",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "W",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C135_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 135,
+    "name": "Reconstruct 135",
+    "difficulty": 2,
+    "move_count": 4,
+    "tier": 2,
+    "source_level_path": "levels/reconstruct/generated-135.json",
+    "tier_label": "Difficulty 2"
+  },
+  "description": "4-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "E",
+    "9",
+    "arrow_down",
+    "T",
+    "V",
+    "arrow_up"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "E",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_up",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "9",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_down",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_down",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C135\n- net_layout: standard_cross\n- difficulty: 2\n- move_count: 4\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=270, flipVertical=true\n- step 2: patternId=9, rotation=0, flipVertical=true\n- step 3: patternId=arrow_up, rotation=90, flipVertical=true\n- step 4: patternId=T, rotation=270, flipVertical=true\n- allowed patternId values for this task: arrow_down, 9, arrow_up, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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."
+  }
+}