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LICENSE

@@ -0,0 +1,21 @@
+MIT License
+
+Copyright (c) 2026 SimVerse Authors
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this dataset and associated documentation files (the "Dataset"), to deal
+in the Dataset without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Dataset, and to permit persons to whom the Dataset is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Dataset.
+
+THE DATASET IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE DATASET OR THE USE OR OTHER DEALINGS IN THE
+DATASET.

README.md

@@ -1,3 +1,173 @@
 ---
 license: mit
+task_categories:
+  - visual-question-answering
+  - text-generation
+language:
+  - en
+size_categories:
+  - 1K<n<10K
+pretty_name: SimVerse
+tags:
+  - benchmark
+  - multimodal
+  - reasoning
+  - spatial-reasoning
+  - video-understanding
+  - tool-use
+configs:
+  - config_name: voi
+    data_files:
+      - split: test
+        path: voi/test.jsonl
+  - config_name: cube1
+    data_files:
+      - split: test
+        path: cube1/test.jsonl
+  - config_name: cube2
+    data_files:
+      - split: test
+        path: cube2/test.jsonl
+  - config_name: lamp
+    data_files:
+      - split: test
+        path: lamp/test.jsonl
+  - config_name: cutrope
+    data_files:
+      - split: test
+        path: cutrope/test.jsonl
 ---
+
+# SimVerse
+
+> ⚠️ **Anonymized for double-blind review.** This dataset is currently undergoing peer review. It is hosted under an anonymous account dedicated to the review process; the author and citation fields are deliberately unfilled. Permanent ownership and citation information will be added after the review concludes. Please do not attempt to deanonymize the maintainers of this dataset during review.
+
+A multi-task benchmark for evaluating multimodal LLMs on **interactive simulation puzzles**. Five independent tasks that share a uniform prompt skeleton and a uniform output contract, so cross-task comparisons are meaningfully apples-to-apples.
+
+## What's in this dataset
+
+| Config | Records | Modality | Output |
+|---|---|---|---|
+| `voi`     |  600 | images (target + base shapes) | shape placements |
+| `cube1`   |  502 | images (blank net + path)     | face → patternId map |
+| `cube2`   |  502 | images (initial net + target) | roll direction sequence |
+| `lamp`    |  610 | image (arm + obstacles)       | per-joint angle list |
+| `cutrope` |  272 | gameplay video                | text command script |
+
+Total: **2,486** levels across 5 tasks.
+
+## Quickstart
+
+```python
+from datasets import load_dataset
+
+# Load one task config
+ds = load_dataset("Sayaka123/simverse2026", "lamp")
+example = ds["test"][0]
+
+# Each example is fully self-contained:
+print(example["prompt"]["system"])     # 5-section system prompt text
+print(example["prompt"]["user"])       # 9-section user prompt text
+print(example["answer"])               # gold answer in the locked schema
+print(example["images_relative_to_config"])  # paths to media (relative to this config dir)
+```
+
+The `prompt` field contains the **exact text** the original benchmark presented to models — see [`docs/PROMPT_SKELETON.md`](https://github.com/Sayaka123/simverse2026/blob/main/docs/PROMPT_SKELETON.md) for the canonical 5-section system + 9-section user structure shared by all five tasks.
+
+## Output contract (all five tasks)
+
+Every task asks the model to end its reply with a single line:
+
+```
+FINAL_JSON: <one-line JSON object>
+```
+
+The JSON's schema is fixed per task (see the per-config README for shape). The dataset's `answer` field uses the **same** schema, so one JSON loader handles both model output and ground truth.
+
+| Task | `answer` schema |
+|---|---|
+| `voi`     | `{"placements": [{"shape", "angle", "vertex", "grid"}, ...]}` |
+| `cube1`   | `{"faces": {TOP: {patternId, rotation}, ...}}` |
+| `cube2`   | `{"directions": ["N","S","E","W", ...]}` (open-ended; engine validates) |
+| `lamp`    | `{"actions": [{"joint", "angle"}, ...]}` |
+| `cutrope` | `{"commands": "...", "reason": "...", "confidence": 0..1}` (open-ended; simulator validates) |
+
+## Files in each config
+
+```
+<config>/
+├── test.jsonl                # one JSON object per line — HF-auto-loadable
+├── data/                      # same records, split into per-level files (frontend-compatible)
+└── images/   or  videos/      # binary media referenced by the JSON
+```
+
+`cube1` and `cube2` additionally ship a `catalog.json` (the frontend's index/manifest), and `cutrope` additionally ships a `source/` mirror of the original frontend level files.
+
+The per-record fields visible in `test.jsonl` are a superset of what's in `data/`. Two extra helper fields appear only in JSONL records:
+
+| Field | Purpose |
+|---|---|
+| `__sample_id__` | The canonical level id (e.g. `"lamp-000"`, `"C123"`) — handy as a primary key. |
+| `images_relative_to_config` (or `video_relative_to_config`) | Media paths rewritten to be relative to the config root, so they resolve from the `Image()` / `Video()` feature loader without further normalization. |
+
+The original media paths inside the JSON record (e.g. `imageAssets.target` for VOI, `image_paths.blank_net_image` for cube1, `video.path` for cutrope) are preserved as the canonical task-native fields — use either depending on your loader.
+
+## Reproducing the benchmark
+
+Each record carries the **complete** prompt the benchmark submits to the model. To reproduce a run from scratch:
+
+1. Read `prompt.system` and `prompt.user` from the record.
+2. Attach the referenced media (image/video) using either `images_relative_to_config` or the task-native field.
+3. Submit to your model with whatever multimodal protocol it accepts.
+4. Extract the line starting with `FINAL_JSON:` from the reply, parse it as JSON.
+5. Compare against `answer` (or invoke the per-task validator from the [SimVerse repo](https://github.com/Sayaka123/simverse2026)).
+
+The accompanying code at <https://github.com/Sayaka123/simverse2026> includes the parser, validator, and runner for every config.
+
+## Per-config details
+
+- [`voi/README.md`](voi/README.md)
+- [`cube1/README.md`](cube1/README.md)
+- [`cube2/README.md`](cube2/README.md)
+- [`lamp/README.md`](lamp/README.md)
+- [`cutrope/README.md`](cutrope/README.md)
+
+## Responsible-AI metadata
+
+The full **datasheet** (Gebru et al. 2018, 7-section format) is in [`datasheet.md`](datasheet.md). The machine-readable RAI metadata is in [`croissant.json`](croissant.json) (Croissant 1.0, including the RAI extension). A human summary:
+
+- **Data collection.** All five tasks are programmatically generated. VOI uses a polygon-rasterization XOR generator; cube1/cube2 use a Python cube-state simulator; lamp uses a forward-kinematics generator with axis-aligned obstacle placement; cutrope is built on top of the open-source [yell0wsuit/cuttherope-h5dx](https://github.com/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.**
+- **Annotation protocol.** Reference solutions are produced by the same generators that create each puzzle. For closed-form tasks (VOI, cube1, lamp), the answer is uniquely determined and machine-verifiable. For open-ended tasks (cube2, 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.
+- **Limitations.** Synthetic puzzles in fixed visual styles per task — models may learn render-style shortcuts. All prompts are English-only. cube1 includes `?` sentinel patterns when faces are under-determined; downstream uses outside the SimVerse evaluation flow may need to filter these. Reference solutions for open-ended tasks are non-unique, so simple string-match scoring is inappropriate; use the bundled engine-based validator.
+- **Biases.** Each task's visual style is uniform across 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. Object-count distributions in cutrope reflect the upstream yell0wsuit corpus.
+- **Personal / sensitive information.** **None.** Fully synthetic; the dataset contains no personally identifiable information, no human-subject data, and no sensitive content.
+- **Intended use cases.** Held-out benchmarking of multimodal LLMs on (a) spatial-pattern reconstruction, (b) multi-step planning under physical constraints, and (c) short-horizon video-to-program inference. **Not** a held-out training set, **not** a real-world capability predictor, **not** a substitute for application-specific evaluation.
+- **Social impact.** Low. Synthetic abstract puzzles unlikely to encode harmful content. Primary risk: benchmark gaming via render-style overfitting if widely adopted.
+- **Maintenance.** All levels are deterministically regenerable from the generators in the accompanying code repository (linked from this card under the post-acceptance camera-ready URL). Schema changes are released as new versioned snapshots.
+
+## NeurIPS 2026 compliance
+
+This dataset is prepared for the [NeurIPS 2026 Datasets & Benchmarks track](https://neurips.cc/Conferences/2026/EvaluationsDatasetsHosting):
+
+- ✅ Hosted on Hugging Face (one of the supported platforms with auto-Croissant generation)
+- ✅ Croissant 1.0 metadata file at [`croissant.json`](croissant.json), with both Core and minimum-RAI fields
+- ✅ Open license (MIT) declared in both the dataset card YAML and Croissant
+- ✅ RAI items addressed in this README and machine-readable in `croissant.json`
+- ✅ Anonymized for double-blind review (see notice above)
+
+Reviewers can validate the Croissant file via <https://croissant.dev/validate>.
+
+## Citation
+
+```bibtex
+@dataset{simverse_2026,
+  title  = {SimVerse: A Multi-Task Benchmark for Multimodal Reasoning on Interactive Simulation Puzzles},
+  author = {<authors>},
+  year   = {2026},
+  url    = {https://huggingface.co/datasets/Sayaka123/simverse2026}
+}
+```
+
+## License
+
+MIT — see [LICENSE](LICENSE).

cube1/data/C321.json

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+{
+  "sample_id": "C321",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> E -> N -> S -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "E",
+    "E",
+    "N",
+    "S",
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C321_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 321,
+    "name": "Reconstruct 321",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-321.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "O",
+    "smile",
+    "T",
+    "X",
+    "I",
+    "diamond"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "T",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "X",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "BACK"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "O",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "diamond",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "smile",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "X",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "I",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "T",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "X",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "I",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "T",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C321\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> E -> N -> S -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=smile, rotation=270, flipVertical=true\n- step 2: patternId=T, rotation=270, flipVertical=true\n- step 3: patternId=X, rotation=90, flipVertical=true\n- step 4: patternId=I, rotation=90, flipVertical=true\n- step 5: patternId=diamond, rotation=0, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- step 7: patternId=O, rotation=270, flipVertical=true\n- step 8: patternId=X, rotation=180, flipVertical=true\n- allowed patternId values for this task: smile, T, X, I, diamond, O, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C322.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C322",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> W -> E -> W -> W -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "S",
+    "W",
+    "E",
+    "W",
+    "W",
+    "S",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C322_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 322,
+    "name": "Reconstruct 322",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-322.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "circle",
+    "star",
+    "heart",
+    "B",
+    "T",
+    "J"
+  ],
+  "start_x": 4,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "B",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "heart",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "RIGHT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "circle",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "J",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "star",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "B",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "heart",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "B",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "heart",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C322\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> W -> E -> W -> W -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=90, flipVertical=true\n- step 2: patternId=J, rotation=0, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=J, rotation=0, flipVertical=true\n- step 5: patternId=T, rotation=0, flipVertical=true\n- step 6: patternId=circle, rotation=180, flipVertical=true\n- step 7: patternId=star, rotation=180, flipVertical=true\n- step 8: patternId=circle, rotation=180, flipVertical=true\n- step 9: patternId=heart, rotation=180, flipVertical=true\n- allowed patternId values for this task: B, J, T, circle, star, heart, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C323.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C323",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> W -> S -> S -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "W",
+    "W",
+    "S",
+    "S",
+    "W",
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "9",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C323_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 323,
+    "name": "Reconstruct 323",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-323.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "arrow_left",
+    "P",
+    "9",
+    "arrow_down",
+    "T",
+    "D"
+  ],
+  "start_x": 4,
+  "start_y": 2,
+  "grid_width": 7,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "P",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "9",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "9",
+      "rotation": 180,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "x": 5,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "9",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "P",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 1,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "FRONT",
+    "LEFT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "arrow_left",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "D",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "P",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "arrow_down",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "T",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "9",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "P",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "9",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C323\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> W -> S -> S -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=9, rotation=180, flipVertical=true\n- step 2: patternId=arrow_down, rotation=0, flipVertical=true\n- step 3: patternId=D, rotation=90, flipVertical=true\n- step 4: patternId=P, rotation=90, flipVertical=true\n- step 5: patternId=9, rotation=0, flipVertical=true\n- step 6: patternId=arrow_down, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=0, flipVertical=true\n- step 8: patternId=P, rotation=270, flipVertical=true\n- step 9: patternId=T, rotation=270, flipVertical=true\n- allowed patternId values for this task: 9, arrow_down, D, P, arrow_left, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C324.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C324",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> S -> S -> W -> S -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "S",
+    "S",
+    "W",
+    "S",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "Y",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C324_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 324,
+    "name": "Reconstruct 324",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-324.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "Z",
+    "2",
+    "Y",
+    "L",
+    "arrow_down",
+    "W"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Y",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "Y",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "FRONT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "Z",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "L",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "Y",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "L",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Y",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C324\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> S -> S -> W -> S -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=180, flipVertical=true\n- step 2: patternId=Z, rotation=90, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=Y, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=0, flipVertical=true\n- step 7: patternId=Y, rotation=0, flipVertical=true\n- step 8: patternId=Z, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, Z, 2, W, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C325.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C325",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> E -> E -> N -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "E",
+    "E",
+    "E",
+    "N",
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C325_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 325,
+    "name": "Reconstruct 325",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-325.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "M",
+    "D",
+    "I",
+    "T",
+    "S",
+    "arrow_left"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 7,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 90,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "x": 5,
+      "y": 1
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "M",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "arrow_left",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "D",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "I",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C325\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> E -> E -> N -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=270, flipVertical=true\n- step 2: patternId=D, rotation=0, flipVertical=true\n- step 3: patternId=M, rotation=180, flipVertical=true\n- step 4: patternId=T, rotation=270, flipVertical=true\n- step 5: patternId=arrow_left, rotation=90, flipVertical=true\n- step 6: patternId=I, rotation=0, flipVertical=true\n- step 7: patternId=T, rotation=180, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- allowed patternId values for this task: I, D, M, T, arrow_left, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C326.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C326",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> E -> N -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "S",
+    "E",
+    "N",
+    "E",
+    "N",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C326_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 326,
+    "name": "Reconstruct 326",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-326.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "4",
+    "M",
+    "I",
+    "star",
+    "O",
+    "diamond"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 7,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "M",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 5,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "TOP",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "4",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "diamond",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "M",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "star",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "O",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "I",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "M",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "star",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "I",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C326\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> E -> N -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=I, rotation=180, flipVertical=true\n- step 2: patternId=M, rotation=90, flipVertical=true\n- step 3: patternId=O, rotation=270, flipVertical=true\n- step 4: patternId=4, rotation=90, flipVertical=true\n- step 5: patternId=M, rotation=0, flipVertical=true\n- step 6: patternId=I, rotation=90, flipVertical=true\n- step 7: patternId=diamond, rotation=90, flipVertical=true\n- step 8: patternId=star, rotation=270, flipVertical=true\n- step 9: patternId=O, rotation=270, flipVertical=true\n- allowed patternId values for this task: I, M, O, 4, diamond, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C327.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C327",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> N -> E -> W -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "E",
+    "N",
+    "E",
+    "W",
+    "S",
+    "S",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C327_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 327,
+    "name": "Reconstruct 327",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-327.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "G",
+    "C",
+    "V",
+    "H",
+    "X",
+    "arrow_right"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "x": 4,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "LEFT",
+    "TOP",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "FRONT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "G",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "C",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "H",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "V",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C327\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> N -> E -> W -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=270, flipVertical=true\n- step 2: patternId=H, rotation=90, flipVertical=true\n- step 3: patternId=G, rotation=270, flipVertical=true\n- step 4: patternId=X, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=X, rotation=270, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=V, rotation=0, flipVertical=true\n- step 9: patternId=C, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, H, G, X, C, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C328.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C328",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> W -> W -> E -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "S",
+    "W",
+    "W",
+    "E",
+    "S",
+    "W",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C328_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 328,
+    "name": "Reconstruct 328",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-328.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "K",
+    "F",
+    "M",
+    "plus",
+    "8",
+    "8"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "8",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "M",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "M",
+      "rotation": 180,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "8",
+      "rotation": 0,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "FRONT",
+    "BOTTOM",
+    "FRONT",
+    "LEFT",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "K",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "8",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "F",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "8",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "M",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "8",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "M",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C328\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> W -> W -> E -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=0, flipVertical=true\n- step 2: patternId=M, rotation=180, flipVertical=true\n- step 3: patternId=K, rotation=180, flipVertical=true\n- step 4: patternId=F, rotation=90, flipVertical=true\n- step 5: patternId=8, rotation=270, flipVertical=true\n- step 6: patternId=F, rotation=90, flipVertical=true\n- step 7: patternId=8, rotation=180, flipVertical=true\n- step 8: patternId=8, rotation=0, flipVertical=true\n- step 9: patternId=M, rotation=90, flipVertical=true\n- allowed patternId values for this task: F, M, K, 8, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C329.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C329",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> W -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "W",
+    "S",
+    "W",
+    "S",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C329_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 329,
+    "name": "Reconstruct 329",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-329.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "arrow_right",
+    "square",
+    "circle",
+    "T",
+    "arrow_down",
+    "arrow_left"
+  ],
+  "start_x": 4,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 8,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 90,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 1,
+      "y": 6
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "BACK"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "arrow_right",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "square",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "arrow_down",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "circle",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C329\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> W -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=90, flipVertical=true\n- step 2: patternId=arrow_down, rotation=180, flipVertical=true\n- step 3: patternId=T, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=180, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=square, rotation=180, flipVertical=true\n- step 7: patternId=arrow_down, rotation=270, flipVertical=true\n- step 8: patternId=T, rotation=90, flipVertical=true\n- allowed patternId values for this task: square, arrow_down, T, arrow_right, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C330.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C330",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> W -> W -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "N",
+    "W",
+    "W",
+    "N",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C330_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 330,
+    "name": "Reconstruct 330",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-330.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "T",
+    "G",
+    "J",
+    "W",
+    "T"
+  ],
+  "start_x": 4,
+  "start_y": 5,
+  "grid_width": 6,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "J",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 4,
+      "y": 5
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 3,
+      "y": 5
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "FRONT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "T",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "J",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "G",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "J",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C330\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> W -> W -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=270, flipVertical=true\n- step 2: patternId=J, rotation=180, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=S, rotation=180, flipVertical=true\n- step 5: patternId=W, rotation=90, flipVertical=true\n- step 6: patternId=T, rotation=0, flipVertical=true\n- step 7: patternId=S, rotation=270, flipVertical=true\n- step 8: patternId=G, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, J, G, S, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C331.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C331",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> N -> E -> N -> E -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "N",
+    "N",
+    "N",
+    "E",
+    "N",
+    "E",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C331_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 331,
+    "name": "Reconstruct 331",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-331.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "E",
+    "2",
+    "B",
+    "1",
+    "S",
+    "arrow_right"
+  ],
+  "start_x": 1,
+  "start_y": 5,
+  "grid_width": 6,
+  "grid_height": 8,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "E",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "1",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "B",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 1,
+      "y": 6
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "x": 2,
+      "y": 6
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "BACK"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "E",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "1",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "S",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "B",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "E",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "1",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "B",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C331\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> N -> E -> N -> E -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=90, flipVertical=true\n- step 2: patternId=B, rotation=90, flipVertical=true\n- step 3: patternId=arrow_right, rotation=90, flipVertical=true\n- step 4: patternId=S, rotation=180, flipVertical=true\n- step 5: patternId=E, rotation=0, flipVertical=true\n- step 6: patternId=1, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- step 8: patternId=arrow_right, rotation=0, flipVertical=true\n- step 9: patternId=2, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, B, arrow_right, S, E, 1, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C332.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C332",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> N -> W -> E -> E -> N -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "N",
+    "W",
+    "E",
+    "E",
+    "N",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C332_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 332,
+    "name": "Reconstruct 332",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-332.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "N",
+    "T",
+    "O",
+    "diamond",
+    "square",
+    "Y"
+  ],
+  "start_x": 3,
+  "start_y": 5,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Y",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "x": 3,
+      "y": 5
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "Y",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "N",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "Y",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "T",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "diamond",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "square",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "O",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Y",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "diamond",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C332\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> N -> W -> E -> E -> N -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=square, rotation=0, flipVertical=true\n- step 2: patternId=diamond, rotation=180, flipVertical=true\n- step 3: patternId=O, rotation=0, flipVertical=true\n- step 4: patternId=N, rotation=0, flipVertical=true\n- step 5: patternId=O, rotation=0, flipVertical=true\n- step 6: patternId=Y, rotation=270, flipVertical=true\n- step 7: patternId=T, rotation=270, flipVertical=true\n- step 8: patternId=N, rotation=180, flipVertical=true\n- step 9: patternId=O, rotation=180, flipVertical=true\n- allowed patternId values for this task: square, diamond, O, N, Y, T, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C333.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C333",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> W -> N -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "E",
+    "W",
+    "N",
+    "N",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C333_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 333,
+    "name": "Reconstruct 333",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-333.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "N",
+    "A",
+    "7",
+    "8",
+    "diamond",
+    "6"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "6",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "8",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "7",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "6",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "8",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "6",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "A",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "8",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "diamond",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "7",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "6",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "8",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "diamond",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "7",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C333\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> W -> N -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=A, rotation=180, flipVertical=true\n- step 2: patternId=7, rotation=0, flipVertical=true\n- step 3: patternId=8, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=6, rotation=270, flipVertical=true\n- step 6: patternId=diamond, rotation=270, flipVertical=true\n- step 7: patternId=8, rotation=90, flipVertical=true\n- step 8: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: A, 7, 8, 6, diamond, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C334.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C334",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> W -> N -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "N",
+    "W",
+    "N",
+    "W",
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C334_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 334,
+    "name": "Reconstruct 334",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-334.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "O",
+    "O",
+    "Q",
+    "circle",
+    "smile",
+    "V"
+  ],
+  "start_x": 3,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "O",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT",
+    "LEFT",
+    "TOP",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "O",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "V",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "O",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "smile",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C334\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> W -> N -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=Q, rotation=180, flipVertical=true\n- step 3: patternId=V, rotation=90, flipVertical=true\n- step 4: patternId=O, rotation=90, flipVertical=true\n- step 5: patternId=smile, rotation=180, flipVertical=true\n- step 6: patternId=O, rotation=0, flipVertical=true\n- step 7: patternId=Q, rotation=270, flipVertical=true\n- step 8: patternId=O, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, Q, V, smile, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C335.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C335",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> E -> S -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "W",
+    "S",
+    "E",
+    "S",
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C335_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 335,
+    "name": "Reconstruct 335",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-335.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "I",
+    "6",
+    "4",
+    "circle",
+    "C",
+    "M"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "M",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "C",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "4",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "M",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "C",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "I",
+      "rotation": 0,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 1,
+      "y": 5
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "I",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "6",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "circle",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "C",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "4",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "circle",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "C",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "4",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C335\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> E -> S -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=0, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=I, rotation=270, flipVertical=true\n- step 5: patternId=C, rotation=270, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=I, rotation=0, flipVertical=true\n- step 8: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: 6, C, circle, I, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C336.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C336",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> N -> N -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S",
+    "W",
+    "N",
+    "N",
+    "W",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C336_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 336,
+    "name": "Reconstruct 336",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-336.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "C",
+    "4",
+    "circle",
+    "3",
+    "D",
+    "L"
+  ],
+  "start_x": 3,
+  "start_y": 2,
+  "grid_width": 5,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "C",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "D",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "L",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "3",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "RIGHT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "C",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "L",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "4",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "3",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "D",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "circle",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "C",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "D",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C336\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> N -> N -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=4, rotation=270, flipVertical=true\n- step 2: patternId=C, rotation=180, flipVertical=true\n- step 3: patternId=D, rotation=0, flipVertical=true\n- step 4: patternId=4, rotation=0, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=L, rotation=0, flipVertical=true\n- step 7: patternId=3, rotation=90, flipVertical=true\n- step 8: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: 4, C, D, circle, L, 3, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C337.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C337",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> W -> E -> W -> S -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "W",
+    "E",
+    "W",
+    "S",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C337_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 337,
+    "name": "Reconstruct 337",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-337.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "plus",
+    "6",
+    "O",
+    "triangle",
+    "M",
+    "K"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 4,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "K",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "triangle",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "M",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 270,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "x": 1,
+      "y": 5
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "FRONT",
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "plus",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "K",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "6",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "triangle",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "O",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "K",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "triangle",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "O",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C337\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> W -> E -> W -> S -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=O, rotation=180, flipVertical=true\n- step 3: patternId=6, rotation=270, flipVertical=true\n- step 4: patternId=O, rotation=180, flipVertical=true\n- step 5: patternId=6, rotation=270, flipVertical=true\n- step 6: patternId=plus, rotation=270, flipVertical=true\n- step 7: patternId=triangle, rotation=270, flipVertical=true\n- step 8: patternId=K, rotation=0, flipVertical=true\n- allowed patternId values for this task: 6, O, plus, triangle, K, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C338.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C338",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> W -> N -> W -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W",
+    "W",
+    "N",
+    "W",
+    "W",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C338_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 338,
+    "name": "Reconstruct 338",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-338.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "4",
+    "L",
+    "5",
+    "I",
+    "8",
+    "H"
+  ],
+  "start_x": 7,
+  "start_y": 3,
+  "grid_width": 9,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "H",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "x": 7,
+      "y": 3
+    },
+    {
+      "patternId": "8",
+      "rotation": 180,
+      "x": 6,
+      "y": 3
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "x": 5,
+      "y": 3
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "I",
+      "rotation": 180,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "TOP",
+    "LEFT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "H",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "L",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "I",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "8",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "5",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "H",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "L",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "I",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "8",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C338\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> W -> N -> W -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=8, rotation=180, flipVertical=true\n- step 2: patternId=4, rotation=180, flipVertical=true\n- step 3: patternId=5, rotation=0, flipVertical=true\n- step 4: patternId=I, rotation=180, flipVertical=true\n- step 5: patternId=H, rotation=0, flipVertical=true\n- step 6: patternId=L, rotation=180, flipVertical=true\n- step 7: patternId=4, rotation=270, flipVertical=true\n- step 8: patternId=8, rotation=270, flipVertical=true\n- allowed patternId values for this task: 8, 4, 5, I, H, L, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C339.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C339",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> N -> E -> N -> E -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "N",
+    "E",
+    "N",
+    "E",
+    "N",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C339_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 339,
+    "name": "Reconstruct 339",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-339.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "N",
+    "D",
+    "A",
+    "smile",
+    "F",
+    "U"
+  ],
+  "start_x": 2,
+  "start_y": 4,
+  "grid_width": 6,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "smile",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "F",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "A",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "D",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "N",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "N",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "U",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "D",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "smile",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "F",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "A",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "N",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "A",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C339\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> N -> E -> N -> E -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=F, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=U, rotation=270, flipVertical=true\n- step 4: patternId=A, rotation=180, flipVertical=true\n- step 5: patternId=D, rotation=270, flipVertical=true\n- step 6: patternId=N, rotation=0, flipVertical=true\n- step 7: patternId=F, rotation=180, flipVertical=true\n- step 8: patternId=D, rotation=0, flipVertical=true\n- allowed patternId values for this task: F, smile, U, A, D, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C340.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C340",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> E -> W -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "E",
+    "W",
+    "N",
+    "W",
+    "N",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C340_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 340,
+    "name": "Reconstruct 340",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-340.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "U",
+    "star",
+    "V",
+    "arrow_right",
+    "F",
+    "A"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_right",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "TOP",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "U",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "A",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "F",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "V",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "V",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C340\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> E -> W -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=V, rotation=0, flipVertical=true\n- step 2: patternId=U, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=0, flipVertical=true\n- step 4: patternId=arrow_right, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=F, rotation=180, flipVertical=true\n- step 7: patternId=arrow_right, rotation=180, flipVertical=true\n- step 8: patternId=V, rotation=90, flipVertical=true\n- allowed patternId values for this task: V, U, arrow_right, A, F, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C341.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C341",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> W -> N -> W -> S -> W -> W -> W -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "W",
+    "N",
+    "W",
+    "S",
+    "W",
+    "W",
+    "W",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C341_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 341,
+    "name": "Reconstruct 341",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-341.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "6",
+    "2",
+    "B",
+    "4",
+    "smile",
+    "D"
+  ],
+  "start_x": 5,
+  "start_y": 2,
+  "grid_width": 8,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "B",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 6,
+      "y": 2
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 5,
+      "y": 1
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "LEFT",
+    "FRONT",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "6",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "D",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "4",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "smile",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "B",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "D",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "B",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C341\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> W -> N -> W -> S -> W -> W -> W -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=B, rotation=0, flipVertical=true\n- step 2: patternId=D, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=smile, rotation=270, flipVertical=true\n- step 5: patternId=D, rotation=0, flipVertical=true\n- step 6: patternId=2, rotation=180, flipVertical=true\n- step 7: patternId=6, rotation=180, flipVertical=true\n- step 8: patternId=4, rotation=180, flipVertical=true\n- step 9: patternId=B, rotation=0, flipVertical=true\n- allowed patternId values for this task: B, D, 4, smile, 2, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C342.json

@@ -0,0 +1,286 @@
+{
+  "sample_id": "C342",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> E -> E -> N -> N -> S -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S",
+    "E",
+    "E",
+    "N",
+    "N",
+    "S",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C342_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 342,
+    "name": "Reconstruct 342",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-342.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "circle",
+    "1",
+    "1",
+    "B",
+    "O",
+    "square"
+  ],
+  "start_x": 1,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "1",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "B",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "1",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "1",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "square",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT",
+    "TOP",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "square",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "1",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "1",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "1",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "1",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C342\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> E -> E -> N -> N -> S -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=1, rotation=180, flipVertical=true\n- step 2: patternId=circle, rotation=90, flipVertical=true\n- step 3: patternId=1, rotation=180, flipVertical=true\n- step 4: patternId=square, rotation=0, flipVertical=true\n- step 5: patternId=1, rotation=0, flipVertical=true\n- step 6: patternId=circle, rotation=270, flipVertical=true\n- step 7: patternId=1, rotation=0, flipVertical=true\n- step 8: patternId=square, rotation=0, flipVertical=true\n- allowed patternId values for this task: 1, circle, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C343.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C343",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> S -> S -> W -> S -> W -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "W",
+    "S",
+    "S",
+    "W",
+    "S",
+    "W",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C343_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 343,
+    "name": "Reconstruct 343",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-343.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "6",
+    "6",
+    "F",
+    "J",
+    "L",
+    "J"
+  ],
+  "start_x": 5,
+  "start_y": 2,
+  "grid_width": 7,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "J",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "L",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "F",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 5,
+      "y": 1
+    },
+    {
+      "patternId": "L",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "J",
+      "rotation": 270,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "L",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_slots": [
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "6",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "J",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "6",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "J",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "L",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "F",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "6",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "6",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "L",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "F",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C343\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> S -> S -> W -> S -> W -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=0, flipVertical=true\n- step 2: patternId=L, rotation=180, flipVertical=true\n- step 3: patternId=J, rotation=270, flipVertical=true\n- step 4: patternId=F, rotation=270, flipVertical=true\n- step 5: patternId=6, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=L, rotation=90, flipVertical=true\n- step 8: patternId=J, rotation=180, flipVertical=true\n- step 9: patternId=6, rotation=270, flipVertical=true\n- allowed patternId values for this task: J, L, F, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C344.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C344",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> N -> E -> E -> S -> E -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "N",
+    "E",
+    "E",
+    "S",
+    "E",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C344_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 344,
+    "name": "Reconstruct 344",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-344.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "diamond",
+    "9",
+    "arrow_left",
+    "arrow_down",
+    "plus",
+    "P"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "diamond",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "9",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "plus",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "P",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "BOTTOM",
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_slots": [
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "diamond",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "P",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_down",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "plus",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "arrow_left",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "diamond",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "plus",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C344\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> N -> E -> E -> S -> E -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=arrow_down, rotation=90, flipVertical=true\n- step 2: patternId=diamond, rotation=0, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=P, rotation=270, flipVertical=true\n- step 5: patternId=arrow_down, rotation=270, flipVertical=true\n- step 6: patternId=plus, rotation=90, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- step 8: patternId=arrow_down, rotation=180, flipVertical=true\n- allowed patternId values for this task: arrow_down, diamond, arrow_left, P, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C345.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C345",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> W -> S -> E -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W",
+    "N",
+    "W",
+    "S",
+    "E",
+    "N",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C345_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 345,
+    "name": "Reconstruct 345",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-345.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "E",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "E",
+    "heart",
+    "arrow_left",
+    "4",
+    "heart",
+    "circle"
+  ],
+  "start_x": 4,
+  "start_y": 3,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "E",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "heart",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "4",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "heart",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "E",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "circle",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "heart",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "4",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "heart",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_left",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "E",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "4",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C345\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> W -> S -> E -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=heart, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=90, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=arrow_left, rotation=0, flipVertical=true\n- step 5: patternId=E, rotation=0, flipVertical=true\n- step 6: patternId=4, rotation=180, flipVertical=true\n- step 7: patternId=arrow_left, rotation=270, flipVertical=true\n- step 8: patternId=heart, rotation=270, flipVertical=true\n- step 9: patternId=circle, rotation=90, flipVertical=true\n- allowed patternId values for this task: heart, E, 4, arrow_left, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C346.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C346",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> N -> N -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S",
+    "N",
+    "N",
+    "N",
+    "W",
+    "N",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C346_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 346,
+    "name": "Reconstruct 346",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-346.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "B",
+    "diamond",
+    "G",
+    "3",
+    "4",
+    "F"
+  ],
+  "start_x": 2,
+  "start_y": 3,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "B",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "4",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "diamond",
+      "rotation": 270,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "4",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "3",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP",
+    "FRONT",
+    "BOTTOM",
+    "BACK",
+    "LEFT",
+    "TOP",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP",
+    "BOTTOM",
+    "BACK",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "B",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "F",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "diamond",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "3",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "B",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "diamond",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "3",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C346\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> N -> N -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=diamond, rotation=270, flipVertical=true\n- step 2: patternId=B, rotation=270, flipVertical=true\n- step 3: patternId=diamond, rotation=270, flipVertical=true\n- step 4: patternId=F, rotation=90, flipVertical=true\n- step 5: patternId=3, rotation=270, flipVertical=true\n- step 6: patternId=4, rotation=90, flipVertical=true\n- step 7: patternId=B, rotation=0, flipVertical=true\n- step 8: patternId=3, rotation=0, flipVertical=true\n- step 9: patternId=F, rotation=180, flipVertical=true\n- allowed patternId values for this task: diamond, B, F, 3, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C347.json

@@ -0,0 +1,300 @@
+{
+  "sample_id": "C347",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S -> W -> N -> S -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "E",
+    "S",
+    "W",
+    "N",
+    "S",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C347_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 347,
+    "name": "Reconstruct 347",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-347.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "E",
+    "2",
+    "T",
+    "G",
+    "arrow_right"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "BACK",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "2",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C347\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S -> W -> N -> S -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=0, flipVertical=true\n- step 2: patternId=T, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=0, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=S, rotation=90, flipVertical=true\n- step 7: patternId=T, rotation=180, flipVertical=true\n- step 8: patternId=2, rotation=90, flipVertical=true\n- step 9: patternId=arrow_right, rotation=270, flipVertical=true\n- allowed patternId values for this task: 2, T, S, arrow_right, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C348.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C348",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> S -> S -> S -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "E",
+    "S",
+    "S",
+    "S",
+    "E",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C348_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 348,
+    "name": "Reconstruct 348",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-348.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "3",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "7",
+    "2",
+    "3",
+    "W",
+    "P",
+    "W"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "3",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "x": 4,
+      "y": 4
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "TOP"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "TOP",
+    "LEFT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "7",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "W",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "W",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "P",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "3",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "W",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "3",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C348\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> S -> S -> S -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=W, rotation=0, flipVertical=true\n- step 2: patternId=3, rotation=180, flipVertical=true\n- step 3: patternId=2, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=0, flipVertical=true\n- step 5: patternId=W, rotation=180, flipVertical=true\n- step 6: patternId=7, rotation=180, flipVertical=true\n- step 7: patternId=P, rotation=180, flipVertical=true\n- step 8: patternId=7, rotation=180, flipVertical=true\n- allowed patternId values for this task: W, 3, 2, 7, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C349.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C349",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> N -> W -> E -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "N",
+    "W",
+    "E",
+    "N",
+    "W",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C349_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 349,
+    "name": "Reconstruct 349",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-349.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "plus",
+    "G",
+    "Q",
+    "arrow_up",
+    "G",
+    "arrow_up"
+  ],
+  "start_x": 4,
+  "start_y": 3,
+  "grid_width": 6,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "x": 4,
+      "y": 4
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "Q",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BOTTOM",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "LEFT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BOTTOM",
+    "BACK",
+    "RIGHT",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "plus",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_up",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "G",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "arrow_up",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "G",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "plus",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "G",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "arrow_up",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C349\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> N -> W -> E -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=arrow_up, rotation=270, flipVertical=true\n- step 4: patternId=arrow_up, rotation=90, flipVertical=true\n- step 5: patternId=arrow_up, rotation=270, flipVertical=true\n- step 6: patternId=Q, rotation=90, flipVertical=true\n- step 7: patternId=arrow_up, rotation=0, flipVertical=true\n- step 8: patternId=plus, rotation=0, flipVertical=true\n- step 9: patternId=G, rotation=90, flipVertical=true\n- allowed patternId values for this task: G, arrow_up, Q, plus, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C350.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C350",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> S -> S -> W -> S -> S -> W -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "S",
+    "S",
+    "W",
+    "S",
+    "S",
+    "W",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C350_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 350,
+    "name": "Reconstruct 350",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-350.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "R",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "R",
+    "N",
+    "P",
+    "H",
+    "V",
+    "arrow_up"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 6,
+  "grid_height": 8,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "R",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "N",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "P",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "R",
+      "rotation": 90,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 4,
+      "y": 4
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 90,
+      "x": 3,
+      "y": 5
+    },
+    {
+      "patternId": "H",
+      "rotation": 180,
+      "x": 3,
+      "y": 6
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 2,
+      "y": 6
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "x": 1,
+      "y": 6
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "BOTTOM",
+    "BACK",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "LEFT",
+    "BOTTOM",
+    "BACK"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "R",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_up",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "N",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "H",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "V",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "P",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "R",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "N",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "V",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "P",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C350\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> S -> S -> W -> S -> S -> W -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=N, rotation=90, flipVertical=true\n- step 2: patternId=P, rotation=90, flipVertical=true\n- step 3: patternId=R, rotation=90, flipVertical=true\n- step 4: patternId=V, rotation=180, flipVertical=true\n- step 5: patternId=N, rotation=270, flipVertical=true\n- step 6: patternId=arrow_up, rotation=90, flipVertical=true\n- step 7: patternId=H, rotation=180, flipVertical=true\n- step 8: patternId=P, rotation=90, flipVertical=true\n- step 9: patternId=N, rotation=90, flipVertical=true\n- allowed patternId values for this task: N, P, R, V, arrow_up, H, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C351.json

@@ -0,0 +1,286 @@
+{
+  "sample_id": "C351",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> E -> N -> W -> N -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "E",
+    "N",
+    "W",
+    "N",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C351_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 351,
+    "name": "Reconstruct 351",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-351.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "heart",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "E",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "smile",
+    "F",
+    "7",
+    "F",
+    "heart",
+    "E"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "E",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "F",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "heart",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "7",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "E",
+      "rotation": 180,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "F",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "E",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "smile",
+      "rotation": 0,
+      "x": 4,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "TOP"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "smile",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "E",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "F",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "7",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "E",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "7",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C351\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> E -> N -> W -> N -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=180, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- step 3: patternId=smile, rotation=270, flipVertical=true\n- step 4: patternId=7, rotation=90, flipVertical=true\n- step 5: patternId=F, rotation=90, flipVertical=true\n- step 6: patternId=E, rotation=180, flipVertical=true\n- step 7: patternId=7, rotation=180, flipVertical=true\n- step 8: patternId=smile, rotation=0, flipVertical=true\n- allowed patternId values for this task: 7, F, smile, E, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C352.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C352",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> N -> E -> E -> S -> E -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "W",
+    "N",
+    "E",
+    "E",
+    "S",
+    "E",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C352_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 352,
+    "name": "Reconstruct 352",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-352.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "V",
+    "K",
+    "U",
+    "7",
+    "N"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 7,
+  "grid_height": 4,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "N",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "U",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "K",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "N",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "7",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "x": 5,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "RIGHT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "N",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "V",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "U",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "7",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "K",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "N",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "U",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "7",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "K",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C352\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> N -> E -> E -> S -> E -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=7, rotation=270, flipVertical=true\n- step 2: patternId=V, rotation=90, flipVertical=true\n- step 3: patternId=S, rotation=90, flipVertical=true\n- step 4: patternId=7, rotation=0, flipVertical=true\n- step 5: patternId=V, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=90, flipVertical=true\n- step 7: patternId=S, rotation=270, flipVertical=true\n- step 8: patternId=U, rotation=0, flipVertical=true\n- step 9: patternId=N, rotation=270, flipVertical=true\n- allowed patternId values for this task: 7, V, S, K, U, N, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C353.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C353",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> W -> E -> W -> S -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S",
+    "W",
+    "E",
+    "W",
+    "S",
+    "E",
+    "S",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C353_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 353,
+    "name": "Reconstruct 353",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-353.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "G",
+    "C",
+    "J",
+    "square",
+    "T",
+    "G"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "square",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "J",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "C",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "C",
+      "rotation": 270,
+      "x": 3,
+      "y": 5
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "TOP",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "BACK",
+    "RIGHT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "G",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "C",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "square",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "J",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "square",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "J",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C353\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> W -> E -> W -> S -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=C, rotation=90, flipVertical=true\n- step 2: patternId=G, rotation=0, flipVertical=true\n- step 3: patternId=T, rotation=180, flipVertical=true\n- step 4: patternId=G, rotation=0, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=square, rotation=90, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=J, rotation=0, flipVertical=true\n- step 9: patternId=C, rotation=270, flipVertical=true\n- allowed patternId values for this task: C, G, T, square, J, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C354.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C354",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> S -> S -> S -> W -> S -> W -> N\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "S",
+    "S",
+    "S",
+    "W",
+    "S",
+    "W",
+    "N"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C354_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 354,
+    "name": "Reconstruct 354",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-354.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "C",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "C",
+    "star",
+    "6",
+    "arrow_down",
+    "P",
+    "A"
+  ],
+  "start_x": 2,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "C",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "P",
+      "rotation": 180,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "6",
+      "rotation": 180,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "A",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "star",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "arrow_down",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "P",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "6",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "arrow_down",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C354\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): E -> S -> S -> S -> W -> S -> W -> N\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=6, rotation=270, flipVertical=true\n- step 2: patternId=star, rotation=180, flipVertical=true\n- step 3: patternId=P, rotation=180, flipVertical=true\n- step 4: patternId=arrow_down, rotation=90, flipVertical=true\n- step 5: patternId=A, rotation=90, flipVertical=true\n- step 6: patternId=6, rotation=180, flipVertical=true\n- step 7: patternId=star, rotation=90, flipVertical=true\n- step 8: patternId=A, rotation=180, flipVertical=true\n- allowed patternId values for this task: 6, star, P, arrow_down, A, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C355.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C355",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> S -> S -> E -> N -> W -> N -> N -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "S",
+    "S",
+    "E",
+    "N",
+    "W",
+    "N",
+    "N",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C355_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 355,
+    "name": "Reconstruct 355",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-355.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "O",
+    "A",
+    "2",
+    "Y",
+    "X",
+    "smile"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 4,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "Y",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "Y",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "A",
+      "rotation": 180,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "smile",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "A",
+      "rotation": 90,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "Y",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "RIGHT",
+    "LEFT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "smile",
+        "rotation": 180
+      },
+      "FRONT": {
+        "patternId": "A",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "Y",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "X",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "2",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "smile",
+      "rotation": 180
+    },
+    "FRONT": {
+      "patternId": "A",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "Y",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "X",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "2",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C355\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> S -> S -> E -> N -> W -> N -> N -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Y, rotation=0, flipVertical=true\n- step 2: patternId=smile, rotation=180, flipVertical=true\n- step 3: patternId=A, rotation=180, flipVertical=true\n- step 4: patternId=2, rotation=90, flipVertical=true\n- step 5: patternId=smile, rotation=90, flipVertical=true\n- step 6: patternId=A, rotation=90, flipVertical=true\n- step 7: patternId=X, rotation=270, flipVertical=true\n- step 8: patternId=Y, rotation=90, flipVertical=true\n- step 9: patternId=X, rotation=270, flipVertical=true\n- allowed patternId values for this task: Y, smile, A, 2, X, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C356.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C356",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> S -> S -> W -> S -> W -> N -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "S",
+    "S",
+    "W",
+    "S",
+    "W",
+    "N",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C356_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 356,
+    "name": "Reconstruct 356",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-356.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "Z",
+    "X",
+    "6",
+    "arrow_left",
+    "star",
+    "Z"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_left",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "star",
+      "rotation": 270,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "X",
+      "rotation": 270,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "star",
+      "rotation": 0,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "TOP",
+    "BACK",
+    "LEFT",
+    "BOTTOM",
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "FRONT",
+    "TOP",
+    "BACK",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "Z",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "Z",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "X",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "arrow_left",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "star",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "Z",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "X",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "arrow_left",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "star",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C356\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> S -> S -> W -> S -> W -> N -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=X, rotation=0, flipVertical=true\n- step 2: patternId=Z, rotation=270, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=star, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=X, rotation=270, flipVertical=true\n- step 7: patternId=star, rotation=0, flipVertical=true\n- step 8: patternId=arrow_left, rotation=0, flipVertical=true\n- step 9: patternId=Z, rotation=90, flipVertical=true\n- allowed patternId values for this task: X, Z, arrow_left, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C357.json

@@ -0,0 +1,286 @@
+{
+  "sample_id": "C357",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> E -> N -> W -> N -> E -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "E",
+    "N",
+    "W",
+    "N",
+    "E",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C357_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 357,
+    "name": "Reconstruct 357",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-357.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "3",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "7",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "3",
+    "D",
+    "W",
+    "7",
+    "G",
+    "Z"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 5,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "3",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "W",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "Z",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "D",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "7",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "Z",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "D",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BACK",
+    "BOTTOM"
+  ],
+  "required_count": 4,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "Z",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "D",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "7",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "W",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "Z",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "D",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "7",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "W",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C357\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> E -> N -> W -> N -> E -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=D, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=270, flipVertical=true\n- step 3: patternId=7, rotation=0, flipVertical=true\n- step 4: patternId=Z, rotation=180, flipVertical=true\n- step 5: patternId=W, rotation=180, flipVertical=true\n- step 6: patternId=D, rotation=90, flipVertical=true\n- step 7: patternId=Z, rotation=270, flipVertical=true\n- step 8: patternId=D, rotation=90, flipVertical=true\n- allowed patternId values for this task: D, W, 7, Z, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C358.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C358",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> E -> N -> E -> S -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "E",
+    "N",
+    "E",
+    "S",
+    "S",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "5",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C358_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 358,
+    "name": "Reconstruct 358",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-358.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "V",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "5",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Z",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "B",
+    "V",
+    "5",
+    "M",
+    "Z",
+    "I"
+  ],
+  "start_x": 1,
+  "start_y": 3,
+  "grid_width": 7,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "B",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "M",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "Z",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "M",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "5",
+      "rotation": 0,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "V",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "Z",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "V",
+      "rotation": 180,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "5",
+      "rotation": 90,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "x": 5,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "FRONT",
+    "TOP",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "B",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "I",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "V",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "M",
+        "rotation": 0
+      },
+      "LEFT": {
+        "patternId": "Z",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "5",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "B",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "I",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "V",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "M",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "Z",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "5",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C358\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> E -> N -> E -> S -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=M, rotation=0, flipVertical=true\n- step 2: patternId=5, rotation=0, flipVertical=true\n- step 3: patternId=V, rotation=90, flipVertical=true\n- step 4: patternId=B, rotation=270, flipVertical=true\n- step 5: patternId=Z, rotation=270, flipVertical=true\n- step 6: patternId=V, rotation=180, flipVertical=true\n- step 7: patternId=5, rotation=90, flipVertical=true\n- step 8: patternId=I, rotation=90, flipVertical=true\n- allowed patternId values for this task: M, 5, V, B, Z, I, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C359.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C359",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> W -> N -> W -> S -> W -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "W",
+    "N",
+    "W",
+    "S",
+    "W",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C359_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 359,
+    "name": "Reconstruct 359",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-359.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "heart",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "B",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "heart",
+    "B",
+    "G",
+    "F",
+    "P",
+    "circle"
+  ],
+  "start_x": 3,
+  "start_y": 3,
+  "grid_width": 6,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "heart",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "B",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "F",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "B",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "B",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "FRONT",
+    "BOTTOM"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "FRONT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "circle",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "B",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "F",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "P",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "G",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "B",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "F",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "P",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "G",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C359\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> W -> N -> W -> S -> W -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=270, flipVertical=true\n- step 2: patternId=F, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=P, rotation=90, flipVertical=true\n- step 5: patternId=B, rotation=270, flipVertical=true\n- step 6: patternId=circle, rotation=90, flipVertical=true\n- step 7: patternId=G, rotation=90, flipVertical=true\n- step 8: patternId=B, rotation=0, flipVertical=true\n- step 9: patternId=circle, rotation=180, flipVertical=true\n- allowed patternId values for this task: G, F, circle, P, B, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C360.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C360",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> W -> W -> S -> E -> S -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "W",
+    "W",
+    "S",
+    "E",
+    "S",
+    "N",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C360_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 360,
+    "name": "Reconstruct 360",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-360.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "X",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "A",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "H",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "smile",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "X",
+    "K",
+    "A",
+    "H",
+    "smile",
+    "square"
+  ],
+  "start_x": 3,
+  "start_y": 1,
+  "grid_width": 5,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "K",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "A",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "smile",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "H",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "X",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "smile",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "square",
+      "rotation": 90,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "K",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "LEFT",
+    "FRONT",
+    "LEFT",
+    "BOTTOM",
+    "FRONT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "BOTTOM"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "X",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "square",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "K",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "H",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "smile",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "?",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "X",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "square",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "K",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "H",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "smile",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "?",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C360\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> W -> W -> S -> E -> S -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=K, rotation=180, flipVertical=true\n- step 2: patternId=smile, rotation=270, flipVertical=true\n- step 3: patternId=H, rotation=90, flipVertical=true\n- step 4: patternId=X, rotation=0, flipVertical=true\n- step 5: patternId=smile, rotation=180, flipVertical=true\n- step 6: patternId=K, rotation=90, flipVertical=true\n- step 7: patternId=smile, rotation=180, flipVertical=true\n- step 8: patternId=square, rotation=90, flipVertical=true\n- step 9: patternId=K, rotation=180, flipVertical=true\n- allowed patternId values for this task: K, smile, H, X, square, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C361.json

@@ -0,0 +1,301 @@
+{
+  "sample_id": "C361",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> E -> S -> S -> S -> N -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "E",
+    "S",
+    "S",
+    "S",
+    "N",
+    "W",
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C361_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 361,
+    "name": "Reconstruct 361",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-361.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "C",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "T",
+    "C",
+    "triangle",
+    "T",
+    "6",
+    "circle"
+  ],
+  "start_x": 2,
+  "start_y": 2,
+  "grid_width": 5,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "C",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "6",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "triangle",
+      "rotation": 0
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 180,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "x": 3,
+      "y": 4
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "LEFT",
+    "BACK",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "BACK",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "T",
+        "rotation": 270
+      },
+      "BOTTOM": {
+        "patternId": "circle",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "6",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "triangle",
+        "rotation": 270
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "T",
+      "rotation": 270
+    },
+    "BOTTOM": {
+      "patternId": "circle",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "6",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "triangle",
+      "rotation": 270
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C361\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): N -> E -> S -> S -> S -> N -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=T, rotation=90, flipVertical=true\n- step 2: patternId=triangle, rotation=180, flipVertical=true\n- step 3: patternId=circle, rotation=180, flipVertical=true\n- step 4: patternId=6, rotation=270, flipVertical=true\n- step 5: patternId=T, rotation=180, flipVertical=true\n- step 6: patternId=6, rotation=270, flipVertical=true\n- step 7: patternId=T, rotation=270, flipVertical=true\n- step 8: patternId=T, rotation=90, flipVertical=true\n- step 9: patternId=triangle, rotation=90, flipVertical=true\n- allowed patternId values for this task: T, triangle, circle, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C362.json

@@ -0,0 +1,287 @@
+{
+  "sample_id": "C362",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> W -> W -> S -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W",
+    "N",
+    "N",
+    "W",
+    "W",
+    "S",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C362_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 362,
+    "name": "Reconstruct 362",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-362.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "8",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "Q",
+    "8",
+    "circle",
+    "G",
+    "triangle",
+    "W"
+  ],
+  "start_x": 6,
+  "start_y": 3,
+  "grid_width": 8,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "Q",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "8",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "G",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "triangle",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "x": 6,
+      "y": 3
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "x": 5,
+      "y": 3
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "circle",
+      "rotation": 90,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "TOP",
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_count": 5,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "Q",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "?",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "G",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "triangle",
+        "rotation": 270
+      },
+      "RIGHT": {
+        "patternId": "circle",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "Q",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "?",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "triangle",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "circle",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C362\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> W -> W -> S -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=triangle, rotation=90, flipVertical=true\n- step 2: patternId=Q, rotation=0, flipVertical=true\n- step 3: patternId=G, rotation=90, flipVertical=true\n- step 4: patternId=W, rotation=270, flipVertical=true\n- step 5: patternId=circle, rotation=90, flipVertical=true\n- step 6: patternId=Q, rotation=180, flipVertical=true\n- step 7: patternId=G, rotation=270, flipVertical=true\n- step 8: patternId=triangle, rotation=0, flipVertical=true\n- allowed patternId values for this task: triangle, Q, G, W, circle, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C363.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C363",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: E -> N -> E -> S -> E -> E -> E -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "E",
+    "N",
+    "E",
+    "S",
+    "E",
+    "E",
+    "E",
+    "S",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C363_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 363,
+    "name": "Reconstruct 363",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-363.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "N",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "9",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "4",
+    "N",
+    "Q",
+    "E",
+    "9",
+    "U"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 9,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "N",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "E",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "9",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 90
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "E",
+      "rotation": 0,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "Q",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "N",
+      "rotation": 90,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "9",
+      "rotation": 270,
+      "x": 5,
+      "y": 2
+    },
+    {
+      "patternId": "E",
+      "rotation": 90,
+      "x": 6,
+      "y": 2
+    },
+    {
+      "patternId": "U",
+      "rotation": 0,
+      "x": 6,
+      "y": 3
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "x": 7,
+      "y": 3
+    }
+  ],
+  "slot_sequence": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "RIGHT",
+    "FRONT",
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "RIGHT",
+    "BACK",
+    "TOP",
+    "FRONT",
+    "LEFT",
+    "BOTTOM"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "U",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "N",
+        "rotation": 270
+      },
+      "BACK": {
+        "patternId": "E",
+        "rotation": 90
+      },
+      "LEFT": {
+        "patternId": "9",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 0
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "U",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "N",
+      "rotation": 270
+    },
+    "BACK": {
+      "patternId": "E",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "9",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 0
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C363\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): E -> N -> E -> S -> E -> E -> E -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=Q, rotation=180, flipVertical=true\n- step 2: patternId=E, rotation=0, flipVertical=true\n- step 3: patternId=4, rotation=270, flipVertical=true\n- step 4: patternId=Q, rotation=270, flipVertical=true\n- step 5: patternId=N, rotation=90, flipVertical=true\n- step 6: patternId=9, rotation=270, flipVertical=true\n- step 7: patternId=E, rotation=90, flipVertical=true\n- step 8: patternId=U, rotation=0, flipVertical=true\n- step 9: patternId=Q, rotation=180, flipVertical=true\n- allowed patternId values for this task: Q, E, 4, N, 9, U, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C364.json

@@ -0,0 +1,288 @@
+{
+  "sample_id": "C364",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: N -> W -> N -> W -> N -> W -> S -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "N",
+    "W",
+    "N",
+    "W",
+    "N",
+    "W",
+    "S",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C364_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 364,
+    "name": "Reconstruct 364",
+    "difficulty": 4,
+    "move_count": 8,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-364.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "8-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "arrow_left",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "arrow_left",
+    "arrow_down",
+    "plus",
+    "U",
+    "O",
+    "P"
+  ],
+  "start_x": 4,
+  "start_y": 4,
+  "grid_width": 6,
+  "grid_height": 6,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "U",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 4,
+      "y": 4
+    },
+    {
+      "patternId": "U",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "O",
+      "rotation": 270,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_left",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "P",
+      "rotation": 90,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_down",
+      "rotation": 0,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "BACK",
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "FRONT",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "BACK",
+    "LEFT",
+    "TOP",
+    "FRONT",
+    "RIGHT",
+    "BOTTOM"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "arrow_left",
+        "rotation": 180
+      },
+      "BOTTOM": {
+        "patternId": "P",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "arrow_down",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "U",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "O",
+        "rotation": 180
+      },
+      "RIGHT": {
+        "patternId": "plus",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "arrow_left",
+      "rotation": 180
+    },
+    "BOTTOM": {
+      "patternId": "P",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "arrow_down",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "U",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C364\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 8\n- roll_sequence (N=up, S=down, W=left, E=right): N -> W -> N -> W -> N -> W -> S -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=U, rotation=180, flipVertical=true\n- step 2: patternId=O, rotation=270, flipVertical=true\n- step 3: patternId=arrow_left, rotation=270, flipVertical=true\n- step 4: patternId=arrow_down, rotation=90, flipVertical=true\n- step 5: patternId=plus, rotation=270, flipVertical=true\n- step 6: patternId=P, rotation=90, flipVertical=true\n- step 7: patternId=arrow_down, rotation=0, flipVertical=true\n- step 8: patternId=plus, rotation=180, flipVertical=true\n- allowed patternId values for this task: U, O, arrow_left, arrow_down, plus, P, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C365.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C365",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> S -> W -> W -> W -> N -> W -> N -> W\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "S",
+    "W",
+    "W",
+    "W",
+    "N",
+    "W",
+    "N",
+    "W"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C365_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 365,
+    "name": "Reconstruct 365",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-365.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "S",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "W",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "Q",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "S",
+    "W",
+    "Q",
+    "plus",
+    "G",
+    "triangle"
+  ],
+  "start_x": 7,
+  "start_y": 2,
+  "grid_width": 9,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "triangle",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "plus",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "triangle",
+      "rotation": 90,
+      "x": 7,
+      "y": 2
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "x": 6,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 0,
+      "x": 6,
+      "y": 3
+    },
+    {
+      "patternId": "S",
+      "rotation": 270,
+      "x": 5,
+      "y": 3
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 4,
+      "y": 3
+    },
+    {
+      "patternId": "triangle",
+      "rotation": 0,
+      "x": 3,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "W",
+      "rotation": 270,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "S",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "Q",
+      "rotation": 0,
+      "x": 1,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "RIGHT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "FRONT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "RIGHT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "S",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "triangle",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "W",
+        "rotation": 90
+      },
+      "BACK": {
+        "patternId": "plus",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "G",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "Q",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "S",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "triangle",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "W",
+      "rotation": 90
+    },
+    "BACK": {
+      "patternId": "plus",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "Q",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C365\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> S -> W -> W -> W -> N -> W -> N -> W\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=G, rotation=180, flipVertical=true\n- step 2: patternId=W, rotation=0, flipVertical=true\n- step 3: patternId=S, rotation=270, flipVertical=true\n- step 4: patternId=plus, rotation=180, flipVertical=true\n- step 5: patternId=triangle, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=W, rotation=270, flipVertical=true\n- step 8: patternId=S, rotation=180, flipVertical=true\n- step 9: patternId=Q, rotation=0, flipVertical=true\n- allowed patternId values for this task: G, W, S, plus, triangle, Q, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C366.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C366",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: W -> W -> N -> N -> E -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "W",
+    "W",
+    "N",
+    "N",
+    "E",
+    "N",
+    "N",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C366_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 366,
+    "name": "Reconstruct 366",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-366.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "I",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "6",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "K",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "I",
+    "2",
+    "6",
+    "K",
+    "J",
+    "F"
+  ],
+  "start_x": 3,
+  "start_y": 5,
+  "grid_width": 5,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "K",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "J",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "F",
+      "rotation": 0,
+      "x": 3,
+      "y": 5
+    },
+    {
+      "patternId": "J",
+      "rotation": 180,
+      "x": 2,
+      "y": 5
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "K",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "F",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "J",
+      "rotation": 0,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "2",
+      "rotation": 90,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "6",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "I",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "x": 3,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "FRONT",
+    "RIGHT",
+    "TOP",
+    "FRONT"
+  ],
+  "required_slots": [
+    "LEFT",
+    "TOP",
+    "BACK",
+    "BOTTOM",
+    "FRONT",
+    "RIGHT"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "I",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "F",
+        "rotation": 0
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 0
+      },
+      "BACK": {
+        "patternId": "K",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "J",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "6",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "I",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "F",
+      "rotation": 0
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 0
+    },
+    "BACK": {
+      "patternId": "K",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "J",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "6",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C366\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): W -> W -> N -> N -> E -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=J, rotation=180, flipVertical=true\n- step 2: patternId=I, rotation=270, flipVertical=true\n- step 3: patternId=K, rotation=90, flipVertical=true\n- step 4: patternId=F, rotation=180, flipVertical=true\n- step 5: patternId=J, rotation=0, flipVertical=true\n- step 6: patternId=2, rotation=90, flipVertical=true\n- step 7: patternId=6, rotation=270, flipVertical=true\n- step 8: patternId=I, rotation=270, flipVertical=true\n- step 9: patternId=2, rotation=180, flipVertical=true\n- allowed patternId values for this task: J, I, K, F, 2, 6, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C367.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C367",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> N -> E -> N -> W -> N -> N -> E -> S\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "N",
+    "E",
+    "N",
+    "W",
+    "N",
+    "N",
+    "E",
+    "S"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C367_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 367,
+    "name": "Reconstruct 367",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-367.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "star",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "T",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "G",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "star",
+    "2",
+    "arrow_right",
+    "T",
+    "G",
+    "1"
+  ],
+  "start_x": 1,
+  "start_y": 4,
+  "grid_width": 4,
+  "grid_height": 7,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 0
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 270
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 270
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "2",
+      "rotation": 180,
+      "x": 1,
+      "y": 5
+    },
+    {
+      "patternId": "1",
+      "rotation": 90,
+      "x": 1,
+      "y": 4
+    },
+    {
+      "patternId": "arrow_right",
+      "rotation": 0,
+      "x": 2,
+      "y": 4
+    },
+    {
+      "patternId": "T",
+      "rotation": 90,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "1",
+      "rotation": 0,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "G",
+      "rotation": 90,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "star",
+      "rotation": 180,
+      "x": 1,
+      "y": 1
+    },
+    {
+      "patternId": "T",
+      "rotation": 270,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "G",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "BOTTOM",
+    "LEFT",
+    "TOP",
+    "BACK",
+    "LEFT"
+  ],
+  "required_slots": [
+    "FRONT",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "LEFT",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "star",
+        "rotation": 90
+      },
+      "BOTTOM": {
+        "patternId": "1",
+        "rotation": 90
+      },
+      "FRONT": {
+        "patternId": "2",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "T",
+        "rotation": 180
+      },
+      "LEFT": {
+        "patternId": "G",
+        "rotation": 0
+      },
+      "RIGHT": {
+        "patternId": "arrow_right",
+        "rotation": 180
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "star",
+      "rotation": 90
+    },
+    "BOTTOM": {
+      "patternId": "1",
+      "rotation": 90
+    },
+    "FRONT": {
+      "patternId": "2",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "T",
+      "rotation": 180
+    },
+    "LEFT": {
+      "patternId": "G",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "arrow_right",
+      "rotation": 180
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C367\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> N -> E -> N -> W -> N -> N -> E -> S\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=2, rotation=180, flipVertical=true\n- step 2: patternId=1, rotation=90, flipVertical=true\n- step 3: patternId=arrow_right, rotation=0, flipVertical=true\n- step 4: patternId=T, rotation=90, flipVertical=true\n- step 5: patternId=1, rotation=0, flipVertical=true\n- step 6: patternId=G, rotation=90, flipVertical=true\n- step 7: patternId=star, rotation=180, flipVertical=true\n- step 8: patternId=T, rotation=270, flipVertical=true\n- step 9: patternId=G, rotation=180, flipVertical=true\n- allowed patternId values for this task: 2, 1, arrow_right, T, G, star, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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/C368.json

@@ -0,0 +1,302 @@
+{
+  "sample_id": "C368",
+  "text_description": "Task: reconstruct the six outer faces of the cube from the blank cross net image and the path-view observation image.\nThe net uses the fixed face names TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT.\nIf a face cannot be uniquely determined, output patternId='?' and rotation=0.\nRoll sequence: S -> E -> N -> N -> E -> S -> E -> N -> E\nThe puzzle images already show the roll path and the observed path-face states.",
+  "net_layout": "standard_cross",
+  "roll_sequence": [
+    "S",
+    "E",
+    "N",
+    "N",
+    "E",
+    "S",
+    "E",
+    "N",
+    "E"
+  ],
+  "observed_path_faces": [
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": true
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": true
+    }
+  ],
+  "image_paths": {
+    "blank_net_image": "images/blank_nets/open.png",
+    "path_sequence_image": "images/path_sequences/C368_path_sequence.png"
+  },
+  "metadata": {
+    "level_id": 368,
+    "name": "Reconstruct 368",
+    "difficulty": 4,
+    "move_count": 9,
+    "tier": 4,
+    "source_level_path": "levels/reconstruct/generated-368.json",
+    "tier_label": "Difficulty 4"
+  },
+  "description": "9-move reconstruct puzzle",
+  "net_faces": [
+    {
+      "patternId": "4",
+      "rotation": 0,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "plus",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "R",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "O",
+      "rotation": 90,
+      "flipHorizontal": false,
+      "flipVertical": false
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "flipHorizontal": false,
+      "flipVertical": false
+    }
+  ],
+  "net_patterns": [
+    "4",
+    "O",
+    "plus",
+    "R",
+    "O",
+    "arrow_up"
+  ],
+  "start_x": 1,
+  "start_y": 2,
+  "grid_width": 7,
+  "grid_height": 5,
+  "true_solution_faces": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "R",
+      "rotation": 90
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 0
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 180
+    }
+  },
+  "bottom_faces": [
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "x": 1,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 1,
+      "y": 3
+    },
+    {
+      "patternId": "plus",
+      "rotation": 180,
+      "x": 2,
+      "y": 3
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 180,
+      "x": 2,
+      "y": 2
+    },
+    {
+      "patternId": "O",
+      "rotation": 180,
+      "x": 2,
+      "y": 1
+    },
+    {
+      "patternId": "R",
+      "rotation": 270,
+      "x": 3,
+      "y": 1
+    },
+    {
+      "patternId": "arrow_up",
+      "rotation": 270,
+      "x": 3,
+      "y": 2
+    },
+    {
+      "patternId": "plus",
+      "rotation": 270,
+      "x": 4,
+      "y": 2
+    },
+    {
+      "patternId": "R",
+      "rotation": 180,
+      "x": 4,
+      "y": 1
+    },
+    {
+      "patternId": "4",
+      "rotation": 270,
+      "x": 5,
+      "y": 1
+    }
+  ],
+  "slot_sequence": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "BACK",
+    "BOTTOM",
+    "RIGHT",
+    "BACK",
+    "TOP"
+  ],
+  "required_slots": [
+    "FRONT",
+    "RIGHT",
+    "BOTTOM",
+    "LEFT",
+    "BACK",
+    "TOP"
+  ],
+  "required_count": 6,
+  "answer": {
+    "faces": {
+      "TOP": {
+        "patternId": "4",
+        "rotation": 0
+      },
+      "BOTTOM": {
+        "patternId": "arrow_up",
+        "rotation": 270
+      },
+      "FRONT": {
+        "patternId": "O",
+        "rotation": 180
+      },
+      "BACK": {
+        "patternId": "R",
+        "rotation": 270
+      },
+      "LEFT": {
+        "patternId": "O",
+        "rotation": 90
+      },
+      "RIGHT": {
+        "patternId": "plus",
+        "rotation": 90
+      }
+    }
+  },
+  "legacy_answer": {
+    "TOP": {
+      "patternId": "4",
+      "rotation": 0
+    },
+    "BOTTOM": {
+      "patternId": "arrow_up",
+      "rotation": 270
+    },
+    "FRONT": {
+      "patternId": "O",
+      "rotation": 180
+    },
+    "BACK": {
+      "patternId": "R",
+      "rotation": 270
+    },
+    "LEFT": {
+      "patternId": "O",
+      "rotation": 90
+    },
+    "RIGHT": {
+      "patternId": "plus",
+      "rotation": 90
+    }
+  },
+  "prompt": {
+    "system": "You are a cube-reconstruction puzzle solver. Given a blank cross net of a cube and a top-down path image showing the bottom-face imprints stamped onto the road as the cube rolls, you reconstruct the patternId and rotation of every outer face.\n\nYou will receive: (a) one blank cross-net image (the unfolded outer surface, with the six face slots TOP/BOTTOM/FRONT/BACK/LEFT/RIGHT), (b) one path-sequence image (top-down view of the cube's roll path with the bottom-face imprints visible), and (c) a structured text body listing the roll sequence, observed path faces, and the allowed patternId values for this task.\n\nYou may reason step by step before the final answer. Place your final answer on the very last line of your reply, in the form: FINAL_JSON: <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: C368\n- net_layout: standard_cross\n- difficulty: 4\n- move_count: 9\n- roll_sequence (N=up, S=down, W=left, E=right): S -> E -> N -> N -> E -> S -> E -> N -> E\n- observed_path_faces (one entry per stamped imprint, in roll order):\n- step 1: patternId=O, rotation=180, flipVertical=true\n- step 2: patternId=plus, rotation=180, flipVertical=true\n- step 3: patternId=arrow_up, rotation=180, flipVertical=true\n- step 4: patternId=O, rotation=180, flipVertical=true\n- step 5: patternId=R, rotation=270, flipVertical=true\n- step 6: patternId=arrow_up, rotation=270, flipVertical=true\n- step 7: patternId=plus, rotation=270, flipVertical=true\n- step 8: patternId=R, rotation=180, flipVertical=true\n- step 9: patternId=4, rotation=270, flipVertical=true\n- allowed patternId values for this task: O, plus, arrow_up, R, 4, ?\n\n## 5. ACTION VOCABULARY\nA complete answer is one map from face name to its `(patternId, rotation)` pair:\n- face: one of {\"TOP\", \"BOTTOM\", \"FRONT\", \"BACK\", \"LEFT\", \"RIGHT\"}.\n- patternId: a string drawn from the allowed list above, or the literal \"?\" sentinel.\n- rotation: integer in {0, 90, 180, 270}.\nA face is \"uniquely determined\" iff the inputs (roll sequence, observed imprints, blank net) constrain its pattern and rotation to exactly one possibility.\n\n## 6. CONSTRAINTS\n- The output must list all six face keys exactly: TOP, BOTTOM, FRONT, BACK, LEFT, RIGHT (no extras, no omissions).\n- Each `patternId` must come from the allowed list, or be the literal \"?\".\n- When `patternId == \"?\"`, `rotation` must be 0.\n- Each rotation must be one of 0, 90, 180, 270.\n- Do not invent new patternIds. The model is scored only against the listed allowed values plus \"?\".\n\n## 7. SOLVING ADVICE\n- Trace the roll one step at a time: which face becomes the bottom after each roll? The path imprint at that step records that face.\n- When a stamped imprint is rotated relative to the original pattern's upright orientation, infer the cumulative rotation that the rolling chain has applied to that face.\n- Faces that never touch the ground may not appear in the imprints; if no other constraint pins them, they are \"?\".\n\n## 8. OUTPUT SCHEMA\nFINAL_JSON: {\"faces\":{\"TOP\":{\"patternId\":<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."
+  }
+}