# Apple-Pi: Physics Infographics Evaluation Subset

A 100-case evaluation subset (50 simulation + 50 realworld) for physics-infographic reasoning evaluation in image and video generation models.

## Overview

This dataset contains ground-truth recordings and annotations for physics scenes spanning 9 simulated tasks and 7 realworld categories. Each case provides full per-frame rendering, instance segmentation, velocity tracking, depth, mask, and human-readable physical-parameter annotations, suitable for evaluating multi-step physics understanding in generative models.

## Folder Structure

```
apple-pi/
├── README.md
├── croissant.json                  # Croissant + RAI metadata
├── selected_cases.json             # Manifest with case IDs and sampling strategies
├── sim_subset/                     # 50 simulation cases
│   ├── at_rest/0/, at_rest/2/, ...
│   ├── circular/0/, circular/newbatch_5/, ...
│   └── ... (9 physics tasks)
└── realworld_subset/               # 50 realworld cases
    ├── Composition/0/
    ├── Gravity/Freefall/1/
    ├── ConservationofMomentum/InelasticCollision/1/
    └── NewtonsFirstLaw/AtRest/1/
```

## Per-Case Contents (Simulation)

Each `sim_subset/<task>/<case_id>/`:

| File / Folder | Description |
|---|---|
| `annotation.txt` | Human-readable physical parameters (mass, velocity, friction, etc.) |
| `physics_duration.txt` | Total physics-valid duration in seconds |
| `formula_info.json` | 4 candidate formulas + correct answer + variable substitution hints |
| `prompt.txt` | Original task prompt |
| `initial_state/` | First-frame data: `rgb_0000.png` (with annotations), `rgb_0000_white_bg.png`, `rgb_0000_white_bg_obj.png` (object only on white), instance segmentation, mapping, depth, density, mask, velocity, camera parameters |
| `instantaneous_velocity/` | Per-object velocity at a target time: `velocity.json`, `velocity_annotated.png`, `mask.npy`, `mapping.json` |
| `instance_segmentation/maps.npz` | Full-sequence instance segmentation maps |
| `mask/maps.npz` | Full-sequence foreground masks |
| `velocity/maps.npz` | Full-sequence per-pixel velocity maps |
| `depth/maps.npz` | Full-sequence depth maps |
| `density/`, `camera_parameters/` | Per-frame density buffers and camera parameters |
| `rgb/0000.png ~ 00NN.png` | Rendered video frames at 24 fps (NN = round(physics_duration × 24)) |

## Per-Case Contents (Realworld)

Each `realworld_subset/<category>/[<subcategory>/]<case_id>/`:

| File / Folder | Description |
|---|---|
| `annotation.txt` | Physical parameters of the recorded scene |
| `annotation_config.json` | Parameter source / unit metadata |
| `formula_info.json` | Same 4-choice formula schema as simulation |
| `physics_duration.txt` | Validated motion duration |
| `initial_state/` | First-frame extraction: `rgb_0000.png`, `rgb_0000_white_bg.png`, `rgb_0000_white_bg_obj.png`, instance segmentation, mapping, mask |
| `instance_segmentation/maps.npz` | Per-frame instance segmentation |
| `mask/maps.npz` | Per-frame foreground mask |
| `instantaneous_velocity/` | Velocity reference at target time: `velocity.json`, `velocity_annotated.png`, `mask.npy` |
| `rgb/video.mp4` | Original video clip |

## Tasks Covered

### Simulation (9 physics tasks, 50 cases)
- `at_rest`, `circular`, `freefall`, `inclined_plane`
- `inelastic_collision`, `perfectly_elastic_collision`, `perfectly_inelastic_collision`
- `projectile`, `uniform_linear`

### Realworld (7 categories, 50 cases)
- `NewtonsFirstLaw/AtRest`
- `Gravity/Freefall`, `Gravity/Projectile`
- `ConservationofMomentum/{InelasticCollision, PerfectlyElasticCollision, PerfectlyInelasticCollision}`
- `Composition` (multi-task)

## Sampling

- **Simulation**: 50 cases selected from a larger 100-case pool with stratified sampling (seed=42, OLD-first); excludes any cases with rendering artifacts.
- **Realworld**: 50 cases sampled from a 157-case pool with stratified sampling proportional to per-subcategory counts (seed=42).

See `selected_cases.json` for full case-ID lists and sampling metadata.

## Intended Use

- Evaluating image-generation and video-generation models on physics reasoning tasks (perception, comprehension, generation).
- Comparing model outputs against ground-truth simulation rollouts and real-video frames.
- Studying instruction-following and prompt-sensitivity in multimodal models.

## Dataset Composition

| Domain | Cases | Avg files/case | Approx total files |
|---|---:|---:|---:|
| Simulation | 50 | ~750 | ~37,000 |
| Realworld | 50 | ~16 | ~800 |
| **Total** | **100** | | ~37,800 |

## License

Released under **CC BY-SA 4.0** (Creative Commons Attribution–ShareAlike 4.0 International).

## Anonymity

This dataset is released for double-blind submission. All identifying information has been removed.

## Citation

```
[Anonymous] Apple-Pi: Physics Infographics Evaluation Subset. 2026.
```