---
license: cc-by-sa-4.0
---

# Apple-Pi

A 100-case evaluation subset (50 simulation + 50 realworld) drawn from a larger **400-case physics benchmark** for evaluating physics reasoning in image and video generation models.

## Folder structure

```
apple-pi/
├── README.md
├── croissant.json
├── selected_cases.json
├── sim_subset/        # 50 simulation cases
└── realworld_subset/  # 50 realworld cases
```

## Per-case contents

**Simulation** (`sim_subset/<task>/<case_id>/`) — generated with **NVIDIA Isaac Sim** (rigid-body PhysX simulator):
- `annotation.txt`, `physics_duration.txt`, `formula_info.json`
- `initial_state/` (rgb_0000 + white-bg variants + instance segmentation + camera params)
- `instantaneous_velocity/` (target-time velocity reference)
- `rgb/0000.png ~ 00NN.png` (rendered video frames @ 24 fps)
- `instance_segmentation/`, `mask/`, `velocity/`, `depth/`, `density/`, `camera_parameters/`

**Realworld** (`realworld_subset/<category>/[<subcategory>/]<case_id>/`):
- `annotation.txt`, `formula_info.json`, `physics_duration.txt`, `annotation_config.json`
- `initial_state/` (first-frame extraction + variants)
- `instance_segmentation/`, `mask/`, `instantaneous_velocity/`
- `rgb/video.mp4`

## Tasks

**Simulation (9 tasks)**: at_rest, circular, freefall, inclined_plane, inelastic_collision, perfectly_elastic_collision, perfectly_inelastic_collision, projectile, uniform_linear.

**Realworld (7 categories)**: NewtonsFirstLaw/AtRest, Gravity/{Freefall, Projectile}, ConservationofMomentum/{InelasticCollision, PerfectlyElasticCollision, PerfectlyInelasticCollision}, Composition.

## Intended use

Zero-shot evaluation of physics reasoning in image- and video-generation models (perception, comprehension, generation tracks). Not intended for training.

## License

CC BY-SA 4.0

## Citation

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