# Data schema

## Row semantics

One Parquet row is one complete trajectory. All arrays with leading dimension `T`
share the row's ordered trajectory time axis.

## Top-level fields

| Field | Type | Meaning |
|---|---|---|
| `trajectory_id` | string | stable public ID, `traj_########` |
| `frame_rate_hz` | float32 | inverse median interval of `timestamps_s` |
| `num_frames` | int32 | shared time dimension `T` |
| `action_label` | nullable string | action/gesture label |
| `timestamps_s` | list<float64>, `T` | trajectory-relative timestamps |
| `hands` | list<HandTrajectory> | active hands; reserved empty source slots are removed |
| `objects` | list<ObjectTrajectory> | rigid object trajectories |
| `contacts` | list<list<Contact>>, `T` | zero or more contacts for every frame |

## HandTrajectory

| Field | Shape | Unit / representation |
|---|---:|---|
| `hand_id` | scalar | row-local ID |
| `side` | scalar | `right` |
| `mano_shape` | `[10]` | MANO beta vector |
| `global_position_world_m` | `[T,3]` | metres, world coordinates |
| `global_rotation_world_rotvec_rad` | `[T,3]` | axis-angle rotation vector, radians |
| `mano_pose_rotvec_rad` | `[T,48]` | MANO axis-angle pose, radians |
| `joint_positions_world_m` | `[T,21,3]` | metres, SNAP/manotorch joint order |
| `urdf_dof` | `[T,28]` | 6 floating-base + 22 finger DoF |
| `urdf_dof_target` | `[T,28]` | controller target in the same DoF order |

The 28-DoF order is:

```text
ARTx, ARTy, ARTz, ARRx, ARRy, ARRz,
j1_thumb_cmc_abd, j1_thumb_cmc_flex, j1_thumb_cmc_twist,
j1_thumb_mcp_flex, j1_thumb_mcp_abd, j1_thumb_ip,
j2_index_mcp_abd, j2_index_mcp_flex, j2_index_pip, j2_index_dip,
j3_middle_mcp_abd, j3_middle_mcp_flex, j3_middle_pip, j3_middle_dip,
j4_ring_mcp_abd, j4_ring_mcp_flex, j4_ring_pip, j4_ring_dip,
j5_pinky_mcp_abd, j5_pinky_mcp_flex, j5_pinky_pip, j5_pinky_dip
```

The recorded 21 positions are 16 MANO/URDF keypoints followed by five fingertips:

```text
palm,
index_mcp, index_pip, index_dip,
middle_mcp, middle_pip, middle_dip,
ring_mcp, ring_pip, ring_dip,
pinky_mcp, pinky_pip, pinky_dip,
thumb_cmc, thumb_mcp, thumb_ip,
thumb_tip, index_tip, middle_tip, ring_tip, pinky_tip
```

## ObjectTrajectory

| Field | Shape | Unit / representation |
|---|---:|---|
| `object_id` | scalar | row-local ID |
| `category` | scalar | object category used by `assets/manifest.json` |
| `position_world_m` | `[T,3]` | metres, world coordinates |
| `rotation_world_rotvec_rad` | `[T,3]` | axis-angle rotation vector, radians |

## Contact

`contacts[t]` is empty when frame `t` has no contact. Each contact contains:

- row-local `hand_id` and `object_id` foreign keys;
- `joint_name`;
- total force vectors in world, joint, object, and optionally wrist coordinates;
- one or more contact points containing normal force and positions.

Wrist-coordinate fields are nullable. Null means the source contract did not provide
that representation; it does not mean a zero vector.

## Invariants

```text
len(timestamps_s) == num_frames
len(contacts) == num_frames
len(each hand time-series field) == num_frames
len(each object time-series field) == num_frames
timestamps_s[t + 1] > timestamps_s[t]
```

Every contact references a hand and object in the same row. Fixed vector dimensions
are encoded in Arrow and preserved through Parquet.

## Schema version

Parquet Arrow metadata contains:

```text
release_schema = hand_object_contact_trajectory
release_schema_version = 1.0.0
row_semantics = one complete trajectory per row
```