FlowWM/causal_droidstd/phi_check/MOTION_SOURCE_README.md

# Where does object motion come from? — three layers, ground truth only, no masks

Run on cached WAFT flow with the robot silhouette removed. **Exterior views only** (wrist Phi
is camera ego-motion). No SAM, no semantic labels, no training.

## Layer 1 — global camera motion: prediction REFUTED

A per-frame homography was fitted by RANSAC on the flow outside the robot and subtracted.

| distance | raw | residual | delta |
|---|---|---|---|
| 0-10 px | +0.781 | +0.785 | +0.004 |
| 10-25 | +0.780 | +0.784 | +0.003 |
| 25-50 | +0.745 | +0.748 | +0.004 |
| 50-100 | +0.698 | +0.702 | +0.004 |
| **>100** | **+0.658** | **+0.656** | **-0.002** |

Only **6.3%** of the flow magnitude was global motion, and the far-field +0.66 is untouched.
The hypothesis that the far-field direction agreement is camera drift is **wrong** — the
exterior cameras really are static (non-robot flow p90 = 0.19 px).

## Layer 2 — Tomasi-Kanade rank: at most one object moves

Trajectories built by chaining flow from a seed grid; W is (2T x P) over points that moved
more than 2 px. Rank <= 4 per rigid object.

| | |
|---|---|
| median rank | **3** (p25 2, p75 3, max 5) |
| rank <= 4 (one object) | **98.9%** |
| rank 5-8 (two objects) | 1.1% |
| rank > 8 | **0.0%** |

Normalised spectrum: 1.00, 0.43, 0.21, 0.12, 0.08, 0.06, 0.05, 0.04, … — the knee is **soft**,
with no rank-4 cliff. That is what cloth looks like, not a rigid body, and it is consistent
with the manipulated objects in these trajectories being towels and cloths.

## Layer 3 — motion mass by source, and a trap worth recording

Common-fate clustering on full-clip trajectories, then a directed graph by lagged
cross-correlation with the gripper's image-velocity series as root.

| | k forced to 4 | **k from rank** |
|---|---|---|
| m0 gripper -> object (hop 1) | 43.9% | **75.0%** |
| **m1 object -> object (hop >=2)** | 48.1% | **0.0%** |
| m_perp lag-0, attaches to nothing | 0.1% | 4.3% |
| m_none | 7.9% | 20.7% |
| hop-1 lag | 0.02 frames | 0.00 frames |
| hop-2 lag | 1.21 frames | no edges |

The first column looked like a textbook result — hop-1 lag 0.02, hop-2 lag 1.21, exactly the
predicted monotonic increase. **It was an artifact.** Fixing k at 4 shreds one deformable
object into four clusters whose parts lead and lag each other, manufacturing 48% of fake
hop-2 edges. Deriving k from the trajectory rank instead makes m1 collapse to **exactly zero**,
which is what Layer 2 independently said. The lag-by-hop test is sound; it was the clustering
feeding it that was wrong.

## What this means for the project

1. **There are no interaction chains in this data.** m1 = 0.0%, and 98.9% of scenes have
   rank <= 4. Nothing here teaches robot -> A -> B, so **do not expect a model trained on it to
   generalise to tool use.** That has to come from different data, not a better loss.
2. **m_perp = 4.3%** is the artifact budget measured without any mask — motion that locks to
   lag 0 but attaches to no cause (shadow, bleed, estimator noise). Small, and now quantified.
3. **m_none = 20.7%** is unattributable motion. Worth a look before trusting any Phi-based
   metric to be complete.
4. The right target metric is the **mass vector matched against GT**, not a single scalar to
   maximise: a hallucinating model dumps everything into m0 and produces m1 = 0 — which on
   this dataset is indistinguishable from correct, so **m1 cannot discriminate here at all.**

## Caveat on the earlier EDA

Re-running the direction/magnitude EDA over all 391 trajectories, panel C's pearson r fell
from 0.348 (60-trajectory sample) to 0.026. The cause is outliers: gripper image speed reaches
5.06e7 px/frame when the EE projects near z=0. The **quintile relationship survives**
(0.0027 -> 0.0242, monotonic across all five), so the coupling is real, but that pearson value
is meaningless without clipping. Layers 1 and 3 here clip gripper speed at 60 px/frame.