[Mattral]

Summary

Two fixes found by the pre-registered blind test on run 1's footage, plus Amendment 2 to the run-2 pre-registration. Everything here precedes any run-2 recording.

1. Encoder crash on empty windows (399164e, carried over: PR #13 was merged before this fix was pushed)
A window with nothing detected in any frame is fully masked. PyTorch's inference fast path raised to_padded_tensor: at least one constituent tensor should have non-zero numel, because the analyzer encodes windows one at a time. Such windows are now unmasked; presence-weighted pooling already discards their frame outputs, so every empty window maps to one "nothing detected" summary. A regression test reproduces the exact error on the old code.

2. Fréchet safeguard misfire (d326435)

• Problem: in a condition where every window was empty (noise_32 in the blind test), all latents are identical and the shrunk covariance is zero. The old ratio test, imag/real > 1e-3 on sqrtm(Σ_A Σ_B), then divided by about 1e-12 and refused, although the distance is exactly ‖μ_A − μ_B‖² + tr(Σ_A).
• Fix: the symmetric formulation tr((Σ_B^½ Σ_A Σ_B^½)^½) = Σᵢ √λᵢ, with eigenvalues clipped at zero. It's exact, has no free parameter (unlike a ridge ε), and is stable for singular and near-singular covariances.
• Verified:
  • matches sqrtm on 20 well-conditioned pairs to 1e-9;
  • V2's published Fréchet values reproduce exactly (0.000263 overall; each per-level value; ρ = +0.943);
  • the exact closed form at Σ_B = 0;
  • continuous as a condition approaches all-empty;
  • against the old code, the near-degenerate test fails.
• Spec 7.1 deviation documented. sqrtm_had_complex_component is kept for API compatibility and is now always False.

3. Amendment 2 (037670a), dated 2026-10-09, before any run-2 data:

• §7.1: the symmetric Fréchet computation. Every condition gets a gap score; none is ranked or dropped by convention on the gap side.
• §8.4, sensitivity, equal prominence: Rules A and B also computed without conditions whose landmark error is undefined. Those are ranked worst by convention, not measurement, so they can contribute partly definitional agreement. Both are reported side by side. If they disagree, the headline says so and no single verdict is claimed.
• §8.3: a per-take breakdown for every condition. In the blind test, under noise at std 20, MediaPipe tracked 100% of frames in two takes and never found the body in the third, so pooled means can hide all-or-nothing behaviour. The present-frames-only gap counts as "not computable" below 3 such windows.
• §12: the blind-test outcome.

The analysis script implements both analyses (rules_all_24, rules_measured_only, rules_disagree) and prints the per-take table.

Blind test, after both fixes (run 1's 3 clean takes, 300 frames each, scores discarded unread): every stage passes, with 24 finite gap scores, finite CIs for both rules, the sensitivity analysis, all secondary analyses, 72 per-take rows and the report.

Verification

• pytest -q: 192 passed (105 s)
• ruff check .: clean
• V2 re-run: values identical to the runbook
• Privacy greps clean
• CI green on 3.10 / 3.11 / 3.12

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