C11 Paired Diagnostic — does D1 materially move τ?

Gate: H-AIF-G4 (fix validation) · Run: 2026-07-21 · Runtime: 308 s Artifact: hierarchical-aif/results/motor_stack_aif/C11-PAIRED-DIAGNOSTIC.json Script: hierarchical-aif/scripts/c11_paired_diagnostic.py

THIS IS A DIAGNOSTIC AT N=5. IT IS NOT THE CORRECTED C11 RESULT AND IT LICENSES NO VERDICT. The corrected C11 U4 result requires the full frozen N=2000 run (H-AIF-G5, ≈20.1 h).

Design

Five bootstrap replicates at the declared seed_base = 20260717. Both arms consume identical motor draws — the RNG is constructed once per replicate and the same sampled list is fed to both builders, so the arms differ only in cluster-grouping semantics. Paired by construction.

Result

• Corrected τ is lower in 5 of 5 paired replicates. Exact two-sided sign test p = 0.0625 — the most extreme result obtainable at N=5, and not below 0.05. Suggestive, not significant.
• Spread widens 1.64×: legacy 0.04986 → corrected 0.08160.
• Collapse fraction (τ < 1e-3) is 0 in both arms, so the U4 collapse criterion itself is not what D1 disturbs — the interval is.
• 4 of 5 corrected τ values fall below the recorded U4 CI lower bound of 0.17658 (0.1186, 0.1563, 0.1587, 0.1332). The recorded interval [0.17658, 0.27020] appears both shifted high and too narrow.

Interpretation

The direction was predicted from the mechanism before the run: collapsing K draws of a motor into one group raises that motor's contribution to L_m^K, over-sharpening its latent and reducing the effective number of exchangeable clusters (80 → 46–59 here). Over-sharpening should produce τ estimates that are higher and less variable than a correct cluster bootstrap. That is exactly what the legacy arm shows relative to the corrected arm.

So D1 is not a cosmetic bookkeeping error. It materially moves the reported quantity, in the direction that favoured the conclusion that was reported ("τ is well determined"). This is confirmatory evidence for the D1 entry in the defect ledger and for withdrawing U4_OK.

What this does NOT establish

• It does not establish the corrected τ interval. N=5 is far below the frozen N=2000.
• It does not establish that the corrected C11 U4 verdict will be UNIDENTIFIED. The corrected spread is wider, but whether it crosses the frozen U4 criterion is unknown until the full run.
• p = 0.0625 does not clear a conventional significance threshold. Five paired replicates cannot, even in the best case.
• The τ values here come from _fit_m7_reduced (reduced optimizer budget), matching the committed C11 U4 path — not from a full-budget M7 fit.

Consequence for scheduling

This raises the priority of the corrected C11 full-N rerun: the affected quantity demonstrably moves, so the withdrawn U4_OK cannot be restored by assertion — only by the ≈20.1 h corrected run at frozen N=2000.