Fairness probe results: is chunk MAE punishing flow for committing to modes?

2026-08-06, ~07:3xZ. Results for Amendment 1 (reads 1–3) and Amendment 2 (read 4, energy score) to the noise-draw pre-registration — the owner’s 21:49Z challenge, instrumented and frozen before any per-draw number existed. Probe: flow-80k, draws=10 heun-30, the frozen 2,458-frame stride-7 subset plan, --dump-draws; analysis fontaine/scripts/draws_fairness.py, report analysis__draws_fairness_k4l2.json. This is the 06:57Z relaunch: the first attempt scored all 2,458 frames and crashed in merge_shards (the mirror of the 04:4xZ bug — empty dump_predictions permuted when only --dump-draws is on; fixed da9ec6a with a regression test, crash log preserved). No banked number was touched — the crash was post-scoring, pre-write.

Instrument gate (E1-style) — draw-0 re-decode

PASSED: draw0_vs_banked_frame_mae_drift = 0.0145 < 0.05. The probe’s draw 0 re-decodes the banked single-draw predictions (same noise key/seed) to a mean per-frame chunk-MAE drift of 0.0145 — cross-run numerics only. The row join carries the hard asserts (truth/valid byte-agreement between probe and banked panel rows), and the degenerate draws=1 validation was re-run green immediately before the npz was opened (anchor 6.6232 reproduced exactly, dispersion and ES interaction exactly zero). All reads below are quotable.

The reads

All numbers on the 2,458 probe frames; pooling valid-element-weighted (the report convention) unless noted. Paired AR/flow-single columns come from the banked npzs through the instrument’s index-join.

• Read 1 cross-checks the full-panel chain: probe mean-of-10 5.4113 vs the chain’s full-panel 5.365 — the stride-7 subset reproduces the ensembling gain (−1.26 vs single draw here). Per-draw pooled spread across the 10 draws: 0.2212 at probe size.
• Read 2 — the oracle mode-match bound is 2.01 below AR’s paired chunk MAE (3.8597 vs 5.8680) and takes first_mae under 1.0. When “sampled a different valid mode” is forgiven entirely, flow is not merely competitive with AR — it is far better.
• Read 3 — dispersion-conditioned deficit (per-frame paired flow-single − AR from the banked npzs; probe pooled deficit +0.7789 frame-mean):

Monotone across all four quartiles; Spearman(dispersion, deficit) = +0.1292. The q4 deficit is 6.2× the q1 deficit — the paired deficit concentrates exactly where the draws disagree. (Frame-level Spearman is weak even though the quartile means are cleanly monotone: dispersion is a systematic but minority contributor to per-frame deficit variance.)

• Read 4 — energy score (strictly proper; Amendment 2): flow 10-draw ES 5.9308 vs AR ES 8.7696 — flow wins by 2.84 under a mode-fair distributional score while losing single-draw MAE on the same frames. Flow single-draw ES 9.8825 (banked single 9.9251 — consistent); interaction term 3.9517, i.e. the value of modeling the distribution rather than sampling from it once.

Verdict against the pre-declared signatures

The unfair-penalty signature FIRED, on every declared criterion:

• Amendment 1’s signature — “deficit concentrating in the high- dispersion quartiles (monotone quartile trend, positive Spearman)” — both hold (monotone 0.23→0.60→0.87→1.42, Spearman +0.13).
• Read 2’s sizing — “best-of-10 at or below AR’s paired chunk MAE” — exceeded by 2.01.
• Amendment 2’s ES criterion — “flow ES ≤ AR ES while flow single-draw MAE > AR MAE” — flow ES is 2.84 better. Per the pre-declared interpretation, this is quantified evidence that the MAE deficit is (at least partly) a scoring-rule artifact, and ES becomes the candidate distributional column for ranking flow arms on the comm holdout.

The modeling-deficit signature (flat quartiles + best-of-10 well above AR) did not fire.

Honest residual, stated with the same discipline: the deficit is positive in every quartile — including q1, where the 10 draws nearly agree (mean dispersion 1.3°, deficit +0.23) — and flow’s per-frame win rate stays below 0.5 everywhere (0.32–0.39). Mode averaging does not explain the whole gap: there is a real, smaller single-draw deficit even where the predictive distribution is tight. “Partly artifact” is the supported claim; “wholly artifact” is not. And per Amendment 1’s honest-limits section, MAE-family reads cannot settle actual rig performance either way.

σ_draw: the direct measurement vs the 0.0159 pin

Direct σ_draw = 0.02367 — SUPERSEDES the model-based 0.0159 pin (1.49×), but stays under both floors, so reopen_floors: false and every dependent band is numerically unchanged (fontaine/scripts/sigma_draw_direct.py, self-oracles O1–O4 green, report analysis__sigma_draw_direct.json).

• Primary (frame-level delta-method): pooled per-frame across-draw std → σ = 0.02367 at panel F_eff 16,488.5 (probe F_eff 2,341.7; frame-level std_η 3.04° pooled, median 1.52°, p90 4.54°).
• Cross-check (pooled-level, n=10): the 10 per-draw pooled MAEs give 0.02522 scaled to panel size; the primary sits inside the χ²₉ 95% band [0.01735, 0.04605].
• Input-drift oracles green: mean-of-draws reproduces the probe report’s chunk_mae; F_eff reproduces the posted 16,488.5; frozen 2,458×10 shape asserted.
• Consequence, exactly as pre-declared in the finalization amendment: σ_draw_final = 0.02367 is the quoted draw-noise sigma from here on; the model-based extrapolation was ~1.5× optimistic, but both verdicts were floor-bound and survive untouched — stable-noise re-bank band stays [6.4882, 6.7582] (0.045 floor binds), SnapFlow 1-NFE adopt band stays ≤ 6.7732 (0.15 floor binds; 3σ = 0.071 < 0.15).

What this feeds

1. The owner’s 21:49Z challenge is answered: yes — chunk MAE punishes flow for committing to modes. The paired deficit concentrates 6× in the dispersed quartile, an oracle valid-mode match beats AR by 2, and a strictly proper score flips the ranking outright. But a smaller real deficit survives in tight-dispersion frames, so MAE unfairness does not fully exonerate the flow recipe.
2. ES as the distributional column (Amendment 2’s pre-declared consequence): candidate for ranking flow arms on the comm holdout, feeding the limit-attribution front — adopting it into any benchmark convention is an owner decision, not taken here.
3. σ_draw_final = 0.02367 replaces the 0.0159 pin in all future draw-noise bands; the two live bands are floor-bound and unchanged.
4. The #18.2 stable-key flip re-bank launched immediately after these reads (gate reopen_floors == false asserted in the launcher) — band [6.4882, 6.7582], hard bitwise controls on state-copy/AR.
5. Attribution screens stay weighted to the AR recipe (owner steer 21:48Z stands), but MAE-based AR-vs-flow rankings should now be read with the ES column alongside — the mainline “flow loses on the panel” summary needs the qualifier “on a mode-averaging-friendly metric.”