Marcin Pawlowski 15ad9f285c
Tighten the statistics in the design-band section
Re-examining §3.2a's inference rather than its numbers found one claim
that was wrong and one that does not survive correction.

Wrong: "two independent tests agree on that onset." The gap test
(countable - unrestricted) and the vs-1.0 test (countable - 1.0) share
the countable arm and are correlated at rho ~ 0.73. The vs-1.0 test is
not confirmation, it is the same measurement with one noisy arm removed
-- which makes it ~1.4x more sensitive, and is why it flags 4 cells
where the gap test flags 1. What IS informative is the contrast between
arms: unrestricted shows chance-level deviation, countable shows a
shortfall concentrated at every uncle cap at the top of the band.

Does not survive: the whole-band pooled gap, -0.00048 +- 0.00033
(t = 2.8). Counting every test in the section -- 15 per-cell gap, 5
pooled-per-delay, 1 whole-band, 30 vs-1.0 = 51 -- Bonferroni requires
z = 3.30. It is now labelled unresolved. The sign imbalance (11/15
negative, p = 0.12) is labelled likewise.

Holds, and more firmly than claimed: delta_max = 5, pooled t = 3.68.
Added a 20 000-draw permutation test on the same cells, which assumes
no distributional form: p = 0.0003, with every other delay at p >= 0.21.
It clears the 51-test Bonferroni threshold. Replicate distributions are
clean (sd ~0.003, |skew| <= 0.5, no outliers), and the peering graph
re-rolls per replicate -- `replicate` is in config.key() and the graph
is seeded from the full-key spawn hierarchy -- so the replicate SEM
captures graph-to-graph variance rather than pseudo-replicating one
graph.

Added a weighted regression of gap on delay as a single pre-specifiable
test with no choice of which delay to inspect: slope -0.00024 +-
0.00012 per slot (t = -2.05). Consistent with a monotone cost, marginal
on its own, and reported as such.

Added the limitation that actually caps the resolution: the comparison
is unpaired. uncle_model enters the config key (which is what makes
--old bit-reproduce the earlier runs), so the two arms share neither
graph nor lottery draws and each comparison pays the between-run
variance twice -- a +-0.0015 per-cell floor, an order of magnitude
above the effect. A paired design would cancel most of it and is named
as the single change that would most improve the measurement.

The §1 summary is corrected to match: indistinguishable from zero up to
delta_max = 4, resolved only at the top of the band at ~0.14%.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
2026-08-05 10:57:51 +02:00
..
2026-07-31 10:04:10 +02:00