Each deviation is taken from a mean fitted on its own orbit, so one degree of
freedom per orbit is spent: dof = sum(n-1) = N - G, the divisor chi2_under a few
lines above already uses. Dividing by N understated the reduced chi^2 and so
overstated the b that brings it to 1 - unevenly, because a low-multiplicity
parent loses a larger fraction of its dof than the higher-multiplicity candidate
it is compared against, and the difference landed on the b RATIO the gates read.
Measured three times independently on disjoint corpora: median ratio inflation
+23.7%, +23.7% and +23.8%, with the corrected ratio lower in 42 of 42 promotions,
so the error pushed toward over-calling. Expect no verdict to move: the b veto
has not been observed to fire on any corpus it has been measured over, and
refused_by=b fired zero times in 25 refusals.
The bounds are left at 1.78 / 2.00 / 0.05 rather than rescaled. They were
calibrated in the old convention, but re-measured on the corrected statistic
against independent space groups they still separate: the genuine maximum is
1.640 and the nearest false step 3.208, so both bounds sit inside the only clean
gap the corrected distribution offers. A second derivation from population
medians argues for 1.38 / 1.56 / 0.07 instead; that is a calibration question for
a battery, not a condition of fixing the arithmetic.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N
leonarski_fandClaude Opus 5
431ac4e3d9