A weakly-scaled genuine high-symmetry crystal (cubic insulin Ins_I_3) was
demoted I23 -> I222: its cubic 3-fold passes the operator-CC gate, but merging
across it inflates the within-orbit chi2 to ~2x the best subgroup - just past
the self-consistency bound. A merohedral twin (Ins_H_2's R3->R32) lands at the
same chi2 ratio, so the ratio alone cannot separate a genuine-but-poorly-scaled
promotion from a twin.
Add a systematic-error test that does separate them. merge_systematic_b solves
for the extra intensity-proportional error b (sigma^2 + (b I)^2) that a point
group's merge must invoke to reach chi2 = 1. A genuine symmetry step gains
multiplicity without intensity-proportional disagreement, so b barely grows
(Ins_I_3 b x1.6 vs its confirmed subgroup); a twin forces non-equivalent
reflections together, so b balloons (Ins_H_2 x2.2). A candidate whose chi2 is
only just past the ratio bound (max_merge_chi2_rescue) is rescued when its
b, relative to the largest confirmed subgroup (by rotation-set inclusion),
stayed within max_systematic_b_ratio.
Battery: 20/24 space-group match (was 19/24) - Ins_I_3 -> I23, every other
crystal bit-identical including the twins that must stay in lower symmetry.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
leonarski_fandClaude Opus 4.8
f81830df4f
