Under a twin law T a reflection whose twin mate is itself (up to the true
group and Friedel) is untouched at every twin fraction. For each index-2
subgroup H of the adopted point group, those are the reflections centric in
the group and acentric in H: centric if the operators the group adds over H
are real, acentric if they are a twin law or a pseudo-symmetry - the one
intensity statistic that still separates the two at fraction 0.5, where
every operator statistic reads "real".
Read on the P1 cross-check merge: epsilon-1 reflections in shells with
<I/sigma> >= 5 (noise inflates every class towards centric), each class
normalised against its own mean in bins of ~100 reflections and within the
two phase classes of a detected pseudo-translation, Wilson outliers above
E^2 = 20 dropped. Reported per subgroup: the added operators, n,
<|E^2-1|> +- SE read absolutely against 0.968 / 0.736, and the centric-over-
acentric Wilson log-likelihood in nats with both densities convolved with
each reflection's error (flooring E^2 at its sigma instead read a genuine
1.2 A lysozyme zone as acentric), with the acentric control beside it.
Log, report prose and TWIN_ZONE_n keys. Nothing reads it back; no decision
changes.
On the reference sets: 6toc P4222, all three subgroups centric (1.04-1.07,
+253 to +534 nats); 6iu9 P3121 over P31 acentric (0.789, -294 nats); 5j23
R32 over R3 acentric (0.805, -304 nats, tNCS-class normalised); lysozyme
P41212 centric (0.90, +476 to +1297); a P21 myoglobin centric (0.930, +135).
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
leonarski_fandClaude Opus 5
3d62388467
