From e94548c614ee0064ef6c8ea720626968164db80e Mon Sep 17 00:00:00 2001 From: Filip Leonarski Date: Wed, 2 Sep 2026 08:44:56 +0200 Subject: [PATCH] docs: the twinning exemption list, and why -1, 2/m and mmm are not on it The stated criterion (a merohedral twin law exists) formally exempts every holohedral Laue class, but the code (TwinningAnalysis.cpp) deliberately keeps the low-symmetry ones eligible because pseudo-merohedral twinning through a special metric cannot be excluded there. Say both halves, and give the reference values of the statistics so the mmCIF numbers can be read. Co-Authored-By: Claude Opus 5 (1M context) Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N --- docs/CPU_DATA_ANALYSIS.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/CPU_DATA_ANALYSIS.md b/docs/CPU_DATA_ANALYSIS.md index fc3bef4e3..4f9b99b71 100644 --- a/docs/CPU_DATA_ANALYSIS.md +++ b/docs/CPU_DATA_ANALYSIS.md @@ -1099,7 +1099,7 @@ Both search merges also drop the **frames whose fitted per-frame scale came out ### 13.2 Twinning check -A Padilla–Yeates $L$-test ($\langle|L|\rangle$, $\langle L^2\rangle$) and the second moment $\langle I^2\rangle/\langle I\rangle^2$ (taken per resolution shell with noise-only shells skipped and Wilson outliers rejected, so a single strong reflection in a collapsed-mean shell cannot skew it) are written to the merged mmCIF as a twinning diagnostic. Twinning is only flagged in Laue classes where a merohedral twin law can exist; the holohedral high-symmetry classes ($4/mmm$, $6/mmm$, $m\bar{3}m$, and $\bar{3}m$ on a rhombohedral lattice) are exempt, so a low $\langle|L|\rangle$ there is reported as a statistical artefact rather than twinning. +A Padilla–Yeates $L$-test ($\langle|L|\rangle$, $\langle L^2\rangle$ — 0.500 and 0.333 untwinned, 0.375 and 0.200 for a perfect twin) and the second moment $\langle I^2\rangle/\langle I\rangle^2$ (2.0 for untwinned acentric data, 1.5 for a perfect twin; taken per resolution shell with noise-only shells skipped and Wilson outliers rejected, so a single strong reflection in a collapsed-mean shell cannot skew it) are written to the merged mmCIF as a twinning diagnostic. A merohedral twin law exists only where the Laue class is a proper subgroup of the lattice holohedry, so in the high-symmetry holohedral classes ($4/mmm$, $6/mmm$, $m\bar{3}m$, and $\bar{3}m$ on a rhombohedral lattice) twinning is never flagged, and a low $\langle|L|\rangle$ there is reported as a statistical artefact instead. The low-symmetry holohedral classes ($\bar{1}$, $2/m$, $mmm$) also admit no strictly merohedral law, but they stay eligible for the flag on purpose: *pseudo*-merohedral twinning through an accidentally special metric cannot be ruled out from the symmetry alone, and those are the classes it happens in. ### 13.3 Outlier rejection