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leonarski_fandClaude Opus 5 8b9598c1c4 twinning: the L-test partners are chosen so a pseudo-translation cannot silence it
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The L-test compares a reflection with a partner a fixed step away, and the step it
used preserves the parity class of a half-integer pseudo-translation - so a
pseudo-body-centring was invisible to it by luck rather than by design. A translation
of one third is not so lucky: it puts the two members of a pair in different
modulation classes, inflates the statistic past the bound that is read as evidence
AGAINST twinning, and the twin call is lost silently on a crystal that has one.

Choose the partners so every pair stays inside one modulation class, which is what
the half-integer case was already getting by accident. The obvious alternative -
lengthening the step until it clears a third as well - was measured and rejected: it
puts the statistic past that bound on more than two thirds of the corpus against a
seventh today.

Measured over a hundred and thirty-seven crystals: a hundred and twenty-nine
unchanged, seven repaired, and exactly one verdict moves - a crystal whose twinning
was being denied by its own pseudo-translation. On a synthetic perfect twin carrying
a one-third translation, both indicators are destroyed before the change and both
return after it.

Nothing branches on this verdict, so no merged intensity moves; the whole effect is
what the report says about the crystal.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N
2026-09-05 20:09:00 +02:00