A translational pseudo-symmetry splits every reflection into two classes by the
parity of its index along the translation, one systematically strong and the other
systematically weak. Where the translation is a half-integer along an axis, those two
classes are exactly the absent class and the control class of a screw along that same
axis - so the absence test divides one by the other and pays the suppression twice,
reading a class that is present but suppressed as extinct, and buying a screw the
crystal does not have.
Measure the modulation along each axis from the intensities and divide it out before
scoring. Per axis, not pooled: on the crystal this was found on it is 0.034 along the
row carrying the false screw against 0.287 and 0.159 along the two rows whose screws
are real, and a pooled estimate under-corrects the row that needs it while
over-correcting the rows that do not. The violation counter is corrected with the
evidence, because candidates rank on the sum of their zones and a correction that only
ever lowers a score can never unseat a screw that has already been added.
The false zone goes from 75.7 nats for its screw to 56.3 against it and from five
violations in ninety to fourteen; the run adopts the deposited group. The two genuine
screws on the same crystal pay 2.4 and 1.2 nats and gain no violations. On a crystal
whose deposit puts a real screw on a row that also carries a half-integer translation,
the correction fires, that screw pays 18.4 nats and still carries 59.5, and the
verdict does not move. Across the corpus nine crystals engage it and one zone changes
state.
Only order-two screws are treated: a three-fold with a one-third translation is left
unanswered rather than answered no.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N
leonarski_fandClaude Opus 5
49938d2a24
