The full-resolution merge-degradation gate divided the added operators' mean
intensity-weighted R by the smallest R anywhere in the crystal. That denominator is an
extreme order statistic, so it has a pole: one unusually clean operator condemns every
other genuine one. It is not a rare accident. A rotation about an axis near the spindle
maps a reflection onto one recorded at nearly the same detector position, so the lab-frame
systematics cancel for that operator alone; measured over the rotation corpus the spread
WITHIN a genuine group reaches 2.0-2.6x, the whole width of the old bound of 2.0. On a weak
cubic crystal whose near-spindle 3-fold read 0.074 against 0.16-0.22 for its ten other
genuine operators, every one of them was refused, the search kept only the group generated
by the reference operator itself (which reads 1.00 by construction), and the same 222
hypothesis on the same merge read 2.45 under a cubic enumeration and 1.02 under an
orthorhombic one - a statistic that moves with which OTHER operators were enumerated.
The added operators are now placed on the scale the crystal itself defines, between the R
of unrelated reflections and the R of the best-agreeing operator:
contrast = (random_pairing_r - r_added) / (random_pairing_r - global_best_operator_r)
random_pairing_r is new: the same intensity-weighted R over shell-matched pairs of
reflections no symmetry relates, measured on the merge (deterministic, no RNG). Both ends
are hypothesis-free, and the form has no pole - an unusually clean reference widens the
denominator by a few per cent instead of driving the divisor towards zero. The test
abstains where the best-agreeing operator is itself no better than half way to unrelated
reflections, i.e. where the merge holds no clean end to measure from, as it already
abstains when there is no second operator at all.
Calibrated over 149 rotation datasets with a known answer, read as the gate reads it:
genuine promotions reach down to 0.77 and the worst false one reads 0.695, so the bound is
0.72. It keeps every refusal the old ratio made on that corpus except the weak cubic one,
which now promotes to its cubic group; the twins that read above the genuine range are
refused by the H gate and the twin-immune zone, as before.
The reported value, the point-group report line, the finalist ledger and the
gate-fired-and-was-overridden note all follow the contrast.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_013nW6FNRP1bBJJ8pfHiByAT
leonarski_fandClaude Opus 5
c8e98faf31