Comment only; the constant stays at 20.
f6bfa5462 moved min_operator_cc to 0.30, which is close enough to the null of
a sparse operator that the pair minimum deserved measuring rather than
assuming. Measured, over 38 crystals and 142 (crystal, pair-count) points,
the null of the normalised operator correlation has mean -0.02 to +0.05 and
standard deviation 1.08/sqrt(n), flat from 20 pairs to 5000. Its tail is the
part worth writing down:
log10 P(null CC >= 0.30) = -1.03 z + 0.69, residual sd 0.14 decades
One decade per standard deviation, where normal theory gives about five. So a
false operator at 20 pairs clears 0.30 on 12.4% of draws, and any calibration
of this gate that reasons from 1/sqrt(n-3) with a normal or Fisher-z tail is
optimistic by one to two orders of magnitude.
It does not bite where the decision is made. Over 314 candidate operators on
36 crystals the sparsest has 520 pairs and none is below 500; the weakest
confirmed operator sits 9.1 sigma above its own null and the strongest
rejected one 42.7 sigma above. Nothing passes on noise. The search's own
<I/sigma> cut is what keeps that null flat - reconstructing the same crystals
from an unfiltered merge reproduces a null floor of 0.10 to 0.20, which is
where the "false CC rises at low pair count" impression came from. That
describes a shrinking merge, not a sparse operator.
A minimum of 251 pairs would buy a per-operator false rate of 1e-3. It was
built and rejected on measurement: SearchSpaceGroup runs twice, once on all
observations, which decides, and once on a Lorentz-filtered merge, which only
reports - and no log prints the second arm's pair counts. Genuine operators
fall to 98 pairs there, so a floor of 251 empties a conjugacy class on one
crystal and makes the report say its filtered merge supports triclinic, about
a merge whose own correlations put every one of those operators 9 sigma clear
at 0.91 to 0.97. Any floor above about 150 does that; any below about 103 is
barely better than 20. A count floor rejects on pair count however decisive
the correlation is, which is why the shape is wrong rather than the value.
The comment records the law, the rejected value, and the form that would work
if this is ever revisited - a significance floor rather than a count floor.
Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01CHMmeM1d489zvNFT7ZMN2P
leonarski_fandClaude Opus 5
64957d5a5f