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leonarski_fandClaude Opus 5 476a849c0e indexing: decide an axis harmonic on which cell explains more of the spots

When two first-pass schemes return cells whose primitive volumes differ by a small
integer, the validation-FRAME count cannot tell them apart: a spurious axis multiple
indexes every frame its true sub-cell does, so both reach 60/60 and the count
saturates. The rule that then decided the pair was unconditionally against the larger
cell, so on a crystal with a real pseudo-translation the true cell could not win in
any scheme order.

Ask the same question at the granularity where it does not saturate: how many of the
validation frames' SPOTS does each cell account for? That comparison leans towards the
smaller cell by construction, and needs no threshold to do so. Acceptance is a
fractional-Miller test, so multiplying an axis by n multiplies that axis's residual by
n: the larger cell places every shared reflection n times less accurately than the
sub-cell does, and loses outright the spots that sit in the tolerance margin. The only
thing that can pay for that loss is the class of reflections the larger cell ADDS -
empty for a spurious multiple, the superstructure's satellite rows for a real one - so
the larger cell wins the count only when the extra periodicity is really there. The
count is taken over the validation frames' whole spot lists, which reach far deeper
into each frame's intensity distribution than the first pass's own accumulation cap,
and a superstructure layer is faintest exactly where that cap cuts.

Measured over the five crystals of this corpus where the two schemes return an
integer-related pair, the larger cell accounts for 1.37x and 1.98x the spots on the two
whose true axis was being halved, and 0.30x, 0.36x and 0.71x on the three where the
doubling is spurious. All five come out right: the two keep the true cell and its
deposited space group, the three reproduce the answer the old rule gave, to the digit.
(One of the three has a bistable first pass - four builds give three answers, one of
them without this change at all - so it is not evidence either way; the other two are
reproducible.)

What the added class holds is computed and reported next to the decision, because it
is the physics the count is a consequence of. It is deliberately NOT thresholded, and
that is the part of this that took the measuring. Refuted along the way:

- An occupancy floor, which is how this was first written. Over the five crystals the
  arbiter is asked about, the emptiest index-n class reads 48.2, 41.6, 37.3, 25.4 and
  7.1 %. The two the larger cell should win are the 41.6 and the 37.3, so the three it
  should lose bracket them on both sides, and a real superstructure elsewhere on the
  corpus reads 3.4 %, below all five. Recomputing the same statistic on the merged
  intensities over a sweep of I/sigma cuts leaves the ordering unchanged, so this is a
  continuum and not two populations: no floor separates them, and no amount of extra
  data would. The bimodality a floor needs was an artefact of a calibration set that
  contained no failure.
- Requiring the two cells to stand in a genuine sub/super-lattice relation, the change
  of basis being integral. Measured, all five pairs are index-n relations to within
  0.016 of an integer - the volume ratio is not the weak link.
- Deciding it on the merge, by integrating and merging both cells. The worst failure
  does announce itself there (CC1/2 0.9994 -> 0.9566, ISa 18.6 -> 1.4), but it costs a
  second full integrate-and-merge, and the successes lose 13-30 % of their ISa where
  another failure loses 27 %, so the metric does not separate them either.
- Requiring the sub-lattice class to be the STRONGER of the two, which is the right
  mechanism but the wrong observable at this point in the run: the sign it turns on
  lives in integrated intensities, and the spot finder reports no spot at all where a
  class is absent, so at first pass the same ratio reads 0.90 against 0.39 and 0.27.
  The ordering survives, the sign does not.

The occupancy is maximally wrong on the worst failure because that cell is not a
superstructure at all. A beam-centre error along the spindle translates the derotated
cloud rigidly, and a lattice shifted by half a spacing is indexable only on a doubled
axis - the shift needed scales as 1/(2L), so a long axis is the easy one to
half-offset. In that doubled setting the even class is empty and the zero layer reads
a negative mean intensity, which no crystal can do, while the odd class carries
everything. Such a cell fits no index-n sublattice at all, so its added class reads the
chance value (n-1)/n, the largest the occupancy can take, and the occupancy test
reports the artefact as more real than any genuine superstructure. The spot count sees
it for what it is, at 0.30x.

So the beam-centre warning below is now suppressed only when the larger cell WINS.
Declining it is a fall back to the default, and that warning - which names the beam
centre and offers --estimate-beam-center - is then the most useful thing the run can
say; on the half-offset mode it is the correct diagnosis.

The same question asked unconditionally of the committed cell, the halved-axis probe,
is not included. Measured over the committed cells of 29 crystals, 19 of 189 axes read
above the 2 % floor it would have used and the largest read 30 %, and those largest
readings are on crystals whose committed cell is already wrong - where doubling an axis
is the wrong response. It rescues one crystal whose superstructure layer reads 3.4 %.
That is not worth the rest.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EFEJG6WBQv8th4UJFNe53N

2026-09-02 12:46:57 +02:00