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didericis a724a50344 Track odd-size universal trend; the n=12 failure is sporadic, not a trend
Add kempe_universal_trend_probe.py (|D[m]| per size across n). Across n=6..13 and
all sizes, the ONLY empty per-size universal is (n=12, m=7): at n=13 size 7 is back
to |D|=2 with more boundaries (579), so the vanishing is sporadic, not monotone.
The lone n=12 breaker is the outer rim of word=UUUDUDUDUDUD bite=(3,11) (most-
alternating 7-up word, antipodal bite), realising 9/10 size-7 necklaces and missing
only 0001112. Correct the earlier "doomed at scale" reading in the findings note:
the uniform shortcut almost always works (near-total coverage) but is fragile to a
single exceptional tile; pairwise gluability still always holds.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
2026-06-11 23:40:48 -04:00
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