Add kempe_rt_composition_probe.py: Ext(T) = boundary necklaces realisable on a
subtree's outer seam by a compatible Kempe-balanced selection; monotone maps over
minimal-antichain families decide whether empty Ext is reachable. Modeling facts
established: the seam is exactly the singleton down apexes (bite apexes have parent
faces on both sides, hence parent-internal); necklace states are exact because a
child attaches with free dihedral placement (dihedral-closed sequence sets).
Result over all no-length-3-boundary tiles n<=14 (7750 tiles, 1966 distinct
relations, 149 leaf, 27 branching): empty Ext is NOT reachable — every assemblable
tree admits a compatible selection, verifying the chain-pigeonhole conjecture
exhaustively for tire trees with treads n<=14 and no separating triangles. The
fixpoint saturates in 2 rounds: restriction does not accumulate along chains.
Tightest subtree pins a size-5 seam to the single necklace 00012; every smallest
minimal Ext contains the blocky/regular state. Relations cached (~6MB) for cheap
extension to larger n. Caveat: terminal facial-triangle leaves not yet modeled.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
d547076cba