Mirror of the up-tooth experiment with the distinguished valid face moved
from the outer face to an inner non-tooth face (root or bite inner-gap).
For each (M(T), inner face) config holding m singleton down-tooth apexes,
record the apex colour sequence (cyclic order, mod colour permutation) over
Kempe-balanced colourings and group configs by their sequence-set. Runs for
m=3,4,5,6 with per-sequence notes, figures, and a config atlas.
Finding: inner faces realise the same parity-admissible sequence vocabulary
and the same distinct-sequence counts (1/4/10/28) as the outer face, i.e.
the Kempe-parity law acts uniformly on every valid face. At m=6 the configs
are the U<->D embedding mirror of the up-m=6 graphs (matching 7 configs,
28 sequences, 127 colourings).
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
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