Note records the closed-chain experiment: forward-propagate state
through SR+PDS tire chains with degenerate-inner T_1 and outer-
triangle T_n (m_n=3). All 10 tested chains converge to the same
final state at L_n — exactly the 6 permutations of {1,2,3}.
Introduces the "outer triangle absorption" framing: distinguishes
H1 (chain-dependent: pigeonhole does real work to filter input to
T_n) vs H2 (T_n-only absorption: T_n's σ_U-projection is intrinsically
the 6 permutations regardless of input). Conjecture: H2 (testable by
single-tire computation).
If H2 holds, items 3-4 of the 4CT-via-tire-decomposition outline
become automatic from local data. If H1, the chain-pigeonhole does
structural work and the question is sharper.
Three-panel figure: (A) closed PDS chain (5,6,5,3) with concentric
levels and source apex; (B) outer-face dual constraint requiring
permutation-of-{1,2,3} on outer triangle; (C) state-size trajectory
showing absorption to 6 at the outer step.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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