Redo step 2 and step 3 under SR (no chord effect, the correct model
under PDS where O-faces are not G-faces).
Step 2 (pairwise, 14 cases): all compatible. T_1's γ-side projection
saturates {1,2,3}^γ under outward PDS (m_1 ≥ γ from step 1), so
intersection = T_2's projection, always nonempty.
Step 3 (chain consistency, 10 chains up to 6 tires): all compatible.
Forward propagation along the chain shows monotonically growing
support sizes (roughly 3x per step), never empties. Free choice
accumulates outward.
Implication: chain consistency under SR + PDS is essentially
automatic for "open" chains. The remaining gap is the boundary
condition at the outermost level (e.g., the outer triangle of a
triangulated sphere has only 6 valid σ-permutations); whether the
forward state always contains one of those is the next experiment.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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