Companion to tire_fiber_data.tex. The chord case forces a modelling
choice for the surrounding G: Steiner-rich (each B_in edge gets its
own sub-triangle, chords are invisible to T'_{f'}) vs Steiner-poor
(each O-face is one G-face, chord set determines feasibility).
Under SP, a tire with k > 3 is infeasible unless O already contains
enough chords to keep every O-face at most 3 B_in edges. With chords:
support is positive but much smaller than SR — π_D never reaches 3^k,
and π_D's shrinkage is m-independent. More chords = smaller faces =
MORE support (each chord splits a hard constraint into easier ones).
Side-by-side data table for (m, k) ∈ {3,4,5,6,...}² with various
chord sets, plus 3-page note documenting the modelling choice and
implications for chain pigeonhole.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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