Section 4: un-stacking lemma (degree-3 removal preserves Phi, proved),
ear-peeling base case (k=0 => 2^(n-2)), reduction to the irreducible
case, and the irreducible lemma as the sole open conjecture (|Phi| >=
5/4 * 2^(n-2), tight at the degree-4/5 patch; wheel = floor(2^n/3) is not
extremal). Records the two dead ends (monotonicity false, universal
toggles insufficient) and ties each claim to its experiment.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
The stacked-only search missed non-stacked disks, and cocircular boundary
points gave degenerate Delaunay (invalid disks, spurious sub-floor |Phi|).
Add floor_diverse_disks.py: 1700+ validated disks per n (convex non-
cocircular boundary, face-count and boundary-edge checks) confirm min|Phi|
= 2^(n-2). Note records that interior structure tends to ENLARGE Phi
(wheel 5 vs fan 4) and that depth adds two faces per one constraint.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Experiments probing the cluster restriction set R_K / Phi: R_K is a Z/3
zonotope (not a GF(3) subspace), the "richness" invariant is an artifact
of non-shrinking annuli, the interface gluing always works on interior
cycles (forced by 4CT), and the maximal constraint achievable on an
n-cycle is a floor of 2^(n-2) -- already reached by the trivial tire.
Note boundary_restriction_structure.tex writes these up.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis