Section 5.6 sketches an inductive route to the simple-resolution md4
surjectivity conjecture:
- Lemma 5.8 (good contraction): every md4 triangulation on n >= 7
vertices has a degree-4 vertex with an md4-preserving diagonal
contraction. Empirically true at n=7..11; proof obligation called
out.
- Lemma 5.9 (lift): given a labelled preimage of the contracted
triangulation, reinserting the contracted vertex at the
diagonal-bounded quadrilateral yields a preimage of the original
triangulation. Proof obligation called out.
- Inductive scheme paragraph chains the two lemmas with the octahedron
at n=6 as the base case, citing the n=7 hand-verification (already
scripted in experiments/inductive_lift_check.py).
Lemmas are stated without proof; the three remaining proof
obligations are explicit.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
e8b2e47e44
