didericis e8b2e47e44 Add contraction-lift proof-strategy sketch toward Conjecture 5.7 ...

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>

2026-05-20 13:47:38 -04:00

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