Updated COMMENTARY.md with a "Lessons from the structural-proof
attempts" section summarizing:
- What worked: the Heawood-face-sum reduction (Theorem
deciding-face-implies-conj-5-1) and tight covering for n_k = 5
configurations.
- What didn't: n_i = 6 lemma (retracted as empirically false),
winding-number invariant (Σ = 0 under alternation, not
contradictory), case-analysis past |S| ≤ 1 (becomes discharging).
- Diagnostic: every global aggregation we've tried gives a quantity
consistent with constancy, not contradicting it. Lemma 5.2's
alternation is the right local consequence but doesn't aggregate
to a contradiction by itself.
- Open: G'-pentagon fallback structural proof; possible stronger
consequences of minimality of G beyond chord-apex.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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