After several rounds of structural attempts and audits, the picture
has stabilized. Updated COMMENTARY.md with a "Final status" section:
- What we have proved: the Heawood-face-sum reduction (tight), the
tight structural cases (a', b', c) covering 94.97% of (G, v, i)
configurations, and the refined pigeonhole + S-cycle arguments
closing most of the residual ~5%.
- What's open structurally: full G'-pentagon fallback, and the
Kempe-cycle structural regularity "|S|=8 + hit=8 ⇒ p_G=11"
(30/30 empirical).
- Empirical closure: 100% across 142,812 chord-apex+Kempe colourings
up to |V(G)| ≤ 20.
- Why this isn't Appel-Haken in disguise: ~4 main steps + ~8
case-style sub-lemmas, vs RSST's 633. The chord-apex+Kempe
restriction does most of the work upfront.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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