dual_decomposition: pentagonal externals lemma + edge naming

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- Name the edges of the reduced-dual construction (merged, spike, sides)
  via a new definition; use these names in lem:chord-apex.
- Add lem:pentagonal-externals with full exhaustive proof: any proper
  3-edge-colouring near a pentagonal face of a cubic plane graph has its
  five external edges forming, up to cyclic rotation, the pattern
  (a, b, c, c, c) with {a, b, c} = {1, 2, 3} (iff).
- Cite the new lemma in the chord-apex proof scaffold as the lifting step.
- Remove the icosahedron experimental remark.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

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didericis

2026-05-22 20:22:00 -04:00

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papers/dual_decomposition_minimal_counterexamples/paper.pdf

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