dual_decomposition: Kempe-cycle lemma through the spike

- Update def:edge-names to distinguish side-0 ({A_i, v_n}) and side-1
  ({A_{i+2}, v_n}); merged and spike unchanged.
- Add a paragraph defining the {a,b}-Kempe cycle in a 3-edge-coloured cubic
  graph.
- Add lem:kempe-spike: in any proper 3-edge-colouring of the reduced dual,
  the {c, c_0}-Kempe cycle through the spike contains side-0 and merged
  (symmetrically for side-1 with c_1).
- Proof by Kempe swap: a hypothetical alternative cycle K containing merged
  but not spike would, after swapping c <-> c_0 on K, give a proper
  3-edge-colouring under which spike and merged disagree --- contradicting
  lem:chord-apex.

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

papers/dual_decomposition_minimal_counterexamples/paper.log

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