- Cut Conjecture 3.8 + Remark 3.9 from Section 3 and move into a new
Section 4 "The Four Colour Theorem from a strengthened conjecture".
- Add Remark 4.X spelling out the implication: clause (4)(i) forces the
cyclic colour pattern (c,a,c,b) on the new 4-face f_n, two opposite
edges of which satisfy the hypothesis of Theorem 3.9 verbatim; case
(ii) is conjecturally reducible to case (i) via a Kempe swap on the
{b,c}-cycle through X_1 X_2. Theorem 3.9 then produces the proper
3-edge-colouring of the contraction, contradicting minimality of G.
- Rewrite the bridge prose into the cubic-contraction definition to
reference Section 4 forward, rather than the conjecture directly.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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