- Conjecture 3.6: add the 4-edge-face criterion as clause (3), with empirical
table through n=21 (complete, 535,182/535,182 pass) plus partial n=22
(641,700 colourings, timed out).
- Conjecture 3.8: strengthening with clause (4) on the b,c-Kempe cycle / 3-colour
alternative on the new face f_n; existential at the witness level. Tested
through n=18 (13,800/13,800 pass).
- Definition + figure for cubic-graph edge contraction (delete edge, smooth the
resulting degree-2 endpoints; equivalent to simple contraction in the dual).
- Theorem: cubic contraction across a 4-face preserves 3-edge-colourability when
the two opposite boundary edges have different colours. Constructive proof:
the two smoothed-in edges inherit the colour of the w_i pair they absorb, and
e_1 is recoloured to the third colour.
- Add 2-panel illustration of the theorem's recolouring.
- Trim Remark 3.7 and 3.9 tables to fit within \textwidth.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
