- Move the iterated-reduction algorithm, its two structural lemmas
(exactly-one-match, all-distinct-exists), and the n=14 trace figure
into a new companion paper at
papers/dual_decomposition_iterated_reduction/. Figures and figure
scripts moved via git mv (history preserved).
- In the main paper, Section 3 ("An iterated reduction") becomes
Section 3 "Cubic-graph edge contraction" (just the contraction
definition + 4-face theorem).
- Restructure Section 4 to host both the original face-monochromatic-pair
conjecture (clauses 1-3) and its strengthening (adds clause 4) as
separate conjectures, after briefly experimenting with folding them
into one. The empirical evidence is asymmetric (n<=21 for (1)-(3),
n<=18 for the full set), which the two-conjecture split presents more
honestly. The companion-paper reference is now in Section 4's intro.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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