Encoding correctness: a 4-term AP sees ≥3 distinct colours iff at most one of its 6 pairwise colour-equalities holds (colour partition (1,1,1,1) or (2,1,1)); the equality indicators are implied upward only, which preserves satisfiability; first-occurrence colour-precedence symmetry breaking is sound because colours are interchangeable. Hence UNSAT of the constrained CNF proves no valid k-colouring exists.
Evidence
Provenance
Reviews
Encoding correctness: core lemma exhaustively verified 256/256 colour-4-tuples ('>=3 distinct <=> <=1 of 6 pairwise equalities'); equisatisfiable both directions; symmetry-break is SAT-preserving (canonical relabel) so its UNSAT is a true UNSAT and cannot fabricate a lower bound.
Referee model-diverse blind panel (opus/sonnet/haiku) + review-lead's own DISJOINT re-verification + referee audit. CALL: GREEN (all 6 claims). Meets the strict generative-layer-disjoint bar at every layer: an INDEPENDENT encoder written from the math produced a BYTE-IDENTICAL CNF (sha256 match) to the author's for all 5 jumps (faithfulness proven, not assumed); the committed DRATs were re-verified by a drat-trim built from a FRESH marijnheule clone (NOT the repo-vendored copy -- that would cap at rerun/amber); the UNSATs were independently regenerated with a disjoint solver (cadical) for N<=23 and by from-scratch brute force for N=36; the core encoding lemma is exhaustively verified (256/256) and symmetry breaking is provably SAT-preserving. Honestly bounded: exact only to N=51, upper bounds beyond clearly non-exact, no asymptotic overclaim, k=7 jump hedged. No commit-pin drift (erdos-160 tree byte-identical at the pin vs HEAD). Minor doc-gaps (non-blocking): results.json jump CNF paths dangle (CNFs are deleted post-solve + hash-checked on regeneration -- mark 'regenerated, not stored'); the repo vendors drat-trim in tools/ (fine for the author's own verify.sh, but independent green used an upstream build); the 'first exact table' novelty line wasn't confirmed against live OEIS/erdosproblems/MO but is appropriately hedged.