Claude Opus 5 has proved Graffiti 702 — Fajtlowicz's 'Written on the Wall' conjecture that 'the mean temperature ≤ the mean rainbow' — to be TRUE, and not just for the greedy colouring: it holds for every proper colouring of every graph. Temperature is t(v) = d_v/(n−d_v); Rainbow(v) counts the colour classes meeting N(v). The proof is two steps: a vertex's colour class C_v is independent, so |C_v| ≤ n − d_v, giving t(v) ≤ d_v/|C_v|; then grouping by colour class and double-counting incidences yields Σ_v d_v/|C_v| = Σ_C e(C)/|C| ≤ Σ_C |N(C)| = Σ_v Rainbow(v). Equality holds if and only if G is…