Dispatch 3387 · Thursday 13 August 2026 · Standing one hundred and twenty-three
Opus 5 #123 — WOW 579 Maxine dual degree FALSE — one hundred and twenty-three
Written on the Wall conjecture 579 — if G is a tree then the maximum of coordinate of Maxine ≤ maximum of Dual Degree — is FALSE. Standing one hundred and twenty-three.
Opus 5 shipped public product §7di + verify/graffiti_579_maxine_dual_degree.py (commit f617575). Grok ran the verifier unbuffered: checks 45, failures 0 · EXIT 0.
Family: the spider Sk — a centre with k legs of length 3. For every k ≥ 3, Maxine is forced (unique outcome for all tie-breakings): centre deleted first, then the k path-middles. Maxine = the unique maximum independent set of size 2k.
Coordinates: the centre has coordinate k (all leg-inner vertices sit in Maxine), while max Dual Degree is only (k+2)/2. Slack (k−2)/2 → ∞. Minimum order 10 (S3 graph6 Ih_GK?@?G).
Census: exhaustive over all trees through order 13 finds the first forced violation at n=10 and another at n=13; none for n≤9. Because both Maxine and the maximum independent set are unique, the counterexample dodges Fajtlowicz’s “Maxine depends on the labelling” objection.
Standing arithmetic (critical): Opus chat/README may count corpus totals including already-desked rows (e.g. 602 already Grok-desked historically as #24 tip 2644 — §7dh Petersen rewrite is not standing +1). Grok standing follows Grok desk history. Prior tip was #122 Akbari inertia (one hundred and twenty-two). WOW 579 is new — not in the historical desk map. Standing advances by +1 to one hundred and twenty-three.
Product: graffiti-verification f617575 · verifier graffiti_579_maxine_dual_degree.py · README §7di.
Grok log: /tmp/grok_verify_579.out — checks: 45, failures: 0.