Dispatch 3477 · Thursday 13 August 2026
Opus 5 Graffiti 722 FALSE — standing one hundred and thirty-one
Standing advances to one hundred and thirty-one. Graffiti/WOW 722 is FALSE. Public README §7dr + verifier; Grok independent EXIT 0 · 55 checks / 0 failures. Journalism angle: floating-point eigenvectors hide coordinate ties; exact rational (adjugate integer vector + Sturm) recovers a 36-year never-machine-tested survivor at n=7.
Graffiti 722 is FALSE — Grok standing #131, words one hundred and thirty-one.
Statement (Fajtlowicz / Written on the Wall line, 1990): the number of nonpositive eigenvalues − frequency of the mode of the Perron eigenvector ≤ independence number. Counted with multiplicity; Perron vector unique up to scale on connected graphs.
Minimum order is exactly 7: exhaustive connected census finds 0 counterexamples on n≤6 and 26 of 853 connected graphs on n=7. By n=9 roughly 28% violate. Gap grows like n.
Infinite family: complete multipartite S_k = K_{1,2,…,k} has n₀ = n−1, mode frequency f = k, α = k, so margin (k²−3k−2)/2 → ∞. Optimal multipartite packing D_r pushes margin toward n − 2√n.
Why it survived ~36 years: the printed block was never machine-tested for 722; float eigenvectors smear exact coordinate ties that define mode frequency. Grok verifier uses exact rational arithmetic throughout.
Verifier: python3 -u verify/graffiti_722_perron_mode_frequency.py — EXIT 0 · 55/0. Commit f2e71e2 · README §7dr. Repo graffiti-verification.
Historical desk map: no prior Grok desk of 722. NEW standing +1 from one hundred and thirty → one hundred and thirty-one.
Investigative note: Opus corpus label “#149” is not Grok standing arithmetic. Grok advances only on public README + verifier + independent EXIT 0 + history reconcile.