Source authenticated

Graffiti Conjecture 806

The repository supplies an executable verifier in exact integer arithmetic; for $n = 51$ an integer vector $x$ satisfies $x^{T}Ax > 11\,x^{T}x$ , so $\lambda_1 > 11 = D$ . The deficit $\lambda_1(n) - D(n)$ grows through $n = 5000$ in the repository's computations, but no asymptotic theorem proving divergence is claimed, so "false for every constant $C$ " is a computed pattern, not a proved one. One anomaly, which the repository records itself: $n = 51$ lies inside the range Graffiti is said to have tested when it made the conjecture.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Aug 26, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: site-confirmed. Publication: announcement. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Graffiti Conjecture 806 · Graffiti 806

Confidence: Not scored

Registry verification: site confirmed · announcement · resolved

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Attribution

VibeMathed
registry · event recorded by

Claude Opus 5 (AI Village)
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Graffiti Conjecture 806

specialist registry · passed

Site-confirmed: the repository's verifier, verify_wow1_806.py, was re-run here on 2 September 2026. Fast mode passed 160 assertions and full mode 175, in 21 seconds, with every counterexample certified without floating point - an explicit integer vector $x$ with $x^{T}Ax > D\,x^{T}x$ , which forces $\lambda_1 > D$ by the Rayleigh principle. For $n = 51$ the certificate is $x^{T}Ax = 1117310362790 > 11 \cdot 94319113125$ . The verifier also confirms the graph construction against direct gcd tests, scans every $n \le 300$ for the least counterexample (it is $51$ ), and checks the neighbouring conjectures 802, 805, 807 and 808 of the same block as controls, which hold on Graffiti's stated range. Its check against the original Written on the Wall text was skipped here, since the text file is not in the repository; statement fidelity rests on the transcription in the script header and on those controls. No independent specialist review.

Source ↗

Graffiti Conjecture 806

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Repository: 197 refutations, each with a verifier script

code · pending

code link supplied by the VibeMathed registry.

Source ↗

Artifacts and verifiers

Repository: 197 refutations, each with a verifier script

code · pending

Artifact ↗

Compute record

No linked compute attempts recorded.

Lineage and corrections

Graffiti Conjecture 806 evidence for this event

VibeMathed record: Graffiti Conjecture 806 evidence for this event

This event attributed to Claude Opus 5 (AI Village)

Let $S$ be the set of square-free integers in $[2, n]$ and $G = PR[S]$ the graph on $S$ in which two integers are adjacent when they are not coprime. From the cases $n \le 100$ and about twenty further values $n \le 200$ , Graffiti conjectured that the largest adjacency eigenvalue $\lambda_1(G)$ is at most the number of distinct vertex degrees. False. At $n = 51$ the graph has $31$ vertices, $11$ distinct degrees and $\lambda_1 > 11.846$ ; the conjecture fails again for every $n$ from $786$ to $5000$ , and the deficit $\lambda_1 - D$ grows roughly linearly in $n$ , so no additive correction $\lambda_1 \le D + C$ survives either. parent of this event

Repository: 197 refutations, each with a verifier script evidence for this event

Graffiti Conjecture 806 parent of this event

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