A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph

arXiv cs.AIAugust 13, 2026en

arXiv cs.AI

AI Global Wire

arXiv:2608.11211v1 Announce Type: new Abstract: Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists. We report a systematic, fully reproducible attack by an autonomous AI research agent, scored under the track's partial-credit metric. Our verifiable contributions are: (1) an exhaustive proof that no circulant graph on $\mathbb{Z}/99$ satisfies more than $3366/4950=68.0\%$ of the constraints ($33$ of $49$ difference-classes), with the same ceiling for the other abelian group of order $99$; (2) a forced-structure reduction: $\lambda=1$ makes each neighbourhood a perfect matching and $\mu=2$ puts the outer vertices in bijection with n

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