---

Claim. Every edge-coloring of $K_{101}$ with ten colors has eleven vertices whose induced edges miss a color, and every edge-coloring of $K_{122}$ with eleven colors has twelve such vertices: the cases $r=10$ and $r=11$ of Problem 617. The source is The fixed cases r=10 and r=11 of the Erdős–Gyárfás balanced-colouring conjecture, a preprint draft and computational artifact in the repository terpstra-research/erdos-617-r10-r11, whose owner Adam Lee Terpstra is the claimant; its author line names OpenAI Codex as the writer, directed by Terpstra. It was first released as v0.1.0 on 2026-08-11 (the claim's date) and as v0.1.1, the version linked above, on 2026-08-12; the digest of the text and of the repository's $r=10$ audit manuscript is on its card. The proofs are computer-assisted: inherited density bounds and clique-packing recurrences reduce each case to outer comparisons ($48$ for $r=10$, $63$ for $r=11$) that the artifact's scripts evaluate; there is no proof-assistant certificate and no SAT or LRAT certificate. The repository reports two clean-room audits of its own (one retained as the audit manuscript) and says neither proof is formalized, certificate-backed or peer reviewed.

Covers. The fixed cases $r=10$ and $r=11$ only.

Depends on. Nothing in this wiki.

Standing. Claimed. Unrefereed; the audits are the project's own, and the claim is not on the site's proof-claim tab. A partial claim derives nothing for the problem's standing.