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Claim. Write $\kappa=(2^{\aleph_0})^+$ and $\mathrm{Col}_\omega(m,\kappa)$ for the coloring property asked by Problem 598. Theorem 5.3 of the report: if the coloring fails for some $\lambda$, then $0^\sharp$ exists; so in every model without $0^\sharp$, in particular under $V=L$, the answer is positive for every $m$. Theorem 6.1: assuming the consistency of the rank-into-rank hypothesis I1, it is consistent that the problem has a negative instance. Together, as the report presents them, the problem read as one question about every infinite $m$ is independent of ZFC relative to the consistency of I1. Theorem 4.1 adds a refinement that settles no instance: if a failure occurs, the least bad cardinal $\lambda^*=\min\{\lambda\ge\kappa:\neg\mathrm{Col}_\omega(\lambda,\kappa)\}$ is regular and $\aleph_0$-closed ($\mu^\omega<\lambda^*$ for every cardinal $\mu<\lambda^*$), so in particular $\kappa^\omega<\lambda^*$, and $\mathrm{Col}_\omega(m,\kappa)$ holds exactly for $m<\lambda^*$.

Hypotheses. The report labels Theorem 5.3 as proved modulo the condensation lemma and Jech's embedding criterion for $0^\sharp$, and Theorem 6.1 as proved modulo Claim 1.10(a) of Garti and Hayut (Math. Log. Q. 65 (2019), 95–104; library card). The negative half is relative to I1 and settles nothing in ZFC.

Standing. The claimant is Patrick White, who published the result on 2026-07-28 as a working report on erdosproblemaday.com, a public ledger of AI-assisted reports on the catalog's problems that names its authors as Patrick White and Claude (Anthropic) and labels each entry by outcome; this entry is labeled PARTIAL, and the ledger states that an entry is not an independently verified claim unless labeled PROVED. The report credits Wu's MathOverflow answer of 2026-05-24 with the same relative independence, which it reproves; the threshold model of Chojecki's note of 2026-04-22 gives the negative half by the same Garti–Hayut forcing. The report is not filed on the site, is not refereed, and no reviewer is recorded, so the claim stays claimed. The site labels the problem OPEN.