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Claim. Starting from a model of CH with Hajnal's coloring, a finite-support iteration of $\sigma$-centered forcings yields a model of $\mathrm{MA}_{\omega_1}(\sigma\text{-centered})$ and $2^{\aleph_0}=\aleph_2$ in which $\omega_1^2\not\to(\omega_1^2,3)^2$ still holds, as the preprint's abstract states. This is the relation of Problem 1169 in a model of ZFC, so ZFC does not refute it, and it holds together with a fragment of Martin's axiom.

Covers. One side of an independence result: the relation holds in the model the preprint builds, so ZFC does not refute it, but nothing here shows that ZFC does not prove it. One side alone leaves the question open, so the result, even once accepted, leaves Problem 1169 open; the accepted pages of Hajnal, Baumgartner and Takahashi already settle the same side.

Depends on. Hajnal 1971: the construction starts from a model of CH with Hajnal's coloring.

Acceptance. None documented. The preprint has no journal record, and the site does not credit it. The claim is therefore claimed.