Proved. The site labels the problem PROVED and credits Michelen and Sawhney [MiSa25], whose Theorem 1.1 gives a convergent point almost surely and whose Theorem 1.2 gives a set of convergent points of Hausdorff dimension one. The accepted claim page Michelen and Sawhney 2025 records the result, on the site's acceptance; the paper is a preprint, so no refereed publication is listed. The frontmatter standing derives from the claim page.