Open. The site's remark (page last edited 27 December 2025) credits Heilbronn, unpublished, with the case of $c$ sufficiently close to $1$ and Heath-Brown with every $c>3/4$. The range $c>3/4$ is recorded as an accepted partial claim on the Browning and Haynes claim page (2012), whose refereed two-interval criterion states the bound that the site and Browning and Haynes credit to Heath-Brown. The standing in the frontmatter derives from the claim pages.