Open, the site's label (OPEN; page last edited 2026-02-01). One pending full claim is recorded: Wang and Grau Ribas's positive-density theorem, a 2026 preprint (later versions by Wang alone) with an author-built Lean development stating that the answer is yes; the frontmatter standing, claimed/proved, follows from it. An accepted partial claim page records Erdős's 1981 theorem for the sequences whose consecutive gaps tend to infinity.