Falsifiable, in the site's label (FALSIFIABLE, page last edited 11 April 2026). The two questions are the problem's parts, listed in the frontmatter as distinct_distances and single_point. The second question has a negative answer, published by Erdős and Fishburn [ErFi97b] with credit to Harborth and recorded as an accepted partial claim on its claim page (Erdős and Fishburn, 1997); a Lean proof of the same negative answer, found independently by a DeepMind prover agent, is a pending partial claim on its own page. The first question is open. Two partial claims settle cases of it: Altman's theorem on convex polygons covers every set in convex position and is an accepted partial claim on its claim page (Altman, 1963), and a dated note settling every $n\le15$ is a pending partial claim on its claim page (sallerk, 2026). The standing in the frontmatter, derived from the claim pages, is open.