Open, the site's label (OPEN; page last edited 28 October 2025). Romanoff's theorem [Ro34] gives positive lower density for every integer $C\ge2$, recorded as the accepted partial claim on Romanoff's claim page (1934); Ding's theorems [Di25], positive lower density for almost every real $C>1$ and for the golden ratio, are the pending partial claim on Ding's claim page (2025). No claim covers every $C>1$, so the problem stays open.