Open, the site's label (OPEN, page last edited 28 October 2025). The one claim recorded, Steinerberger 2025, is partial: it reduces shift two to the equation $\phi(m)+\phi(m+\phi(m))=m$, puts every solution into two branches by its odd part, and claims to settle the first branch, whose solutions are six doubling families with odd part in $\{1,3,5,7,35,47\}$; the second branch, the question of which $n$ reach a solution, and every other shift stay open.