Generic smoothness conjecture for the Signorini free boundary

Consider the Signorini problem, also known as the thin obstacle problem, and its free boundary. Generic smoothness conjecture. Generically, the free boundary in the Signorini problem is smooth. This is the thin-obstacle analogue of Schaeffer's conjecture for the classical obstacle problem. The paper establishes generic smoothness when $n+1\leq 4$, while its broader validity beyond those dimensions remains open.