Lawson's Clifford torus uniqueness conjecture

Let $T\subset S^3$ be an embedded minimal torus, and let $T_{\mathrm{Cl}}$ denote the Clifford torus in $S^3$. Lawson's conjecture. There exists an isometry $F$ of $S^3$ such that

$$F(T)=T_{\mathrm{Cl}}.$$

In other words, up to ambient isometries, the Clifford torus is the unique embedded minimal torus in $S^3$. The conjecture is a fundamental rigidity question for embedded minimal surfaces in the three-sphere; the supplied source does not establish whether it has been resolved.