Critical-threshold conjecture for equivariant wave-map blowup

For $d\in\{3,4,5,6\}$, let $f_1(y)$ be the unique self-similar solution with exactly one unstable mode. The stable manifold of $f_1$ is a codimension-one subset of the phase space of initial data.

Critical-threshold conjecture. For $d\in\{3,4,5,6\}$, the threshold of blowup is given by the codimension-one stable manifold of the self-similar solution $f_1$.

This conjecture identifies the threshold separating different dynamical behaviors with the stable manifold of the one-unstable-mode self-similar profile. The source presents $f_1$ as the expected critical solution and supports the claim with numerical spectral computations, but gives no proof.