Radiative Uniqueness Conjecture for bubbling wave maps

Let $\boldsymbol{u}_c(t)$ denote the constructed blow-up solution from Part (a) of Theorem~, and let $\boldsymbol{u}(t) \in \mathcal{H}_1$ be any other solution that blows up backwards-in-time at $t=0$ with the same radiation field $\boldsymbol{u}^*_0$. Radiative Uniqueness Conjecture. The two solutions are equal:

$$\boldsymbol{u}(t)=\boldsymbol{u}_c(t).$$

The conjecture would imply unique continuation of blow-up wave maps past the singularity while preserving the energy and the topological class of the solution. The source provides no resolution, so the conjecture remains open.