The conjecture that Tarski biconditionals imply uniform biconditionals under Fujimoto interpretability

Let $U$ be a Vaught theory and let $N:{\sf R}\lhd U$. For theories or axiom sets $\alpha$ and $\Gamma$, write \alpha\mathrel{\text{\textcolor{gray}{\blacktriangleright}}}_U\Gamma for Fujimoto interpretability over $U$. Let ${\sf TB}^{-}_N$ denote the Tarski biconditionals and ${\sf USB}^{-}_N$ the corresponding uniform biconditionals. Tarski-to-uniform conjecture. If \alpha\mathrel{\text{\textcolor{gray}{\blacktriangleright}}}_U{\sf TB}^{-}_N, then \alpha\mathrel{\text{\textcolor{gray}{\blacktriangleright}}}_U{\sf USB}^{-}_N. The conjecture remains unresolved; the paper notes that variants of the proof strategy might potentially refute it.