Witt-realization conjecture for UMTCs at prescribed central charge

Let $\EuScript{C}$ be a unitary modular tensor category (UMTC), and let $c$ be a central charge satisfying

$$c_{\EuScript{C}}^{\mathrm{top}}=c\pmod 8.$$

Witt-realization conjecture. There is at least one unitary vertex operator algebra (VOA) $V$ of central charge $c$ such that $\operatorname{Mod}_V$ is a UMTC Witt equivalent to $\EuScript{C}$. The conjecture weakens exact realization of a prescribed UMTC to realization of its Witt-equivalence class, subject to the topological central-charge congruence.