The modular-data determination conjecture

Let $\mathcal{C}$ be a modular category, and let $(S,T)$ be its modular data. Modular-data determination conjecture. The $S$ and $T$ matrices of $\mathcal{C}$ determine it up to ribbon equivalence. The source explicitly says this is open; modular data determine fusion rules, but whether they determine the full ribbon category remains unresolved. The conjecture has since been disproved by counterexamples.