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Inequivalent modular tensor categories with identical $S$, $T$ and $W$
It remains an open question whether the modular data $(S,T)$ together with the Whitehead-link matrix $W$ determine a modular tensor category up to ribbon equivalence. We answer negatively by constructing two braided-inequivalent Dijkgraaf--Witten modular categories for $(\mathbb Z/p\mathbb Z)^3$ for
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