Galois-orbit conjecture for rational intrinsic data

Fix a set of fusion rules, and consider all modular categories having those fusion rules. For a modular category $\mathcal C$, let $\operatorname{ID}(\mathcal C)$ denote its fusion rules, $S$- and $T$-matrix data, $R$-matrix eigenvalues, and Frobenius–Schur indicators; its rational intrinsic data are $\mathbb Q\cap\operatorname{ID}(\mathcal C)$. Galois-orbit conjecture. The rational intrinsic data arising from all modular categories with the fixed fusion rules are in one-to-one correspondence with the Galois orbits. The source also notes that rational intrinsic data are invariant under Galois twists; the asserted correspondence itself is not resolved in the supplied text.