6 problems

Let $d$ be the net parameter, let $\langle\!\langle G\rangle\!\rangle_d$ denote the corresponding net evaluation, and consider the unnormalized probability distribution…

Let $Q=\tau+2$ for DFib or $Q=2$ for the toric code, and let $\beta_c$ denote the Potts-model critical inverse temperature. For a net $G$, write $\langle G\rangle_\tau$ for its iso…

Let $\tau=\frac{1+\sqrt{5}}{2}$ and consider the DFib topological phase together with its connection to the $Q=\tau+2$ state Potts model. DFib critical-temperature conjecture. The…

String-operator realization conjecture. There exist string operators associated to the simple objects of $Z(\mathcal{C})$ such that, when they are used to define $F$-symbols and…

Entanglement-bootstrap representative conjecture. Every two-dimensional gapped phase with gappable boundary has a representative state satisfying the entanglement bootstrap axioms…

Levin–Wen classification conjecture. Levin–Wen string-net models exhaust all possible gapped phases with gappable boundary, and these phases are labeled by unitary modular tensor c…