Intertwiner-algebra determination conjecture for conformal quantum field theories

Let a conformal quantum field theory have an associated hyperfinite type $4\mathrm{II}_1$ intertwiner algebra encoding combinatorial and topological data, and let the energy-momentum algebra have central charge $c$, considered modulo $8$. Intertwiner-algebra determination conjecture. Conformal quantum field theories are fixed by their associated type $4\mathrm{II}_1$ intertwiner algebras, up to a possibly discrete ambiguity related to the $c$ modulo $8$ phenomenon. The conjecture is motivated by the existence of Ising-like models with the same fusion and braid-group structure as the Ising model, while the discrete ambiguity is expected to produce a discrete family of theories.