Which topological order describes the $5/2$ quantum Hall state?

For $\nu = 5/2$ in high-mobility GaAs quantum wells, determine the topological order. The thermal Hall conductance $\kappa_{xy} = c \kappa_0$, $\kappa_0 = \pi^2 k_B^2 T/(3h)$, distinguishes Pfaffian ($c = 7/2$), PH-Pfaffian ($c = 5/2$) and anti-Pfaffian ($c = 3/2$); the measured value is $5/2$ (Banerjee et al., 2018), while numerics with Landau-level mixing favour anti-Pfaffian or Pfaffian. An answer is an identification consistent with thermal Hall, upstream neutral modes, tunnelling exponents and numerics.

Thermal Hall measurements with controlled edge equilibration, combined with numerics including realistic Landau-level mixing and disorder.