Wang–Zhou conjecture on realizations of abstract topological recursion

Let $4\mathcal W_{g,n}4$ be the abstract $n$-point functions of the abstract quantum field theory of fat graphs. Under a suitable Feynman-rule realization, let $4\mathcal C4$ be the realized spectral curve and let $B(x_1,x_2)$ be the realization of the abstract Bergmann kernel $4\mathcal W_{0,2}4$. Wang–Zhou's topological-recursion conjecture. The Eynard–Orantin invariants associated to $4\mathcal C4$ and $B(x_1,x_2)$ are the realizations of the abstract $n$-point functions $4\mathcal W_{g,n}4$. This is established for the Hermitian one-matrix model and fat-graph enumeration, while the general realization problem remains open.