Defines metric Möbius graphs for Klein surfaces, proves a refined Norbury recursion on weighted lattice counts, derives a refined Witten-Kontsevich recursion, and explicitly computes the refined Euler characteristic of the moduli space.
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A B-twisted Landau-Ginzburg model plus topological gravity on the worldsheet is shown to be the exact dual of any interacting one-matrix model, with matrix traces mapping directly to vertex operators and correlators agreeing to all orders in genus and 't Hooft coupling.
New structural results for generating functions enumerating b-angulations of surfaces are obtained from Toda integrability for b=3,4 and Hodge-GUE correspondence for b=2ν, implying the Gharakhloo-Latimer conjecture.
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