Generalised Ordinary vs Fully Simple Duality for n-Point Functions and a Proof of the Borot–Garcia-Failde Conjecture

Abstract We study a duality for the n -point functions in VEV formalism that we call ordinary vs fully simple duality. It provides an ultimate generalisation and proper context between maps observed by Borot Garcia-Failde. Our approach allows to transfer algebraicity properties systems of related this duality, gives direct tools analysis singularities. As application, give proof recent conjecture Garcia-Failde on topological recursion maps.