The cut-and-join description conjecture for Chekhov–Eynard–Orantin topological recursion

The Chekhov–Eynard–Orantin topological recursion is a recursive procedure associated with data on a spectral curve; for simple ramification points, it can be related to cut-and-join operators acting on generating functions. The operators $\widehat{W}_{a}$ and $\widehat{J}_k$ denote the operators appearing in this description. Cut-and-join description conjecture. The Chekhov–Eynard–Orantin topological recursion with simple ramification points can always be described by the cut-and-join formula with operator $\widehat{W}_{a}$ cubic in $\widehat{J}_k$. Higher ramification points correspond to the higher cut-and-join operators. This proposes a systematic relation between geometric topological recursion and the algebraic cut-and-join formalism, with higher ramification providing higher-order cut-and-join operators.