Artemev's singular-part conjecture for dual topological-recursion amplitudes

Let $A^{(g),\vee}_n(k_1,\dots,k_n)$ be the amplitudes obtained from topological recursion after applying the $x-y$ swap to the minimal-string spectral curve, and let $A^{(g),\mathsf{sing}}_n(k_1,\dots,k_n)$ denote the singular-in-$u^2$ part of the original amplitudes. Here $g\geq 0$, $n\geq 1$, and $k_1,\dots,k_n\in\{1,\dots,p\}$.

Artemev's conjecture. Up to a suitable normalization, $A^{(g),\vee}_n(k_1,\dots,k_n)$ coincides with $A^{(g),\mathsf{sing}}_n(k_1,\dots,k_n)$ for $g\geq 0$, $n\geq 1$, and $k_1,\dots,k_n=1,\dots,p$.

This is the amplitude-level formulation of the resonance-transformation claim after the $x-y$ swap. The paper presents a proof of Artemev's conjecture, so the stated identification is resolved.