Conjecture B for $X_{10}$ and its genus-two mirror

Abstract

We prove Conjecture B of Akhtar--Coates--Corti--Heuberger--Kasprzyk--Oneto--Petracci--Prince--Tveiten unconditionally for the normalized family of maximally mutable Laurent polynomials with prescribed $T$-binomial edge coefficients associated with the degree-10 orbifold del Pezzo hypersurface $X_{10}\subset\mathbb{P}(1,2,3,5)$. An explicit $S$-extended quantum-period calculation determines the affine mirror map $\lambda=a-346$ and proves that the regularized quantum period equals the classical period as a formal power series throughout the family.