Integral Regulators on Mirror Curves with Mass Parameter

In 2015, Codesido-Grassi-Marino laid the foundation of a connection between local CY 3-folds and the spectra of operators attached to their mirror curves in the context of Topological String Theory. In a 2024 paper with C. Doran and M. Kerr, the author previously deduced two consequences of this conjecture; one relating zeroes of higher normal function to the spectra of operators of genus one curves, the other connecting integral regulators of $K_2$-classes on mirror curves to dilogarithm values at algebraic arguments. We now show that the latter continues to hold in the presence of a mass parameter, thus expanding the range of the conjecture.