Rhoades' finiteness conjecture for modular-form corrections of a mock theta function

For fixed integers $a,b,A,B$, let $f_{a,b,A,B,h,k}$ be the modular forms used to cancel the singularities of $g_2(\zeta_b^a q^A;q^B)$ as $h/k$ ranges over $\mathbb{Q}$. Rhoades' finiteness conjecture. For any fixed $a,b,A,B$, as $h/k$ ranges over $\mathbb{Q}$, only finitely many modular forms $f_{a,b,A,B,h,k}$ are needed to cancel the singularities of $g_2(\zeta_b^a q^A;q^B)$. The paper states that its main theorem completely solves Rhoades' question and provides finite formulas for the resulting constants, so the conjecture is resolved here.