The motivic PT generating-series conjecture for Enriques fiber classes

Let $Q$ be the Calabi–Yau threefold considered in the paper, let $f$ be the fiber class, and let $\mathcal{PT}_{n,df}$ denote the motivic stable-pair invariants in class $df$. Let $t$ and $\tilde t$ be the refinement variables, let $E$ be a smooth elliptic curve, let $Q$ also denote the relevant fiber object, and let $\chi_{t,\tilde t}([E]^{\mathrm{vir}})$ and $\chi_{t,\tilde t}([Q]^{\mathrm{vir}})$ be their refined motivic Euler characteristics.

Motivic PT generating-series conjecture. The generating series of the fiber-class invariants is given by the displayed infinite-product and plethystic-exponential formula.

The formula is obtained conditionally from the refined chi-independence expectation for generalized Donaldson–Thomas invariants and Toda’s equation. It predicts all motivic stable-pair invariants in these fiber classes, but the parser supplies no evidence that the conjectural evaluation has been proved.