Stratum logarithmic GW/PT correspondence

Let $(Y\mid\partial Y)$ be a toric threefold pair, let $\beta$ be a curve class, let $\bm\mu$ be a vector of partitions, and let $[[![\sigma,\vartheta,\upalpha][!]]$ be a stratum class, where $\sigma$ is a cone, $\vartheta$ is an equivariant cohomology class, and $\upalpha$ is an equivariant cohomology class on the corresponding evaluation stratum. Let $d_\beta$ be the anti-canonical degree of $\beta$, and write $\ell(\mu_j)$ and $|\mu_j|$ for the length and size of the $j$th partition. Stratum GW/PT correspondence. The series

$$\mathsf{Z}_{\mathsf{PT}}\!\left(Y\mid\partial Y; q \mid [\![\sigma, \vartheta, \upalpha]\!]\mid \bm{\mu}\right)_\beta$$

is the Laurent expansion of a rational function in $q$. Under $-q=e^{iu}$,

$$(-iu)^{d_\beta+\sum \ell(\mu_j)-|\mu_j|}\,\mathsf{Z}_{\mathsf{GW}}\!\left(Y\mid\partial Y; u \mid [\![\sigma, \vartheta, \upalpha]\!]\mid \bm{\mu}\right)_\beta = (-q)^{-d_\beta/2}\,\mathsf{Z}_{\mathsf{PT}}\!\left(Y\mid\partial Y; q \mid [\![\sigma, \vartheta, \upalpha]\!]\mid \bm{\mu}\right)_\beta.$$

This extends the primary logarithmic GW/PT correspondence to stratum invariants, including the non-exotic and exotic classes introduced through subdivisions. The source presents this as a strata conjecture; no resolution status is supplied in the provided text.