Reflective forcing at the first $\omega_1$-Mahlo cardinal

A cardinal $\kappa$ is $\omega_1$-Mahlo when the set of regular cardinals below $\kappa$ has the relevant $\omega_1$-stationarity property; $(\kappa,\omega_1)$-reflective forcing denotes the forcing notion satisfying the paper's defined reflection condition at parameters $\kappa$ and $\omega_1$.

Consistency conjecture. It is consistent, relative to the existence of large cardinals, that there is $(\kappa,\omega_1)$-reflective forcing where $\kappa$ is the first $\omega_1$-Mahlo cardinal.

This conjecture proposes that the hypotheses used in the paper's reflection theorems are close to optimal. The supplied text gives no resolution or large-cardinal consistency proof, so the status is open.