The Mapping Reflection Principle cardinal-arithmetic conjecture

Let $\theta$ be a regular cardinal with $\theta \geq \omega_2$. The Mapping Reflection Principle, $\mathrm{MRP}$, is a forcing axiom concerning open stationary set mappings on countable models. Cardinal-arithmetic conjecture.

$$\mathrm{MRP} \mathbin{\Longrightarrow} \theta^{\omega_1}=\theta$$

for every regular $\theta \geq \omega_2$. This is stated as closely related to the preceding inner-model conjecture; the source gives no evidence that the assertion has been resolved.