Conjectured asymptotic MSE of the mismatched Bayes estimator

Consider the rank-one rectangular observation model $\bY$ and the mismatched Bayes estimator $M_{\mathrm{mis}}(\bY)$. Let $\lambda$ and $\lambda_*$ denote the estimation and true signal-to-noise parameters, respectively, and let $\mu$ be the asymptotic noise singular density. Define $M(\lambda,\lambda_*)$ and $Q(\lambda,\lambda_*)$ as in the source. Mismatched Bayes MSE conjecture.

$$\lim_{n\to\infty}\operatorname{MSE}_n(M_{\mathrm{mis}}(\bY))=\frac{1}{2}\left(1-2M(\lambda,\lambda_*)+Q(\lambda,\lambda_*)\right).$$

Here the formulas for $M$ and $Q$ include the indicator function and the asymptotic noise singular density. The claim is presented as a consequence of the preceding log-partition-function conjecture, so it remains conditional on establishing that conjecture rather than being a proved theorem in the paper.