Exactness conjecture for the continuous-time zero-delay rate bound

Let $R^*(D)$ denote the infimum mutual-information rate over generalized causal reproductions $\mathsf{GCR}$ whose long-term distortion is at most $D$, and let $R(D)$ denote the rate function obtained from the continuous-time linear Gaussian sensor optimization. The paper establishes $R^*(D)\leq R(D)$ for every $D>0$. Exactness conjecture. The lower bound is attained for every positive distortion level:

$$R^*(D)=R(D), \\; D>0.$$

This would identify the semidefinite-representable function $R(D)$ with the fundamental performance limitation associated with continuous-time zero-delay source coding. The conjecture is motivated by corresponding discrete-time results, while the text does not report a proof or disproof.