Strong form of the variance estimate conjecture for stationary Gaussian processes

Let $N(T)$ denote the number of zeroes in an interval of length $T$ of a non-degenerate stationary Gaussian process (SGP), with covariance function $r$ and parameter $\sigma$ as in the paper. Strong-form variance conjecture. The estimate referred to in the source as the variance estimate holds for any non-degenerate SGP.

This removes the additional limsup condition in the weak form and asserts the variance estimate in full generality for non-degenerate stationary Gaussian processes. The source gives no resolution, so the conjecture remains open.