Variance-growth conjecture for interval-graph estimators

Let $X(\infty)$ be the limiting estimator produced by the memoryless iterative process on an interval graph of length $n$, and let $Z(\infty)$ be the benchmark estimator used in the paper. Variance-growth conjecture.

$$\operatorname{Var}[X(\infty)]\propto \sqrt{n}\operatorname{Var}[Z(\infty)].$$

The paper motivates this claim from the conjectured Gaussian coefficient profile: although the mean-square error tends to zero, the iterative estimator becomes increasingly inefficient relative to $Z(\infty)$ as the interval length grows. Its precise asymptotic meaning and proof remain open.