Conjecture on the variance of the normalized Euler totient function in intervals

Let $R_0(x):=\sum_{n\leq x}\frac{\varphi(n)}{n}-\frac{x}{\zeta(2)}$ and, for an interval of size $H$, let

$$R_0(x;H):=R_0(x+H)-R_0(x)=\sum_{x<n\leq x+H}\frac{\varphi(n)}{n}-\frac{H}{\zeta(2)}.$$

Let $H=\Theta(x^\delta)$ for some fixed $0<\delta\leq 1$. Variance conjecture. Then

$$\frac{1}{X}\sum_{x\leq X}R_0(x,H)^2\sim \frac{1}{6\zeta(2)}-\frac{1}{6\zeta(2)^2}.$$

This predicts the discrete mean square, and hence the variance, of the normalized Euler totient function over intervals whose length is a fixed power of the endpoint. The cited results establish mean-square information for the unrestricted remainder term, but the stated interval variance remains conjectural in the source.