Universal variance conjecture for primes in short intervals over number fields

Let $K$ be an algebraic number field with $[K:\mathbb Q]=n$, let $m:K\to\mathbb R^n$ be an embedding, and let $\|\cdot\|$ be a norm. Define

$$\pi_K(x;H):=\#\{\omega\in\mathcal O_K:\ \omega\text{ is a prime element},\ \|m(\omega)-x\|\leq H\},$$ $$E_K(X;H):=\frac{1}{\operatorname{vol}(B_X^{\|\cdot\|})}\int_{\|x\|\leq X}\pi_K(x;H)\,d^nx,$$

where $B_X^{\|\cdot\|}=\{x\in\mathbb R^n:\|x\|\leq X\}$. With $\mathfrak R_K$ as above, define

$$\widetilde\pi_K(x;H):=\pi_K(x;H)-\frac{1}{\mathfrak R_K}\sum_{\substack{\|m(\alpha)-x\|\leq H\\|N(\alpha)|>1}}\frac{1}{\log|N(\alpha)|},$$ $$V_K(X;H):=\frac{1}{\operatorname{vol}(B_X^{\|\cdot\|})}\int_{\|x\|\leq X}\widetilde\pi_K(x;H)^2\,d^nx.$$

Universal variance conjecture. For $\delta\in(0,1)$ and $H=X^\delta$,

$$V_K(X;H)\sim(1-\delta)E_K(X;H).$$

The expectation has a field- and norm-dependent asymptotic, whereas this conjecture predicts a universal multiplicative relation for the variance. The paper provides heuristic and numerical evidence but no resolution.