Ratios-Conjecture prediction for the variance of Gaussian primes

Let $K=X^\lambda$ with $0<\lambda<1$, and let $C_f$, $C_\Phi$, $C'_\Phi$, $\widetilde\Phi$, $C_{\Phi,\zeta}$, $C_{\Phi,L}$, and $A'_\Phi$ be the constants defined in the paper. Ratios-Conjecture variance conjecture. For some constant $\epsilon>0$ depending on $\lambda$,

$$\frac{\operatorname{Var}(\psi_{K,X})}{C_fX^{1-\lambda}}= \begin{cases} C_\Phi\log X+\Delta_\Phi+O_\Phi(X^{-\epsilon}),&\frac12<\lambda<1,\\ C_\Phi(2\lambda\log X)-K_\Phi+O_\Phi(X^{-\epsilon}),&\lambda<\frac12, \end{cases}$$

where

$$\Delta_\Phi:=C'_\Phi-\pi^2\widetilde\Phi\left(\frac12\right)^2,$$

and

$$K_\Phi:=C_{\Phi,\zeta}-C_{\Phi,L}-A'_\Phi+2\pi^2\widetilde\Phi\left(\frac12\right)^2+C_\Phi\left(\log\left(\frac{\pi^2}{4}\right)+2\right).$$

This is the paper's lower-order-term prediction obtained from the Ratios Conjecture. The supplied text gives no resolution.