Conjectural one-level density formula for the family $\mathcal{F}(K)$

Let $\mathcal{F}(K)=\{L_k(s):1\le k\le K\}$, let $M=\log K$, let $f$ be the test function, and let $W_f$, $S_\zeta$, $S_L$, $S_{A'}$, and $S_\Gamma$ be the integrals defined in the source, with $(\mathcal{C}')$ the horizontal line $\operatorname{Im}(\tau)=-Mc'/\pi$. Conjectural one-level density formula.

$$D_1(\mathcal{F}(K);f)=W_f+S_\zeta+S_L+S_{A'}+S_\Gamma+O\left(K^{-\frac12+\epsilon}\right).$$

The formula assembles the gamma-factor, zeta-factor, auxiliary $L$-function, and arithmetic contributions predicted by the ratios calculation; the source gives no resolution status.