Finite-ray prediction accuracy hypothesis for prime numbers

Let $r_{p_0}$ be a ray with $p_0\in\overline{C}$. Let $l$ denote the number of correct decimal digits available in the floating-point arithmetic, and let $n^*(l)$ be a finite index. For odd $m=2n^*(l)+1$, let $\tilde p_{mp_0}$ be the natural number predicted by formulae (34) and (35), and let $x$ be a solution of equation (36) whose right-hand side is $p_{(m-1)p_0}$. The prime number associated with the ray is denoted by $p_{mp_0}$. Finite-ray prediction accuracy hypothesis. For every ray $r_{p_0}$ with $p_0\in\overline{C}$, there exist finite numbers $l$ and $n^*(l)$ such that $\tilde p_{mp_0}$ lies closer to $p_{mp_0}$ than $x$ does. This compares the proposed finite-domain approximation with the usual logarithmic-integral inversion; the source provides numerical motivation but no proof or resolution.