A bounded-depth positivity inequality for zeta-zero configurations and simple critical zeros under a narrow-box hypothesis

This preprint proves a computer-assisted bounded-depth positivity inequality for finite conjugation-invariant configurations of complex points of the type arising from rescaled zeros of the Riemann zeta function. For an explicit even piecewise-linear kernel $g_A$ supported in $[-1,1]$, the paper proves $\int_{-1}^{1} g_A(a)|E_Z(a)|^2,da \ge 2|Z|-\kappa(Z)$ for every finite conjugation-invariant configuration $Z$ satisfying $\mathrm{dep}(Z)\le 33/200$. The universal statement is reduced, through exact identities and a combinatorial certificate, to a finite family of explicit inequalities verified using rigorous ball arithmetic and exact rational arithmetic. As an arithmetic consequence, assume that for all sufficiently large $T$, every zero $\rho=\beta+i\gamma$ of the Riemann zeta function with $T