Source Code and Numerical Results for a Parameter-Free Spectral Test of the Riemann Hypothesis via Explicit-Formula Confinement

Version 3 — Major Update This repository contains the Python implementation, datasets, figures and LaTeX preprint for the paper: "Source Code and Numerical Results for a Parameter-Free Spectral Test of the Riemann Hypothesis via Explicit-Formula Confinement (v3)" Core Idea We construct a completely parameter-free confining potential directly from the explicit formula of the prime number theorem: V(u) = e^(-u/2) × [Li(e^u) + |π(e^u) − Li(e^u)|] This potential is coupled to a symmetric Berry-Keating-type operator: H = (1/2)(u d/du + d/du u) + 1/2 + V(u) Numerical diagonalization on logarithmic grids reproduces the non-trivial zeros of the Riemann zeta function with very high accuracy. Main improvements in v3: • Prime horizon extended from 10^7 to 10^9 (two orders of magnitude) • Grid resolution increased to N = 16384 • Systematic convergence study showing clear improvement with larger X_MAX • Validation extended up to the 35th non-trivial zero (γ_n ≈ 118.79) • Maximum absolute error reduced to ~ 3.19 × 10^{-7} at X_MAX = 10^9 • Improved smoothing of the oscillatory term and more robust solver Key Result At X_MAX = 10^9, the computed resonances match the known Riemann zeros with errors typically between 10^{-7} and 10^{-8} for most low-lying zeros — entirely without fitting parameters. This work provides one of the strongest numerical spectral realizations of the Riemann zeros obtained from a purely arithmetic construction to date. Files included: • Z-SUSY Framework – Explicit Formula (to n).py — Complete production script • Riemann_ZSusy_V3.pdf — Updated preprint (v3) • High-resolution figures (potential, spectral matching, convergence) • CSV tables with detailed errors and convergence data Previous versions remain accessible in the version history.