What Makes the Zeros of the Riemann Zeta Function Repel Each Other, and What Does Not: A Controlled Numerical Separation of the Riemann-Siegel Sum

This document presents a rigorous numerical experiment designed to isolate the exact mechanism that causes the nontrivial zeros of the Riemann zeta function to repel each other. By performing a controlled numerical separation of the classical Riemann-Siegel formula into three nested pieces, the study measures the pair correlation and repulsion exponent of each piece separately. The main empirical finding is that the strong repulsion typical of these zeros is neither generated by the arithmetic of the frequencies (based on primes) nor by the phase supplied by the functional equation. The sole ingredient responsible for the effect is the "moving cutoff"—the truncation length of the sum, which grows as the height increases.