Spectral Rigidity and Phase Cancellation of the Riemann Zeta Zeros

In this paper, we investigate the convergence and spectral behavior of the explicit Chebyshev--Riemann formula. By analyzing the modulus of the spectral series associated with the non-trivial zeros $\rho$, we establish the conditions under which this oscillating term achieves a minimum amplitude, thereby constraining the real part of each zero to satisfy $\mathrm{Re}(\rho) = 1/2$.