Mathematical analysis reveals connections between off-line zeros and the Riemann Hypothesis, suggesting implications for number theory.
We establish an unconditional instability theorem for hypothetical off-line zeros of the Riemann zeta function. The Off-Line Instability Theorem proves that for sigma > 29/34, the tension function Tau(sigma, T) = Tsigma - 1/2 / N(sigma, T) diverges as T increases, where N(sigma, T) counts zeros with Re(rho) > sigma and Im(rho) < T. Off-line zeros far from the critical line are structurally self-defeating: their prime counting oscillation grows faster than their allowed density. The threshold sigma = 29/34 is arithmetically determined by the Ingham-Huxley density estimate. A conditional reduction follows: if the Molina Spectral Instability Conjecture holds (divergence for all sigma > 1/2), then the Riemann Hypothesis is true via the integrality of the counting function. This reduction is strictly weaker than RH and reduces to improved zero density estimates. Part of the Formulametrics Research Program.
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Juan Gabriel Molina (2026) studied this question.
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