Version 5.0 update: This version introduces a structural reinterpretation of spectral-edge instability. Instability is no longer treated as a dynamically generated phenomenon, but as the manifestation of a loss of coherence under recursive amplification. The edge-phase sum Σₙ is reinterpreted as a trace of coherence rather than its origin. Amplification A(δ) does not produce instability; it reveals configurations that cannot sustain internal coherence under iteration. This connects the observed phase rigidity to a deeper requirement of recursive coherence. Version 4.0 update: This version introduces numerical validation on 500 zeta zeros (k = 2000 phases), spectral edge analysis A(δ), and a bridge toward infinite configurations via resonance counting and pair correlation heuristics. We investigate the behaviour of Li-type coefficients under symmetric off-critical deformations of the nontrivial zeros of the Riemann zeta function. We identify a spectral-edge instability mechanism: once the associated factors leave the unit circle, exponentially amplified contributions emerge, governed by an oscillatory edge-phase sum. We prove that exact cancellation of this oscillatory term is structurally rigid and generically impossible, reducing the Riemann Hypothesis to a phase-rigidity problem. Numerical experiments reveal a sharp transition between local stability and global instability under increasing deformation. This work provides a structural and dynamical perspective on the Riemann Hypothesis, isolating a concrete instability mechanism and a precise analytic target for future investigation.
Romeo et al. (Fri,) studied this question.
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