Spectral-Edge Instability and Phase Rigidity in Li-Type Data: A Structural Reduction of the Riemann Hypothesis

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.