A Geometric Stability Conjecture for the Nontrivial Zeros of the Riemann Zeta Function

We formulate a conjecture asserting that the nontrivial zeros of the Riemann zeta function ζ(s) lie on the critical line Re(s) = 1/2 not by analytical coincidence, but as a necessary consequence of a universal geometric stability principle. The conjecture is grounded in a one-parameter arithmetic deformation of ζ(s) and is supported by numerical evidence presented in two companion papers. The central object is the whisker trajectory — the curve traced by the local minimum of the deformed modulus as the deformation parameter varies — and the integrated deviation S(c), whose asymptotic quadratic scaling S(c) ~ α c² with universal coefficient α is proposed as the characterising geometric signature of the critical line. The conjecture, if proved, would imply the Riemann Hypothesis as a corollary. This is the third paper in a series. Companion papers: Colombo, P. (2026). "A Universal Quadratic Law Governing the Local Geometry of Riemann Zeros." Zenodo. https://doi.org/10.5281/zenodo.20213580 — Colombo, P. (2026). "Whisker Trajectories of the Riemann Zeros under Arithmetic Deformation." Zenodo. https://doi.org/10.5281/zenodo.20214685