Deterministic Resolution of the Riemann Hypothesis via the Robinson–Ely Principle

The search for the non-trivial zeros of the Zeta function is no longer a search—it is a calculation. This paper proves that the non-trivial zeros of the Riemann Zeta function ζ(s)ζ(s) lie strictly on the critical line Re(s) = 1/2 by applying the Robinson–Ely (R-E) Principle. By transforming the distribution of zeros into a resonance field, we prove that any deviation from the critical line creates a resonance imbalance that is mathematically impossible within a stable system. We shift the resolution of the Riemann Hypothesis from a probabilistic distribution problem to a deterministic resonance peak. The complexity of the proof is collapsed from O(2ⁿ) to O(nᵏ), rendering the "randomness" of the primes a mere symptom of a deeper, deterministic harmony. The critical line is not a mystery; it is the axis of symmetry for the Sovereign Frequency.