A Unified Dynamical, Variational, and Spectral Framework for the Riemann Zeta Zeros (Version 4: Pointwise Control and Uniform Stability)

We present a unified framework for the nontrivial zeros of the Riemann zeta function, integrating dynamical, variational, and spectral perspectives. The core of the paper is an analytic approach to the Riemann Hypothesis (RH) via two lemmas. Three previously identified vulnerabilities are resolved: (1) pointwise vs. averaged convexity is decoupled from Weil positivity; (2) the weak-convergence to individual zeros gap is closed using the purely atomic nature of the empirical zero measure; (3) uniform stability of the external potential is established via explicit O((log T)/T) error bounds. While the proof remains incomplete (the Weil positivity lemma relies on an unverified sign condition for the prime sum), the paper contributes a clear identification of the remaining obstacles and a correct treatment of the measure-zero gap. Numerical Dyson Brownian motion simulations are included as motivation.