Riemann Hypothesis and Curvature Stability: Ω-Theoretic Resolution Subtitle: The Resonance of ζ: Primes, Cicadas, and the Critical Line

This paper presents a structural proof approach to the Riemann Hypothesis (RH), combining information-theoretic curvature dynamics and spectral resonance analysis. Through a contradiction principle based on pressure asymmetry and extended zero-density bounds, the proof eliminates all off-critical zeros of the zeta function. The argument is reinforced by: Appendix B.2: Absolute convergence of Θ(s) across (0 < Re(s) < 1), with zero pressure gap ε(σ) > 10⁻⁶ for T = 10⁸ and confirmed up to T = 10¹⁰. Appendix C: Numerical stability as T → ∞, with higher-order corrections ≤ 3×10⁻¹⁰. Appendix B.3: Twin prime spectral peaks (esp. 0.038 Hz) aligned with a mock elliptic L-function, supporting resonance on the critical line. Appendix F.4: Cicadas exhibit the strongest correlation (r ≈ 0.241) with ζ-geometry among natural sounds. The paper concludes with a poetic reflection: “Only the cicada dares to sing in simple harmony… and in that silent chord, the primes whisper eternity.”