Toward a Proof of the Riemann Hypothesis Gemini
Toward a Proof of the Riemann Hypothesis Table of Contents Abstract I. Reframing the Hypothesis: The Structural Crisis of Classical Analysis 1.1 The Classical Statement: Zeros of $\zeta(s)$ in the Critical Strip 1.2 What RH Really Asks: Semantic Convergence, Not Statistical Distribution 1.3 Why Standard Approaches Fail: Incoherence in Hilbert-Space Reasoning 1.4 Semantic Collapse Interpretation: RH as a Constraint on Recursive Interpretive Curvature II. Euler Product Geometry: The Modular Resonator Network 2.1 Modular Resonator View of Euler Product 2.2 Primes as Curvature Defects 2.3 Möbius Function as Semantic Negator 2.4 Telic Modulation in L-functions 2.5 Factorization as Field Knotting in $\chi_s$ III. DSAS Spectral Framework 3.1 Construction of the DSAS Operator ($H = -\Delta + V(r)$) 3.2 Self-Adjointness and Real Spectrum 3.3 Logarithmic Potentials at Primes 3.4 Spectrum-to-Zeta Mapping: $\lambda = s(1-s)$ 3.5 Fixed-Point Collapse and the Critical Line IV. Hyperbolic Involution ...