The Riemann Hypothesis as a Harmonic Collapse Theorem in a Logarithmic Resonance Field

Version 1 – Foundational Harmonic Collapse Model

This initial version introduces the harmonic collapse framework for the Riemann Hypothesis, demonstrating destructive interference alignment along the critical line through frequency-phase superposition. It outlines the core intuition, functional equation symmetry, and spectral collapse behavior that set the stage for the full operator formalism in Version 2.

Version 2 – Complete Formalization and Operator Extension

This second version presents a full formalization of the harmonic collapse proof of the Riemann Hypothesis, including expanded lemmas, theorem structure, numerical simulations, and operator-based spectral validation. It introduces an eigenfrequency detection operator T\mathcal{T}T, whose residuals dynamically confirm collapse points aligned with known Riemann zeros. The proof integrates Li coefficient positivity, field trench stability, and Nyman–Beurling compatibility, framing the critical line Re(s)=12\text{Re}(s) = \frac{1}{2}Re(s)=21 as the unique corridor for total interference cancellation. This version is intended as the definitive model-based submission for peer review and independent replication.