A Quasi-Orthogonal Spectral Framework Toward the Riemann Hypothesis

This manuscript develops a spectral and operatorial framework related to the Riemann Hypothesis through localized explicit-formula analysis, dyadic spectral decomposition, and quasi-orthogonal arithmetic structures. The work introduces a dyadic Hilbert-space architecture combining logarithmic oscillatory suppression, Diophantine spectral separation, and Cotlar–Stein type almost-orthogonality mechanisms in order to study the stability of residual off-diagonal interactions arising from the Weil explicit formula. Rather than presenting an unconditional proof of the Riemann Hypothesis, the manuscript proposes a conditional spectral rigidity program in which the global confinement of non-trivial zeros is connected to the suppression of coherent long-range arithmetic resonances across dyadic scales. Generative AI tools were used during the drafting process for transcription, formatting, language polishing, and structural organization of the manuscript. The author retained full responsibility for all mathematical content, claims, proofs, and interpretations presented in this work. The manuscript is released as a research preprint intended for open mathematical scrutiny, discussion, and future refinement.