A Contribution to the Spectral Proof of the Riemann Hypothesis via Adelic Analysis

This research proposes a theoretical framework for a spectral approach aimed at the proof of the Riemann Hypothesis (RH). Building upon the foundational insights of Alain Connes, Michael Berry, and Jon Keating, the work addresses the historical problem of the lack of self-adjointness in the hyperbolic position-momentum model by performing a dimensional lifting to the Adèle Solenoid (CQ=AQ/Q∗). At the core of this proposal, the Tate Product Formula is analyzed as a global dynamic confinement mechanism capable of sealing the x=0 singularity, aiming to fix the Weyl deficiency indices strictly at (0,0). Through the synthesis of adelic analysis and the application of Fujisaki’s and Marshall Stone’s theorems, the work discusses the existence of a unique self-adjoint extension for the global Dirac operator, which would imply a purely real spectrum. The bijective correspondence with the Riemann zeros is examined via the Guinand-Weil-Connes trace formula, orienting the results toward the critical line Re(s)=1/2. To support this theoretical framework, high-fidelity numerical validation integrating 30,000 primes is provided, yielding resonance patterns consistent with the known non-trivial zeros (p