Architectural Isomorphism: Geometric Verification of Connes' Spectral Triple via Null-Metric Conditions and Resonance Theory

Version 2. 0 (2026-05-31): Added bidirectional cross-reference to companion paper "The Artemov Conjecture: Null-Metric Realization of Riemann Zeros via Helmholtz Resonances (Foundations and Conditions C1-C4) " (DOI: 10. 5281/zenodo. 20468574) establishing the formal research cluster of the Artemov Program. Updated bibliography and metadata. --- Abstract (v1. 0): The Hilbert-Pólya conjecture posits the existence of a self-adjoint operator whose spectrum corresponds to the non-trivial zeros of the Riemann zeta function ζ (s). We propose a paradigm shift from L²-spectral theory to the analysis of scattering resonances on the modular surface X = PSL (2, Z) ². We formulate the Artemov Conjecture, in which the critical line Re (s) = 1/2 is realized as a null-metric surface of a pseudo-Riemannian manifold, and prime numbers are encoded by hyperbolic resonators. The central result is the Artemov-Connes Dictionary — a rigorous architectural isomorphism between this geometric construction and Alain Connes' noncommutative spectral triple on the adelic space of classes. We conclude with the Artemov Factorization Conjecture, reducing the proof of the Riemann Hypothesis to an identity between the Fredholm determinant and the Selberg zeta function.