Published June 1, 2026 | Version 2.0

Part–2: Spectral Program – Architectural Isomorphism

Description

Part 2 of the Spectral Program.

This paper establishes an architectural bridge between the geometric framework of null-metric surfaces and Alain Connes' noncommutative spectral triple. The result is the Artemov–Connes Dictionary — a term‑by‑term correspondence between classical resonance geometry and noncommutative algebra on the adelic class space.

This part is interpretive: it provides a conceptual dictionary, not new rigorous theorems. The rigorous No‑Go results are proven in Parts 3–5.

Keywords: spectral geometry, Riemann Hypothesis, noncommutative geometry, Connes' spectral triple, adeles, Artemov–Connes Dictionary, null-metric surfaces.

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Related works

Is continued by
Preprint: 10.5281/zenodo.20672908 (Part 2) (DOI)
Preprint: 10.5281/zenodo.20673422 (Part 3) (DOI)