What question did this study set out to answer?

The aim is to establish a connection between spectral barriers and the Riemann Hypothesis within ZFC.

June 22, 2026Open Access

The C5' No-Go Theorem: Artemov's Spectral Barrier for the Riemann Zeta Function in ZFC

Puntos clave

The aim is to establish a connection between spectral barriers and the Riemann Hypothesis within ZFC.
Established isomorphism between resonance geometry and Connes’ noncommutative spectral triple.
Proved the Phase-Volume Obstruction related to local potentials on modular surfaces.
Identified Condition C5' as a spectral barrier in the adelic space.
Proved RH is equivalent to the discreteness of the spectrum of the scaling operator D.

Resumen

This paper is the fourth in a series. In Part 1 1, we established an architectural isomorphism between classical resonance geometry and Connes’ noncommutative spectral triple. In Part 2 2, we proved the Phase-Volume Obstruction, showing that local potentials on the modular surface cannot generate the Selberg Euler product. In Part 3 3, we isolated Condition C5’ as the spectral barrier in the adelic space, proving that RH is equivalent to the discreteness of the spectrum of the scaling operator D.

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