The Extended Zeta Function and Possible Projection Effects in Particle Physics: Neutrino Phases, Effective Planck Shifts, and the Hubble Tension

2025 · doi:10.22541/au.176055033.36695191/v1
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Abstract

We analyse the φ-Hurwitz extension of the Riemann zeta function as a mathematical origin of apparent Planck-scale variations. The projection from the extended helical embedding to the observed 3+1 spacetime introduces anisotropic measure factors. These yield apparent shifts of ℏ obs = ℏ(1+δ), even if ℏ is constant in the extended space. We formulate explicit neutrality conditions under which the Standard Model remains invariant, but under the discussed assumptions the violation of these conditions could produce testable artefacts across cosmology, hydrodynamics, and molecular helices. Whether neutrinos are fundamental particles or manifestations of such projection-induced h-fluctuations remains undecidable, in close analogy to the Riemann Hypothesis itself.
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Abstract

We analyse the φ-Hurwitz extension of the Riemann zeta function as a mathematical origin of apparent Planck-scale variations. The projection from the extended helical embedding to the observed 3+1 spacetime introduces anisotropic measure factors. These yield apparent shifts of ℏ obs = ℏ(1+δ), even if ℏ is constant in the extended space. We formulate explicit neutrality conditions under which the Standard Model remains invariant, but under the discussed assumptions the violation of these conditions could produce testable artefacts across cosmology, hydrodynamics, and molecular helices. Whether neutrinos are fundamental particles or manifestations of such projection-induced h-fluctuations remains undecidable, in close analogy to the Riemann Hypothesis itself. Supplementary Material File (zeta_particles.pdf) - Download - 188.12 KB Information & Authors Information Version history Copyright This work is licensed under a Creative Commons Attribution 4.0 International License

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Authors Metrics & Citations Metrics Article Usage 236views 115downloads Citations Download citation Thomas Richter. The Extended Zeta Function and Possible Projection Effects in Particle Physics: Neutrino Phases, Effective Planck Shifts, and the Hubble Tension. Authorea. 15 October 2025. DOI: https://doi.org/10.22541/au.176055033.36695191/v1 DOI: https://doi.org/10.22541/au.176055033.36695191/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu.

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