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ZENODO
Preprint . 2025
License: CC BY
Data sources: ZENODO
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2025
License: CC BY
Data sources: Datacite
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Topological Phase Structure in Prime Distribution and Riemann Zeta Zeros: Observations from Magnetometric Measurements

Mathematics → Number Theory Physics → General Physics
Authors: Ptak, Jan;

Topological Phase Structure in Prime Distribution and Riemann Zeta Zeros: Observations from Magnetometric Measurements

Abstract

We report magnetometric measurements that reveal field nodes at angular positions 140° and 310° across three materials: neodymium (ferromagnetic), ferrite (ferrimagnetic), and gold (diamagnetic). This consistency across materials with different magnetic properties suggests, but does not yet prove, material-independence. These angles correspond to boundaries defined by the Euler totient function φ(360): phases φ with GCD(φ, 360) > 1 cannot host primes p > 5, by elementary divisibility. Analysis of 195 Riemann zeta zeros (from Odlyzko tables, mapped to phase via t mod 360°) indicates a statistically significant difference in zero spacing between sectors defined by these nodes (t = 2.35, p = 0.02), while prime gaps show no comparable asymmetry. This observation, though preliminary and dependent on the chosen mapping, may be suggestive for spectral approaches to the Riemann Hypothesis.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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Average
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