Topological Phase Structure in Prime Distribution and Riemann Zeta Zeros: Observations from Magnetometric Measurements
Description
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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Ptak_Phase_Geometry_Primes.pdf
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- Mathematics → Number Theory Physics → General Physics