Riemann Zeta-Phase Winding in Simultaneous Resonance Theory

This paper examines the structural and energetic relationship between the discrete phase geometry of Simultaneous Resonance Theory (SRT) and the continuous analytical ordinates of the Riemann zeta function. Within a strict framework of non-temporal simultaneity, a discrete dyadic phase grid is mapped into a non-temporal Keplerian profile through a parameter-free elliptical-torsion construction derived from the fundamental SRT baseline constants. The study establishes a correspondence between the modular phase-winding and eigenvalue structure of the SRT grid and an invariant periodic wave pattern within the continuous Riemann landscape. This relationship is governed by a compressed precession operator. The Law of Inherent Energy Decay and a Spectral Flux Balance condition subsequently define the analytical boundary at which continuous logarithmic phase space maps into stable resonant organization around the SRT observer axis. By connecting discrete algebraic structure, continuous phase space and the energetic constraints of matter-closure, the resulting construction offers a consistent, unfitted geometric model illustrating how the Riemann zeros emerge naturally from the boundary conditions of matter-closure.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-09-17
DOI
https://doi.org/10.5281/zenodo.22810755
Primary Topic
Advanced Thermodynamics and Statistical Mechanics
Type
preprint
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Riemann Zeta-Phase Winding in Simultaneous Resonance Theory

Johanna Maria Beekmans
Zenodo (CERN European Organization for Nuclear Research)
Advanced Thermodynamics and Statistical Mechanics
preprint

Riemann Zeta-Phase Winding in Simultaneous Resonance Theory

Johanna Maria Beekmans
preprint en

Abstract

This paper examines the structural and energetic relationship between the discrete phase geometry of Simultaneous Resonance Theory (SRT) and the continuous analytical ordinates of the Riemann zeta function. Within a strict framework of non-temporal simultaneity, a discrete dyadic phase grid is mapped into a non-temporal Keplerian profile through a parameter-free elliptical-torsion construction derived from the fundamental SRT baseline constants. The study establishes a correspondence between the modular phase-winding and eigenvalue structure of the SRT grid and an invariant periodic wave pattern within the continuous Riemann landscape. This relationship is governed by a compressed precession operator. The Law of Inherent Energy Decay and a Spectral Flux Balance condition subsequently define the analytical boundary at which continuous logarithmic phase space maps into stable resonant organization around the SRT observer axis. By connecting discrete algebraic structure, continuous phase space and the energetic constraints of matter-closure, the resulting construction offers a consistent, unfitted geometric model illustrating how the Riemann zeros emerge naturally from the boundary conditions of matter-closure.

Zenodo (CERN European Organization for Nuclear Research)
Advanced Thermodynamics and Statistical Mechanics
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