PreprintCC BY 4.0Zenodo
The Spectral Geometry of Fractal Prime Structures: Adèlic Dilation Flows, Unitary Information Regulators, Coercive Resolvent Decoupling, and Cauchy–Poisson Prime Dynamics
Abstract
The spatial distribution, fine-scale intermittency, and gap fluctuations of prime numbers exhibit multi-scale complexity that eludes classical fractal analysis. Naive gap-ratio formulations flatten asymptotically (\lim_{n \to \infty} D_{\text{naive}}(n) = 1.0), while heuristic attempts to couple prime distributions to dimensional physical constants violate the rank-3 dimensional homogeneity of mechanics (\det \mathbf{A} = 2 \neq 0).
This paper establishes the foundational architecture of the Spectral Geometry of Fractal Prime Structures, unifying discrete arithmetic combinatorics, non-Archimedean valuation trees, continuous adèlic operator dynamics, and the macroscopic topology of the Cosmic Web.
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BibTeX
@misc{tudor2026spectral,
title = {{The Spectral Geometry of Fractal Prime Structures: Adèlic Dilation Flows, Unitary Information Regulators, Coercive Resolvent Decoupling, and Cauchy–Poisson Prime Dynamics}},
author = {August Tudor},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23514251},
url = {https://zenodo.org/records/23514251},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Spectral Geometry of Fractal Prime Structures: Adèlic Dilation Flows, Unitary Information Regulators, Coercive Resolvent Decoupling, and Cauchy–Poisson Prime Dynamics
AU - August Tudor
PY - 2026
DA - 2026/10/20
PB - Zenodo
DO - 10.5281/zenodo.23514251
UR - https://zenodo.org/records/23514251
AB - The spatial distribution, fine-scale intermittency, and gap fluctuations of prime numbers exhibit multi-scale complexity that eludes classical fractal analysis. Naive gap-ratio formulations flatten asymptotically (\lim_{n \to \infty} D_{\text{naive}}(n) = 1.0), while heuristic attempts to couple prime distributions to dimensional physical constants violate the rank-3 dimensional homogeneity of mechanics (\det \mathbf{A} = 2 \neq 0). This paper establishes the foundational architecture of the Spectral Geometry of Fractal Prime Structures, unifying discrete arithmetic combinatorics, non-Archimedean valuation trees, continuous adèlic operator dynamics, and the macroscopic topology of the Cosmic Web.
ER -