A_Topological_Reinterpretation_of_Primality__The_Mobius_Classifier_and_Symbolic_Zeta_Dynamics

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1. Verfasser: Barker, Joshua
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Sprache:Englisch
Veröffentlicht: Zenodo 2025
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author Barker, Joshua
author_facet Barker, Joshua
contents <p>This record presents a speculative, unified framework that recasts aspects of number theory in symbolic and topological terms. The work develops a Möbius-inspired classifier for natural numbers, interprets primes as topologically non-degenerate states, and introduces a corresponding “Möbius Zeta Function” built as a Dirichlet-type series over these structurally coherent integers.</p> <p>Within this viewpoint, primes are treated as resonance-like objects in a symbolic projection space, and the associated zeta-type function is interpreted as a formal sum over these modes. The framework also sketches a graph-theoretic setting, in which Laplacian- and Hamiltonian-like operators on a symbolic projection graph are used to heuristically discuss spectral features reminiscent of those appearing in the study of the Riemann zeta function.</p> <p>The aim of this work is <strong>interpretive rather than demonstrative</strong>: it does not claim a proof of the Riemann Hypothesis or any new rigorous results about ζ(s). Instead, it offers a geometric and resonance-based language for thinking about primality, zeta functions, and spectral analogies, with all “collapse” and “standing wave” terminology intended as heuristic metaphor.</p> <p>Earlier drafts of this project appeared as four separate preprints; this version consolidates and clarifies the core ideas into a single concept paper and should be considered the primary reference.</p>
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spellingShingle A_Topological_Reinterpretation_of_Primality__The_Mobius_Classifier_and_Symbolic_Zeta_Dynamics
Barker, Joshua
Prime numbers
Möbius transformation
Riemann Hypothesis
Zeta function
Spectral theory
Topological number theory
Projection degeneracy
Dirichlet series
Hilbert–Polya
Laplacian graphs
Ontological classifiers
<p>This record presents a speculative, unified framework that recasts aspects of number theory in symbolic and topological terms. The work develops a Möbius-inspired classifier for natural numbers, interprets primes as topologically non-degenerate states, and introduces a corresponding “Möbius Zeta Function” built as a Dirichlet-type series over these structurally coherent integers.</p> <p>Within this viewpoint, primes are treated as resonance-like objects in a symbolic projection space, and the associated zeta-type function is interpreted as a formal sum over these modes. The framework also sketches a graph-theoretic setting, in which Laplacian- and Hamiltonian-like operators on a symbolic projection graph are used to heuristically discuss spectral features reminiscent of those appearing in the study of the Riemann zeta function.</p> <p>The aim of this work is <strong>interpretive rather than demonstrative</strong>: it does not claim a proof of the Riemann Hypothesis or any new rigorous results about ζ(s). Instead, it offers a geometric and resonance-based language for thinking about primality, zeta functions, and spectral analogies, with all “collapse” and “standing wave” terminology intended as heuristic metaphor.</p> <p>Earlier drafts of this project appeared as four separate preprints; this version consolidates and clarifies the core ideas into a single concept paper and should be considered the primary reference.</p>
title A_Topological_Reinterpretation_of_Primality__The_Mobius_Classifier_and_Symbolic_Zeta_Dynamics
topic Prime numbers
Möbius transformation
Riemann Hypothesis
Zeta function
Spectral theory
Topological number theory
Projection degeneracy
Dirichlet series
Hilbert–Polya
Laplacian graphs
Ontological classifiers
url https://doi.org/10.5281/zenodo.17688703