A_Topological_Reinterpretation_of_Primality__The_Mobius_Classifier_and_Symbolic_Zeta_Dynamics
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2025
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| _version_ | 1866901962693279744 |
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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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17688703 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| 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 |