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August 20, 20260 citationsOpen Access

Prime Numbers as Spectral Artifacts of Continuous Quantum Geometric Systems

Prime Numbers as Spectral Artifacts of Quantum Geometric Systems

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Overview

Theoretical analysis demonstrates that prime numbers emerge as spectral projections of continuous quantum geometry, suggesting discrete arithmetic derives from continuous physical foundations.

Key Points

  • To establish a mathematical framework determining whether prime numbers emerge as spectral artifacts from a continuous quantum geometric substrate rather than fundamental discrete entities.
  • Derived formal logical deductions from five mathematical foundations: primality base-independence, Gödelian incompleteness, Tennenbaum’s non-categoricity theorem, integer ring dependency, and the Montgomery-Odlyzko correspondence.
  • Formulated a computational implementation protocol specifying Hamiltonian operator construction under π-φ geometric entanglement constraints.
  • Proved that prime numbers necessarily arise via spectral projection from continuous quantum geometric systems.
  • Provided a structural mathematical explanation for the quantum chaotic signatures observed in prime number distributions.

Cite This Study

A 2026 study studied this question.

synapsesocial.com/papers/6a86b4cb8a91293e6a1cc463https://doi.org/10.5281/zenodo.17566147
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Also Consider

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  1. 1A Geometric Origin of Prime Numbers: The Prime-Property Generator as a Geometry-First Model of Primality2026
  2. 2Shui's Axiomatic System of Double-Layer Topological Shells in Arithmetic — A Complementary Foundation for Geometric Number Theory2026
  3. 3Shui's Axiomatic System of Double-Layer Topological Shells in Arithmetic ― A Complementary Foundation for Geometric Number Theory2026
  4. 4Prime Modes in the Field Matrix A Resonance-Based Bridge Between Number Theory and Physics2025
  5. 5Prime Modes in the Field Matrix A Resonance-Based Bridge Between Number Theory and Physics2025