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April 1, 20260 citationsOpen Access

Manifesto on the Structural Rigidity of Odd Natural Numbers Foundational Theory of Projective Primality and Information Manifolds

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SGSilvio GabbianelliMitsubishi Gas Chemical (Japan)

Key Points

  • The research aims to redefine prime numbers based on their structural relationships in number theory.
  • Defined prime numbers as a consequence of the structural properties of a pencil of lines on a Cartesian grid.
  • Integrated previous theories on information manifolds and modulo-12 lattices to support the framework.
  • Analyzed major number theory conjectures such as Goldbach, Riemann, and Twin Primes in relation to the proposed theory.
  • Demonstrated that prime numbers can be seen as a ‘mirror image’ of structural saturation in defined systems.
  • Outlined how major conjectures are deterministic outcomes of the new theoretical framework.

Abstract

This paper proposes an epistemological shift in Number Theory by defining the set ofprime numbers P as the necessary and mirror image resulting from the incomplete saturationof a proper pencil of lines F on a discrete Cartesian grid. By integrating previous research onInformation Manifolds and the Modulo-12 Lattice, we demonstrate that major conjectures(Goldbach, Riemann, Twin Primes) are deterministic consequences of the system’s structuralrigidity.

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Cite This Study

Silvio Gabbianelli (2026) studied this question.

synapsesocial.com/papers/69ccb6fd16edfba7beb88d57https://doi.org/10.5281/zenodo.19334660
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