August 16, 2025Open Access

Relativistic Algebra over Finite Ring Continuum

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Formal reconstruction of number systems highlights observer-dependent arithmetic in finite fields, suggesting new mathematical frameworks.

Relational analogues of conventional number classes eliminate dependence on infinity, forming a new arithmetic framework.
Explicit mappings preserve algebraic properties while redefining integers, rationals, reals, and complex numbers through finite fields.
Framework uses dense grids generated from primitive roots, enabling proportional reasoning without invoking infinity.
Establishes coherent foundations for mathematics, physics, and logic in a paradox-free universe characterized by relational finitude.

Yosef Akhtman (2025) studied this question.

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Formal reconstruction of number systems highlights observer-dependent arithmetic in finite fields, suggesting new mathematical frameworks.