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October 17, 2025Open Access

Euclidean-Lorentzian Dichotomy and Algebraic Causality in Finite Ring Continuum

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Analysis reveals a fundamental dichotomy in finite fields, showing algebraic causality links Lorentzian structure with invariants.

A finite ring continuum analysis shows a distinct euclidean-lorentzian dichotomy that impacts our understanding of causality.
Symmetry-complete prime shells illustrate that genuine lorentzian forms cannot exist within single space-like layers, indicating structural limitations.
An explicit lorentz transformation is derived, preserving the Minkowski form and reaffirming concepts from special relativity within finite-field arithmetic.
The study’s results highlight how the algebraic features of special relativity emerge and clarify the relationship between euclidean and lorentzian structures.

Yosef Akhtman (2025) studied this question.

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