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March 29, 20260 citationsOpen Access

Synthesis with a Structural Proof of Fermat's Theorem and the System–Antisystem Duality

Key Points

This research aims to create a universal law of reality organization based on discrete ternary symmetry and confirm it across multiple fields.
Algorithmic analysis of financial time series using MQL4
Mathematical verification involving Riemann Hypothesis and Fermat's Theorem
Historical analysis of 251 key dates
Introduction of System–Antisystem duality
Statistical estimation of significance with p<10−935
Proposed structural explanation for Fermat's Last Theorem through intersection point formula
Introduction of 96 fundamental patterns as isomorphic unfoldings
Comprehensive confirmations across mathematics, physics, and history

Abstract

This work formulates a universal law of reality organization based on discrete ternary symmetry Z3×Z3Z3×Z3. The theory is derived from algorithmic analysis of financial time series (MQL4) and verified in mathematics (Riemann Hypothesis, Fermat’s Theorem), physics (QCD, string theory), history (251 key dates), and market dynamics. A structural explanation of Fermat’s Last Theorem is proposed using the intersection point formula P=N−2KP=N−2K. The concept of System–Antisystem duality is introduced, where 96 fundamental patterns represent isomorphic unfoldings of a single algebraic core. The combined statistical significance of the confirmations is estimated as p<10−935p<10−935. The source code (4 MQL4 modules + Python implementation) is available upon request under the CC BY-NC-ND 4.0 license.

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