What question did this study set out to answer?

The aim is to redefine the Goldbach Conjecture using a geometric model rather than classical number theory.

February 5, 2026Open Access

Deterministic Asymptotic Constraints on the Goldbach Conjecture: The Central Symmetry Model and Tetaton Search Algorithm

Key Points

The aim is to redefine the Goldbach Conjecture using a geometric model rather than classical number theory.
Shift perspective to Central Symmetry on the number line.
Utilize the Tetaton Algorithm to scan prime distribution.
Employ Modulo 6 filtering to reduce search space.
Conduct arbitrary precision tests on integers from 2 to 158 digits.
Proves the existence of solutions is an arithmetic necessity.
Demonstrates search costs remain under Cramér’s bounds.
Verifies asymptotic consistency of the model across tested numbers.

Abstract

This study redefines the Goldbach Conjecture by shifting the perspective from classical additive number theory to a geometric "Central Symmetry" problem on the number line. The proposed Tetaton Algorithm scans the prime distribution around the midpoint n of an even integer 2n within a search space reduced by Modulo 6 filtering. The study proves that the existence of a solution is not random but an arithmetic necessity, and that the search cost (kmin) remains below Cramér’s bounds (ln n)2 regardless of the number’s magnitude. Arbitrary Precision tests conducted on numbers ranging from the "Genesis Singularity" (2n ≤ 12) to 158-digit integers using a PHP/GMP-based engine verify the asymptotic consistency of the model and the cryptographic density of the generated "Numerical DNA" topology. Keywords: Goldbach Conjecture, Central Symmetry, Tetaton Algorithm, ModularFiltering, Numerical DNA, Cryptographic Entropy.

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