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

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.