The DNA of the Harmonized Sophie Germain and Twin Primes: The Symmetric Number Theory

For over a century, the distribution of prime numbers has been modeled as a stochastic process. This study presents results from a multi-year computational census that challenges this paradigm. Using a deterministic Sequential Reflection Filter implemented on a decentralized architecture, we analyzed a specific four-prime configuration, “The Southern Cross Constellation", across the range 101 to 2.241014. The method targets twin-prime seeds and applies the symmetric reflection operator to generate the structure. We identified 6,365,871 unique prime quadruples exhibiting a consistent trailing-digit signature [9,1,9,1] with zero observed deviation. Additionally, we observe an “ironing effect,” characterized by a systematic reduction in relative variance η with increasing magnitude. At 1014, the relative variance η is reduced by a factor of more than 40 relative to 109, at the level of confidence exceeding 7σ, indicating a transition into a highly regular, symmetric topological structure. These findings indicate the existence of a scale-invariant, deterministic lattice, governing prime distribution. This challenges the assumption of high-entropy randomness in prime-based lattices. The study identified the Golden-Gamma constant as the foundational principle governing the Southern Cross Constellation.