Orbit-Regularized Verification of the Strong Goldbach Conjecture: Empirical Evidence of 10^9 Zero Counterexamples Based on Mod 30 Orbit Locking

Within the framework of orbit regularization, I present a systematic large‐scale verification of the strong Goldbach conjecture. Based on the eight orbit classes modulo 30, every prime greater than 5 necessarily falls into the set {1,7,11,13,17,19,23,29}. Consequently, the decomposition of any even in- teger N as a sum of two primes is precisely locked into a few orbit pairs.By means of the 8 × 8 addition table, the 64 ordered orbit combinations are reduced to 15 residue classes modulo 30, amounting to 36 unordered orbit pairs. For all 15 residue types up to 10^9, I have examined 499,999,986 even numbers and found that every single one admits at least one representation as a sum of two primes — zero counterexamples. All programs are written in pure Python and run on a personal laptop with 16GB RAM; the complete verification up to one billion takes about 13.6 minutes. This result reduces the verification of the strong Goldbach conjecture from “unrestricted search over the whole space” to “deterministic orbit‐pair search.” This paper is not about “proving the conjecture” but about “how to verify the conjecture efficiently using orbit regularization.”