Orbit-Regularized Verification of the Strong Goldbach Conjecture: Empirical Evidence of 10⁹ 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 10⁹, 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. ”