Goldbach and the Triple Interface Method

This a research program titled the "Triple Interface Method". Its aim is to solve the Goldbach conjecture. This manuscript presents a modular tripartite “engine” for tackling the binary Goldbach problem. The argument is broken into a small set of auditable modules—how energy is spread across rational frequencies, how bilinear short-shift correlations are controlled, how nuisance low-frequency effects are cancelled, and how average positivity is converted into pointwise positivity for every even number in a range. Each outputs a quantitative bound; together they feed a simple closing ledger that leaves only mild, standard number-theory inputs (distribution in very small moduli and a positive main term) and a routine finite base. The machinery of the paper has been coded in Lean 4 and the repo is available to the public.