Binary Goldbach via the Circle Method with Explicit Constants: A Certificate-Driven Draft

We present a circle-method framework with explicit constants that, together with certified

numerical bounds arising from the Deshouillers–Iwaniec (DI) spectral large sieve and a calibrated

Selberg majorant, yields a strictly positive lower bound for the binary Goldbach representation

integral for all large even integers. The architecture splits into major arcs, boundary-localized

minor arcs, and a final glue inequality. Constants are provided as machine-checkable certificates

(JSON) produced by short Python scripts.