Double Reciprocity and a Bilinear Kloosterman Estimate in a Goldbach-Type Dispersion Framework

This version 1.0 promotes the manuscript to a proof-level version of a dispersion framework for the binary Goldbach problem. The manuscript develops a non-classical dispersion architecture based on three central analytic mechanisms: a double reciprocity reduction, a conductor factorization and uniform counting step, and a bilinear Kloosterman estimate in the proper central rank (2) range. These mechanisms are inserted into a dyadic Heath--Brown proof ledger and combined with the removal of higher prime powers and a fourth-root return from the dispersion variance. The main analytic claim is formulated as a closed implication from the dyadic dispersion ledger, the double reciprocity mechanism, the conductor factorization and counting lemma, and the bilinear Kloosterman core to a genuine Goldbach representation for all sufficiently large even integers. This version also includes a final consistency audit, a verification map for independent reading, and a chapter explaining why the framework is not a classical Bombieri--Vinogradov-type dispersion argument. The purpose is to make the logical dependencies of the proof explicit and to isolate the precise location of the analytic gain.