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

This version 0.4 further strengthens the logical organization and internal verification of the manuscript following additional critical feedback. The main additions are a new chapter explaining why the proposed reciprocity--conductor framework should not be read as a classical Bombieri--Vinogradov-type dispersion argument, and a more explicit comparison between the present analytic architecture and standard distribution-level obstructions. This version also clarifies the exact removal of the local main contribution (M(r,k)) before the variance argument, and gives a detailed verification of the fourth-root return from the dispersion variance to the original minor block. These additions make explicit that the variance acts only on the residual oscillatory component, with no hidden structured contribution left inside the error term. The manuscript remains a technical verification note. It does not claim to settle the binary Goldbach conjecture. Its purpose is to isolate and invite independent verification of the analytic mechanisms arising in this Goldbach-type dispersion framework: the double reciprocity reduction, the conductor factorization and counting, the bilinear Kloosterman estimate, and their global insertion into the dispersion variance.