A Structural Finite-Depth Reduction of the Strong Goldbach Conjecture via MSAT and Dyadic Rondo Transport

This paper provides a complete finite-depth structural reduction of the strong Goldbach conjecture based on the MSAT (Matsuura Structural Additive Transfer) framework and a dyadic transport mechanism (Rondo expansion). All finite congruence obstructions, local additive constraints, and structural multiplicative barriers are eliminated explicitly and unconditionally. The conjecture is shown to be equivalent to a single analytic statement—the Prime Emergence Hypothesis (PEH′)—concerning prime occurrence in a sparse dyadic family of linear forms. No circle method, zero-density estimates, or global analytic averaging are used in the structural part of the argument. The remaining analytic core is isolated precisely, providing a clear interface for future analytic approaches. This work is intended as a structural foundation and reduction framework rather than an unconditional proof.