MSAT: A Structural Additive Transfer Framework for Scaffolded Resolution of Additive Existence Problems

This paper introduces MSAT (Matsuura Structural Additive Transfer), a methodological framework for reorganizing additive existence problems into structurally transparent and reusable forms. Rather than attempting to resolve specific conjectures such as Goldbach-type problems, the paper constructs complete and fully explicit proofs for carefully chosen scaffold problems, while isolating all remaining unresolved difficulty into a single structural mixing condition. The contribution of this work is methodological rather than problem-specific: it provides a reusable research infrastructure that systematically transports researchers to the immediate vicinity of the true structural bottleneck shared across multiple additive conjectures.