A Propagation-Based Reformulation of the Goldbach Conjecture

This paper proposes a propagation-based reformulation of the Goldbach Conjecture.Instead of investigating directly whether a given even integer admits a Goldbach partition, the present work studies the persistence of Goldbach partitions between consecutive even integers.A propagation operator is introduced together with a propagation property P(n). The central result of the paper is the Propagation Incompatibility Theorem, which establishes that the existence of a first Goldbach counterexample is incompatible with the propagation property of the immediately preceding even integer. The framework transforms Goldbach from a problem concerning the existence of prime partitions into a problem concerning their stability and propagation. The main contribution of the work is the introduction of a propagation framework and a minimalcounterexample interpretation of Goldbach partitions.