Schrödinger Equation From Coherent Persistence

This paper derives Schrödinger evolution as a structural consequence of coherent persistence rather than as a postulate of quantum mechanics. Starting from minimal requirements for viable propagation—linearity, norm preservation, and continuity—we show that admissible evolution must be unitary and generated by a self-adjoint operator. The resulting Schrödinger equation describes reversible propagation within the space of viable states, while irreversible selection arises separately from the return operation. This separation clarifies the relation between unitary dynamics and measurement without introducing collapse mechanisms or stochastic dynamics. Schrödinger evolution thus emerges as the unique form of continuous, coherence-preserving propagation compatible with structural closure and return, completing the dynamical layer of the Structural Coherence framework.