The Structural Origin of Schrödinger Dynamics from the Order-Projection Principle

This note examines the structural origin of Schrödinger-type time evolutionfrom minimal assumptions formulated in terms of histories, noncommutativeoperations, and projection. Without invoking quantum postulates, wave interpretations, or specificHamiltonian models, we show that continuous-time, reversible, andinformation-preserving evolution of history ensembles is necessarilygenerated by an anti-self-adjoint operator, leading to a Schrödinger-typedifferential equation. Within this framework, the appearance of complex-valued structure andunitary evolution arises as a structural requirement rather than as anindependent assumption. The wavefunction is interpreted as a reversiblerepresentation of ensembles of admissible histories, while state reductionis described as an irreversible effect induced by projection. The purpose of this work is not to modify quantum mechanics or itsexperimental predictions, but to clarify the minimal structural conditionsunderlying its dynamical form and to delineate the scope and limitations ofthis approach. Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own.