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

⚠️ CORRECTION NOTICE (added 2026): The author has since identified serious errors in this work through a systematic adversarial audit. The central claims of this record should not be relied upon. Specific issues found across this research program include implementation errors (e.g., conflation of signed cosine with cos²), circular definitions, proof gaps, results that reduce to known theorems, and effects that vanish under proper null models and direct-influence correction. This record is left online for transparency and as a documented case, not as a valid result. For the author's current, audited methodology, see the later work on classical-baseline auditing of quantum-like contextuality claims: https://doi.org/10.5281/zenodo.20680607 — A. Ogasawara 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.