Irreversible Projection as a Minimal Origin of Quantum Structure

⚠️ 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 manuscript explores structural aspects of irreversible projection and sequential operations under minimal assumptions.Rather than introducing new physical postulates, it examines how order dependence and relational representations arise in systems subject to information deletion. The analysis focuses on the structural consequences of projection processes and discusses connections to phase-like representations, interference-type effects, and approximate reversibility in weak-projection regimes. The work is intended as a formal and conceptual contribution to the study of order-dependent dynamics across physical and computational systems.No modification of standard quantum theory is proposed.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.