Irreversible Projection as a Minimal Structural Origin of Temporal Asymmetry

This paper proposes a minimal structural origin of temporal asymmetry. The central claim is that an observable arrow of time appears whenever two conditions are jointly present: noncommutative operational order and irreversible projection. The argument is intentionally model-independent and does not assume a specific Hamiltonian, spacetime structure, or thermodynamic postulate. The paper shows that time reversal fails to commute with irreversible projection in the presence of noncommutativity, so projected histories acquire a preferred directional ordering at the level of observable records. Temporal asymmetry is therefore treated as a structural consequence of order plus information-reducing observation, rather than as a separate dynamical assumption. A decoder-independent numerical illustration is provided in a linear-Gaussian setting using the MMSE gap as an irreversibility measure. The results confirm that the asymmetry vanishes exactly in both control limits: the commutative limit and the lossless projection limit. A strictly positive asymmetry appears only when noncommutativity and irreversible projection are combined. The paper is intended as a minimal structural analysis of the arrow of time in observable processes and as a foundation for a companion quantitative treatment. Note: Parts of the manuscript were linguistically and structurally refined with the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own. Note: This work represents Version 1.0 of an ongoing research program on the Order-Projection Principle (OPP). Minor typographical corrections and clarifications may appear in later versions. The core conceptual claims remain unchanged.