Order-Projection Principle: A Minimal Origin of Phase-Dependent Observables Across Systems

⚠️ 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 paper introduces the Order-Projection Principle (OPP), a minimal andmodel-independent framework describing when order-dependent observables becomevisible in systems combining noncommutative operations and irreversibleprojection. This record is provided for archival and priority purposes. This manuscript was prepared by the author, with AI tools used for language drafting and organization. The scientific content and conclusions are the author’s own.