This work presents a minimal and controlled study of order-projection–based computationin a purely classical setting. Under a strict phase-only representation in which amplitude information is removed,we show that conventional intensity-based readout becomes informationless,while weak but reproducible discriminative structure can still be recoveredby combining noncommutative operation histories with irreversible projectionand geometry-aware readout. The reported results are intentionally modest in magnitude and are not intendedto demonstrate computational speedup, optimal performance, or quantum advantage.Instead, the purpose of this study is to establish the existence and reproducibilityof phase-structured information that is inaccessible to standard classical readoutbut becomes observable under appropriate order-projection evaluation. This manuscript focuses on the structure, limitations, and interpretationof such order-dependent signals, and clarifies both what is achievedand what is explicitly not claimed.The results may be of interest for discussions of measurement structure,history dependence, and the boundary between classical and quantum information processing. This preprint is provided for documentation and disclosure purposes.No claims of universality, optimality, or complexity-theoretic advantage are made. 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.
John Jude Hathway (Tue,) studied this question.