Structured Correlations in Order-Projection-Based Computation

This work provides a structural and semantic analysis of order-projection-based computation, focusing on the nature of the computational resources identified in a preceding study.Rather than introducing new experimental results, the paper clarifies how weak but reproducible phase-structural signals should be interpreted, what is and is not amplified, and why such behavior does not imply equivalence to quantum computation. The analysis distinguishes between strict ranking metrics and probabilistic success measures, reinterprets pseudo-unitary updates as visibility amplifiers rather than computational primitives, and demonstrates that performance improvements arise from structured correlations across phase channels rather than from increased dimensionality.It further shows that effective search requires preserving the geometric character of phase through low-dimensional representations. By explicitly identifying the limits of the framework, this work positions order-projection-based computation as an intermediate regime between conventional intensity-based classical methods and full quantum models, without assuming quantum states or quantum hardware.The paper completes a two-part account of order-projection-based computation by providing the conceptual interpretation and constraints corresponding to the experimental existence results reported previously.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.