Coherent Euclidean Structures with Internal Orientational Parameters

Version 2: This version improves the formal presentation of the article, refines several proofs and definitions, and strengthens the structural interpretation of coherent Euclidean structures as a bridge between effective geometry and suppressed internal structure. It also clarifies the metric compatibility of the orientational operator, the role of structural projection, and the status of the regular regime as canonical rather than exhaustive, while preserving the article’s central thesis and its role within the MGQC research program. Abstract This article introduces a formal class of coherent Euclidean structures designed to distinguish geometrically effective directions from internal orientational degrees…