Recursive Continuity Geometry Across Physical Scale: From Quark Relations to Macroscopic Structure

Paper 1 of 8 in the Recursive Continuity Geometry Across Physical Scale series. This paper presents a shared cross-scale formalism for mapping how active lower-scale relations become persistent higher-scale units. It follows physical closure from quark–gluon relations through hadrons, nuclei, atoms, molecules, materials, biological assemblies and macroscopic continua. The framework integrates Recursive Continuity Geometry with Structural Fingerprint Method Version 2.0, Persistence Fingerprint Analysis, the Persistence Locking Mechanism, Admissibility Interrogation Topology and Lineal Continuity Traversal Mathematics. It maps relation, constraint, admissible closure, persistence locking, interrogation, reconstruction and continuity handover without replacing the governing equations of any physical domain. The paper includes a shared mathematical spine, two numerical operationalisations and a complete cross-scale testing and falsification programme.