Archive — Ω Relational Geometry

This record is retained for archival transparency. It presents an earlier stage of the Reality Mechanics framework and has been superseded by the consolidated document corpus: “Reality Mechanics: A Relational Framework for Emergent Structure — Document Corpus v1.0” (DOI: 10.5281/zenodo.19014030). RM-05 introduces Ω Relational Geometry, a structural instrument for analysing nested relational containment within the Reality Mechanics framework. Following the architectural description of nested relational structure in RM-04 (Reality Mechanics Core), this document defines a representation of containment structures using binary trees (Ω-trees) and introduces a minimal scalar invariant that measures structural configuration. Local reassociation between containment structures is represented through Tamari rotations, forming the adjacency graph of the associahedron. This provides a configuration space for nested relational structures while remaining independent of domain-specific interpretation. Ω Relational Geometry therefore provides a minimal, domain-agnostic measurement instrument for analysing containment structure and its transformations within relational systems.