Structural Invariants

This paper provides a principled account of why dimensionless invariants must arise in any admissible representation of a closure-first relational ontology. In the Coherence-Relational Blockworld (cRBW) framework, reality is identified with a single globally admissible relational structure, while representations introduce arbitrary descriptive elements such as units, coordinates, and parameterizations. We show that only quantities invariant under admissible transformations of representation—specifically, dimensionless relational ratios—can carry ontic significance.

We formalize classes of invariants as equivalence classes under admissible transformations and define structural invariants as those that remain stable under rescaling (NPRF), representational freedom (RN), and admissibility-preserving operations (PRG/CRG). Using Grassmannian representations, we demonstrate that invariants arise from geometric relations between subspaces rather than from temporal evolution or observer-dependent slicing.

This framework replaces model-dependent identification of physical constants with a structural criterion grounded in admissibility and representation-independence. It establishes that the existence of invariant classes is necessary, while the identification of specific invariants as fundamental requires demonstration of stability across admissible representations.