Representation Equivalence and Framework Plugins in the Scalar Temporal Field Ontology

The Scalar Temporal Field Ontology (STFO) is formulated across multiple mathematical representations, including scalar-field actions, elastic temporal congruence dynamics, disformal effective metrics, and information-geometric constructions. This paper establishes that these formulations are not distinct theories or revisions, but representationally equivalent framework plugins acting on a single fixed ontology. Criteria for representation equivalence are defined, invariant ontological content is identified, and common STFO representational layers are classified. This work serves as the canonical interpretive reference for reading, citing, and extending the STFO corpus.Update: This update introduces a dedicated interpretive paper, “Representation Equivalence and Framework Plugins in the Scalar Temporal Field Ontology,” whose sole purpose is to formally clarify the relationship between the multiple mathematical formulations used across the STFO corpus. No new axioms, fields, couplings, equations, predictions, or empirical claims are added. All existing results, derivations, and conclusions remain unchanged. The update explicitly establishes that: All STFO formulations (scalar-field actions, elastic congruence dynamics, disformal metrics, and information-geometric constructions) are representation-equivalent. These formulations function as framework plugins, selected by physical regime and calculational convenience, not as distinct theories or revisions. The underlying ontology—time as a physical scalar field τ determining causal ordering—remains fixed and unique. This clarification is intended to prevent misinterpretation of representational diversity as ontological multiplicity, to stabilize citation practices, and to provide a single canonical reference for representation-level questions across the STFO archive. Scientific content, predictions, and experimental interfaces are unchanged.