Functional Equivalence Class Hypothesis (FECH): A Meta-Theoretical Statement

The Functional Equivalence Class Hypothesis (FECH) proposes a domain-agnostic framework in which function—rather than surface implementation—serves as the primary ontological unit for reasoning about conceptual systems and models. FECH articulates (1) a compact ontology of functional primitives and (2) principled criteria for grouping distinct implementations into functional equivalence classes (FECs) based on observable invariants, including input–output relations, compositional behavior, and interaction profiles. It further characterizes canonical transformation and embedding relations that map members of a given FEC to one another while preserving these invariants. Positioned explicitly at the meta-theoretical level, this statement emphasizes structural, operational, and mapping invariants that support robust transfer, modular composition, and defensible claims of conceptual equivalence across representational substrates. FECH also highlights inherent limits of identifiability: multiple internal models may generate indistinguishable observable behavior, constraining reliable inference about internal structure from external performance alone. Accordingly, formal identifiability results, proofs, and domain-specific operationalizations are intentionally deferred to subsequent publications. This preprint establishes authorship and priority for the FECH conceptual framework while preserving flexibility for downstream formalizations, metrics, and empirical instantiations.