E.18.2:4.2 - Expression families
| Expression family | Use when it describes | Required boundary |
|---|---|---|
| graph, hypergraph, network expression, DSM, DMM, MDM, or matrix | dependency, internal transfer, exact cross-member relation, adjacency, interface placement, clustering, or change propagation inside one selected TFS or across one selected TFS network | not the selected TFS or network: apply E.18’s one-TFS identity and selection constraints or E.18.NET’s membership, boundary, and cross-member relation rules to select that ontic subject; E.18.2 defines only this description; not work occurrence, gate passage, or evidence |
| mathematical path or path slice | reachability, carried relation, currentness slice, refresh locality, or crossing-local replay | not a project procedure or performed sequence |
| tuple, record, slot relation, or typed relation expression | slot positions, relation arity, locus typing, and value placement | not a new U-kind and not a replacement for A.6.5 slot discipline |
| morphism, composition, category, operad, optic, or wiring expression | composition, interface, substitution, transfer law, or decomposition of selected transformations | not proof that the represented work can be performed or that interfaces are semantically compatible |
| quotient, fold, coarsening, refinement, or factorization | coarser/finer partitioning, aggregation, retained/lost structure, and alternative decomposition | not an identity claim without preserved/lost structure and return condition |
| algebra, semiring, equation system, or constraint system | operation law, conservation, admissible composition, or constraint propagation over the selected structure | Apply A.6.0 for a separately needed formal-substrate declaration, A.6.1 for a reusable law-governed operation declaration and its application or realization claims, and the relevant subject and evidence patterns for any empirical-law claim. The mathematical expression alone establishes none of those claims. |
| learned representation, embedding, simulation object, or differentiable surrogate | approximate structure, optimization, similarity, or predictive proxy over transformation-flow structure | not architecture adequacy, OOD guarantee, causal proof, or release readiness by itself |
These families are prompts for recovery, not a taxonomy of new FPF kinds. A local expression may combine several families; the record still names exactly one selected TFS or network subject, one current described part when relevant, and the declared use.