E.24.UK:4.2a - Durable Membership and C.3 Projection

Durable U-kind membership and C.3 classification remain distinct, but C.3 now relies on an admitted meta-kind. E24UK-AR-UKIND-R5-01 admits U.Kind; its individuals are reusable intensional classification distinctions recovered through candidate domain, operative membership condition, intended member/non-member boundary, and continuity rule. A KindSignature, source or practice label, scheme, extension, assertion, or publication is not that kind individual.

For an independently identified candidate x, membership in an admitted durable subject kind K still follows the direct predicate M_K under the accepted settlement. A C.3 U.Kind individual may declare or reuse that predicate for typed reasoning without admitting another public U.* kind. A row, spelling, record, or unresolved evaluation changes neither the direct predicate nor the world-side extent.

E24UK-AR-USUBKINDOF-R5-01 separately admits U.SubkindOf as a same-individual dependent kind under U.Relation. Its individuals are the same relation occurrences already admitted under U.Relation whose exact ordered kind participants satisfy C.3.1’s criterion-entailment branch or exhaustive deliberately closed-domain branch within declared applicability. Scheme and signature editions qualify the obtaining test and assertion; they are not participants or occurrence-identity discriminators.

For any other same-individual-dependent admission, the settlement states M_Kd(x) -> M_Kr(x) and the same individual keeps root identity. For identity-dependent, the cited rule defines or constrains a two-place dependence relation from the distinct dependent individual to one exact root-kind individual and supplies every additional discriminator. A root reference alone closes neither form.

The recovered A.2.2 capability need takes the reject exit in section 4.2c: ordinary holder-ability claims remain usable without a second kind or an invented dependence relation. U.Structure follows the accepted A.22 architecture instead. A.22 identifies one context-independent selected organization from four and only four discriminators: exact independently identified constituents, exact selected obtaining relation occurrences, exact constraints as applied, and one named selection-use frame. E24UK-AR-USTRUCTURE-R12-01 records the root admission. A bounded-context label, system, team, subsystem, model, method, work occurrence, result episteme, description, view, graph, table, representation, publication, or use does not supply that identity.

BoundedModelUseStructure and A.22’s conditional crossing-analysis specialization are same-individual dependent predicates over already identified U.Structure values. The same structure individual keeps its A.22 identity; satisfying the corresponding A.22:4.1c condition adds the specialization and implies U.Structure membership. The bounded-model-use name has a current F.17 row. The crossing-analysis condition is strictly conditional on independently governed exact obtaining crossing occurrences plus all four A.22 base discriminators; because no positive member exists, its NameCard label remains local and pending and is not consumed here as public vocabulary. Neither condition adds a second structure individual, root identity, ambient-context discriminator, holonhood, agency, description identity, or view identity. An A.2.6 claim-scope value or membership fact affects the selection only when an exact applied constraint refers to it; that applied constraint, not the bare scope or membership outcome, occupies the third discriminator. A scope, context, label, view, publication, representation, or selected use alone creates neither the base structure nor specialization membership.

The three A.1.1 relation-kind designations consumed by the bounded-model-use test are current through UTS.ModelApplicabilityRelation.FPFCore.2026-07-25, UTS.ModelUseRelation.FPFCore.2026-07-25, and UTS.ModelExpressionCoherenceRelation.FPFCore.2026-07-25. Those F.17 rows publish only the names. A.1.1 defines each relation; the corresponding passage states its predicate, participants, obtaining condition, and occurrence-identity rule. A row, NameCard, matching token, or appearance in this registry makes no occurrence obtain and grants no BoundedModelUseStructure membership.

A project that needs bounded quantification may use an admitted U.Kind individual through C.3.2. If the kind’s membership criterion cites an already governed durable subject-kind predicate, that projection neither admits another durable kind nor creates an automatic U.SubkindOf fact. A project-specific kind remains an individual of U.Kind without acquiring its own public U.* label; proposing such a label reopens E.24.UK for that subject kind.