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Library / First Principles Framework (FPF) - Core Conceptual Specification
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C.3.2:4 - Four Objects and One Applicability Result

ObjectMeaningIdentity and governor
U.Kind individual and orderThe intensional kind and any obtaining U.SubkindOf facts used by typed reasoning.C.3 and C.3.1; not this declaration, a practice/source label, or a new public-kind admission.
KindSignatureA U.Signature declaration episteme whose exact EntityOfConcern is the kind.A.6.0 and C.2.1 govern the episteme and its editions.
classification judgmentOne evaluation for an admissible exact candidate, kind, signature edition, and slice, returning true, false, or unknown.C.3.2; it is not a direct relation occurrence or guard result by default.
KindExtension(k, slice)An optional set-valued representation of admissible candidates judged true for the pinned signature edition and slice.Local calculation unless C.29 governs a claim-bearing use.

ClassificationAdmissibility(candidate, kind, signatureEdition, slice) returns admissible or not-applicable. It is a precondition result, not another kind or membership value. not-applicable means the candidate fails the declared candidate ValueKind/interpretation or the slice falls outside signature applicability; no classification judgment is formed.

Scope is not attached to the kind. A KindSignature episteme may have its own U.ClaimScope; a separate classification assertion has the scope of that assertion; and U.ContextSlice remains an evaluation input.