A.6.0:4.6 - Specialize declaration use without minting another root kind

A signature profile is a constrained use of the same U.Signature kind. The profile states which content is current and which neighboring patterns define or constrain later use.

profile = FormalSubstrate. Declare vocabulary and terms, inference kinds, formal laws, applicability, and the actual declaration dependencies carried in the signature’s claim content. A.6.1 separately governs OperationAlgebra, operation designators, typed argument and result positions, admission conditions, application, and realization. An A.6.1 declaration may cite the FormalSubstrate signature. When a mathematical object is selected as a lens for another entity, C.29 governs the lens-use claim.

profile = PrincipleFrame. Write the postulates and invariants, then name the observable distinction each one requires: what must be observed or compared to tell whether the frame’s claim holds. Cite the separately identified characteristic or measurement declaration that makes that distinction checkable; units, scales, CHR:ReferencePlane values, comparators, and normalizations remain under A.17, A.18, C.16, CHR, A.19.CPM, and A.19.UNM. If the text decides whether a proposed operation application, run, or gate may proceed, move that decision to A.6.1 or the direct evaluation and gate pattern, including A.21/C.11 where applicable. A PrincipleFrame may state what a decision must respect, but it is not that admission decision. For ordinary reuse, apply the frame’s Applicability and the direct subject rules for any reference-plane or model-use-structure question. When the receiving claim needs an exact semantic relation between two local senses whose interpretation bases differ, first recover the two exact F.17 local senses; cite an F.9 Bridge only if its direct predicate obtains and state the bounded-use claim, direction, preservation, loss, and any required reliance separately. Cited declarations remain independently identified objects, not extra PrincipleFrame identity components.

State a relation between two signatures directly as refinement, conservative extension, equivalence, or another independently governed relation only when that relation’s own predicate obtains. Before using the refinement label, compare all three reusable content duties: Vocabulary, Laws, and Applicability. Name the terms preserved, added, or removed; the laws preserved, strengthened, or changed; and whether the population, time, CHR:ReferencePlane, and claim scope stay the same, narrow, or widen. An unexplained applicability widening fails the refinement claim; use another direct relation whose predicate explicitly permits the widening instead of hiding it under refinement. Use a C.29 morphism only when a mathematical structure-preservation claim is actually current.