A.6.4:4.2 - Formal declaration and object boundaries

Repeated formal use may be declared in an A.6.0 U.Signature(profile=FormalSubstrate) episteme. That declaration is about the local subtype EntityOfConcernRetargetingMorphism; it is not the subtype, one arrow, a use claim, or an application occurrence.

SubjectKind     = local formal subtype EntityOfConcernRetargetingMorphism of EpMorphism
RangedValueKind = admitted ordered-pair range over exact U.Episteme values satisfying the declared endpoint-kind constraints
ResultKind      = omitted; r is the declared subject, not an operation result
Applicability   = selected formal substrate and endpoint and arrow-family conditions

X and Y are exact C.2.1 epistemes. r : X -> Y is one local mathematical arrow in the selected formal substrate. Its identity uses the exact endpoints, arrow rule or designator, and the selected substrate’s equivalence criterion; the endpoints alone do not identify it. The declaration states which parts of X and Y’s claim content, exact EntityOfConcern, and effective ReferenceScheme remain the same or differ. If r’s rule reads a representation or another separately obtaining relation, it names the exact occurrence and compares endpoint facts without changing that occurrence.

A.6.4 reuses the one A.6.2 formal model: category Ep, endpoint-only thin category EoCBase, dom, cod, identities, compose, and the declared mapping α. For retargeting arrow r, α(r)=u_{α(X),α(Y)} is the unique formal endpoint arrow between the independently different EntitiesOfConcern. It records only that endpoint difference and deliberately forgets r’s arrow rule; it is not an independently declared domain or world-side relation. The local classification function entityOfConcernChangeMode returns retarget for r and records the same endpoint difference. It classifies only the endpoint-change mode; it adds no domain-function evaluation or second retargeting calculus.

The bounded-use assertion q, current-case judgement, and any application occurrence remain separate. Add A.6.5 SlotSpecs only inside an exact reusable direct-relation declaration; they are not fields of r, X, Y, or q.