E.17.0:4.7.4 - Schemes, scope, transformation, and change

Recover S_dep from E_dependent, S_base from E_base, and S_decl from D. They are three uses of existing U.ReferenceScheme, outside r and its RelationSignature. G may designate exact endpoints, claim values, and declared names through those schemes; designation is neither occurrence obtaining, truth, nor historical participation.

Keep claim-scope widen, narrow, and refit under A.2.6 when no local-sense translation is needed. Use translate only when scope membership must be expressed between exact local senses: require an obtaining F.9 Bridge between their exact SchemeSenseCell values, the separate affirmative claim for that translation’s direction, rule, and tolerance, and the current A.10 or B.3 reliance branch. Scheme difference, same spelling, token reuse, or translation intent triggers no Bridge.

Use A.6.3.RT when the dependency use needs a representation-scheme transition. Recover exact source and receiving epistemes and their construction, preservation, loss, and admissible use when that reliance-facing use requires them. Open RepresentationSchemeTransitionRelation@Context only when the actual transition occurrence is itself material and all six required participants—one independently selected BoundedModelUseStructure : U.Structure, the preserved EntityOfConcern, source and receiving representation epistemes, and source and receiving scheme-description epistemes—plus actual representation-transformation Work are independently recoverable. The @Context suffix is the retrieval label for that A.1.1 use, and Work belongs to the obtaining test rather than the participant tuple. Apply A.6.3.RT’s same-EntityOfConcern, preservation, loss or recoverability, and tuple-plus-scheme-pair identity rules; add a transition-description episteme only when its receiving use needs one. Add C.29 only for a current mathematical lens. Use F.9 separately when the claim actually needs a Bridge between distinct local senses. If interpretation or the proposed dependency use lacks a required basis, name that exact gap and block only that use; the absence of a six-participant transition occurrence or Bridge by itself blocks neither the direct dependency judgment nor a supported exact construction.

Changing only J, an assertion or occurrence description, evaluation result, basis, provenance, production, later-use relation, or representation leaves r unchanged while its endpoint pair is fixed. It also leaves D unchanged while exact <G_dependencyUse,r,S_decl> is fixed. Unknown support does not make an obtaining r non-obtaining, and support for a negative claim creates no positive r. A changed representation transition invalidates judgments that depended on that transition, but changes r only when an endpoint episteme or the direct predicate also changes.

Progressive stopping rule. Use the lightest sufficient rung: readable dependency assertion; reusable RelationSignature when declaration reuse matters; D only for a named A.22 selection-use claim; J only for inspectable inference; evaluation work and exact participation only when evaluation is current; local A.15.PROD only for a needed result-inception or completion claim; provenance, assurance, representation transition, mathematical lens, scope translation, and Bridge only at their own triggers. No higher rung proves a lower-rung occurrence.