A.2.6:5 - Solution - Overview

USM keeps the following things distinct:

• U.ContextSlice - one addressable value identified independently of the predicate that later inspects it;
• ContextSliceSet - the mathematical ValueKind Set[U.ContextSlice], used for scope extensions and finite target sets;
• U.Scope - one durable scope value whose extension is one exact ContextSliceSet value;
• U.ClaimScope, U.WorkScope, and U.PublicationScope - C.3 specializations for claim, capability, and publication uses;
• membership semantics, mathematical scope algebra, and reusable operations - three separate layers: the bivalent predicate, its C.29 set representations, and the exact A.6.1 declarations used only when a receiving use needs an actual application and binding.

The primitive claim-scope question is member(x, S) for exact slice x and exact scope S. Intersection handles serial dependence. spanUnion is allowed only for independently supported areas. widen and narrow change the extension; refit preserves it while changing only a scope expression or parameterization. translate is used only when exact local-sense content must cross an obtaining F.9 Bridge and a separate affirmative C.2.1 claim names this translation’s direction, rule, and tolerance. A receiving guard relies on that claim through a passing A.10 disposition or, when an actual named assurance claim is current, a B.3 AssuranceResult for the same use with disposition=supported-for-use; a different label or reference scheme alone selects none of these.

One exact U.ClaimScope may participate in a ModelApplicabilityRelation. That relation, its actual obtaining extent, a selected A.22 structure, a membership evaluation, and a table displaying members remain separate.

Lexical commitments. In normative text and guards, use Claim scope (G), Work scope, and Publication scope. Source words such as applicability, envelope, generality, capability envelope, or validity may remain only when quoted or explained; they do not name additional scope kinds.