A.2.6:6.2 - U.Scope - set-valued scope

U.Scope is a durable value with one exact extension of mathematical ValueKind ContextSliceSet. U.ClaimScope, U.WorkScope, and U.PublicationScope are its C.3 specializations for receiving uses; the specialization does not copy the extension or add another identity discriminator.

For exact scope S and exact slice x, the primitive delimitation semantics is:

member(x, S)

The predicate has the exact slice and exact scope as arguments. It is not by itself an explicitly individuated U.Relation occurrence. Included slices satisfy it; excluded slices do not. The excluded area is not materialized as an unbounded complement entity.

For effective reference scheme RS, define extension_RS(S) := { x : U.ContextSlice | member(x, S) }. Two scope designators resolve to the same extensional U.Scope value when their extensions contain exactly the same independently identified slices under the same or explicitly reconciled reference scheme. An equivalent predicate expression, unit conversion, factoring, or publication change can preserve that value; a boundary change that adds or removes even one slice identifies another scope value.

A set or predicate expression, table, diagram, or query result can represent or designate a scope or a set of evaluated slices under C.29 and C.2.1.

USM admits subset, intersect, spanUnion, translate, widen, and narrow over exact scope extensions. refit is a same-extension normalization: it changes a predicate expression, units, or factoring while preserving member(x,S) for every exact slice under the effective reference scheme. A changed expression may require another declaration or claim-bearing episteme edition under its direct governor; it identifies another U.Scope only when the extension changes.

If a receiving use requires stable identity for membership occurrences, A.2.6 must first declare a direct relation kind with exact participant meanings, obtaining condition, recurrence rule, and non-optional occurrence-identity rule under A.6.REL. Until then, do not use ScopeDelimitationRelation, ScopeDelimitationMode, or ScopeDelimitationInterval.