Standing Carrier Identity Closure

A Same-Scope Exhaustion Theorem for Source-Distinct Physical Realizations under AASC This paper develops a clean-room theorem for determining when source-distinct physical realizations represent genuinely distinct standing carrier identities and when they are merely different source or provenance presentations of one target-relative carrier. For a fixed target-frozen carrier comparison scope, the paper defines the complete standing continuation signature: the totality of target-authorized witness outputs after all licensed same-scope continuations. Equality of these signatures is shown to induce the unique admissible standing-carrier identity quotient compatible with stable reference, carrier descent, identity-preserving redescription, reuse consistency, bivalent standing, no same-act repair, and the absence of a second same-scope admissibility-bearing classifier. The central result establishes that: source multiplicity does not by itself imply carrier multiplicity; every elementary source variation is exhaustively classified as anchor, tensor, or skin/provenance; finite composite source differences decompose into anchor motion, tensor-determined same-scope content, and skin/provenance remainder; any finer quotient retains an unwitnessed distinction and is over-resolved; any coarser quotient identifies a target-witnessed difference and is under-resolved; a singleton standing-carrier identity exists exactly when the complete continuation-signature image is singleton; a genuinely non-singleton quotient is final for same-scope identity and cannot be collapsed by provenance, simplicity, representative choice, ranking, or another auxiliary classifier. The paper further separates identity closure from physical realization. If the final standing-carrier quotient is non-singleton, a structural pre-lock singleton can arise only through one of two lawful routes: an independently formed realized-carrier trace or an impossibility theorem excluding all rival classes. In the absence of either route, the strongest valid endpoint is irreducible structural underdetermination at carrier resolution. An explicit activation theorem makes the application burden fail-closed. Before any carrier count is accepted, the target-specific witness and continuation interface must be independently frozen and shown to exhaust the relevant definedness, compatibility, failure, quotient-factorizing, and continuation loci. Failure to discharge this activation certificate does not license a singleton conclusion. The result provides a general framework for separating source-generated candidate multiplicity, standing carrier identity, and realized carrier selection without silently changing the target, importing a preference, or promoting provenance data into an unauthorized physical classifier. Principal theorem package The manuscript establishes: Carrier-interface activation and target-completeness. The unique standing-carrier quotient by continuation-signature equality. Anchor–tensor–skin exhaustion for source differences. No promotion of source labels or auxiliary classifiers. Exhaustive adjudication of proposed carrier distinctions. Post-quotient realization exhaustion. A necessary-and-sufficient singleton criterion based on signature-image cardinality. The framework is formulated under the Admissibility And Standing Constraint (AASC) and is intended for later application to concrete carrier-classification and particle-structure problems.