Admissible Record Construction in Physically Non-Selective Quantum Regimes

A Kernel-Role Determinacy Theorem for Record Fixation, Fixed-Domain Quotients, Finite Measurement-Boundary Compatibility, and Boundary-Trace Normal Form This manuscript develops a fixed-domain AASC analysis of the quantum measurement problem centered on admissible record-role fixation rather than outcome production alone. Its governing claim is that AASC is not an optional interpretive overlay on physics: once a physical record is asserted as a non-degenerate determinate object under fixed-domain use, admissibility, standing, reference, and irreversibility are already active as minimal necessity conditions of objecthood. The paper studies physically non-selective quantum regimes, especially Everettian branching structures, in which multiple stable post-measurement records are physically realized without a privileged selector fixing one record as the standing evidential continuation for downstream reuse. It distinguishes physical record occurrence from the stronger requirement that a record stand as the same evidential object across retained reuse, prospective reuse, deliberation, comparison, and theory-level confirmation. The central theorem establishes that once measurement records are required to support standing-bearing downstream use, admissible record-fixation assignments are structurally forced. The manuscript proves that admissible record-fixation assignments form a forced same-domain realization space, standing-bearing evidential content factors through a unique measurement-record quotient, alternative same-scope equivalence relations collapse, fixation commutation is necessary for theory-level evidential stabilization, and unresolved admissible multiplicity yields assignment-relative evidential lineage rather than construction-relative evidential determination. A major addition in this version is an explicit finite quantum measurement construction integrated into the manuscript body. The finite development defines a two-branch measurement carrier with fine and merged records, denominator-two weights, a balanced amplitude witness, density numerator tables, selective and non-selective instruments, environment records, projective branch maps, finite effects, zero-product projector/repeatability structure, and cross-surface compatibility. It proves that record, pointer, density, instrument, channel, effect, projector/repeatability, decoherence, Born-weight, and coarse-record surfaces agree on the declared finite branches while no declared non-selective surface supplies a hidden fine-record selector. The associated Lean 4 formalization has been synchronized through release v0.9.1. It verifies the finite measurement-boundary stack over declared carriers and hypotheses, including the corrected zero-effect/projector layer, finite selector-boundary facts, closed-stack endpoint, and audit manifest. The formalization is finite, conditional, and manuscript-facing: it does not claim to derive full Hilbert-space quantum mechanics, general POVM/PVM theory, full operator algebra, physical decoherence theory, the continuum Born rule, physical selection, interpretive truth, or a physical no-collapse theorem. The manuscript further develops asymmetry-source exhaustion for admissible record-fixation, Everettian asymmetry exhaustion, fail-closed fixation conditions, selector-exhaustion for interpretation packages, and boundary-trace fixation as the residual admissible normal form. A persistence-bearing continuation bridge connects measurement-record fixation to realized continuation loci and standing-bearing downstream reuse. Under this interpretation, measurement records are not merely abstract evidential objects but persistence-bearing continuation anchors within admissible fixed-domain lineage structure. The result is not a collapse dynamics, hidden-variable theory, or new physical law. Its claim is st