Spectral Relational Anchors for Quantum Subsystem Identification: A\-posteriori Factor Certificates, Recover\-Abstain\-Reject Logic, and Dimension\-Stable Expander Designs

Abstract

Version 1.1 of a finite-dimensional mathematical preprint on robust quantum subsystem identification from relational operator estimates in a common physical matrix-algebra gauge. The paper gives spectral obstruction and localization certificates from a normalized commutator Laplacian, simple matrix-factor discrimination, generic matrix-unit witness construction, a witness-producing REJECT/ABSTAIN/RECOVER procedure using one uncertainty set throughout, explicit finite-error ambiguity radii, outward-rounded post-gap certification, a one-sided relative-expander robustness design principle, a Weyl-versus-expander asymptotic separation, and a first-order tangency theorem explaining quadratic normal distance to the matrix-factor orbit. Standard commutant, JBD, approximate-C*-algebra, TPS-geometry, and expander ingredients are not claimed as new individually.