BKT-43A Formalization of Relational Closure and Non-Closure Estimators for Quantum-State Stability

This record provides the bilingual publication package of document BKT-43A/USC-RA1/ZENODO-20260707-v13, entitled “Formalization of Relational Closure and Non-Closure Estimators for Quantum-State Stability”, with the subtitle “A New Class of Mathematical-Physical Tools for Studying and Diagnosing the Stability of Quantum Systems. ” The work presents a family of relational closure and non-closure estimators as a coherent mathematical-physical apparatus for diagnosing the stability of quantum states. The core formalism includes a sectoral closure estimator, an attractor-topological-spectral extension, a logarithmic multichannel aggregator, a covariance-aware variant, a geometric estimator based on the Bures distance, and a differential-dynamical layer. The article includes a canonical tabular compendium of the formulas, parameters, formal meaning, and physical interpretation of the estimators. The model-computational verification is based on Bell-state dephasing, the Bures channel, quantum Fisher information, Lindblad dynamics, a finite Kitaev-chain test, and the analysis of quantum-error correlations. The results have formal and computational status: they confirm the internal consistency of the definitions, agreement with analytic results of the reference model, and correct treatment of channel redundancy by the covariance-aware estimator. They do not yet constitute external experimental validation. This record continues earlier models and published formal materials. In particular, it develops the sectoral (₄₅₅) and (₄₅₅, ₀ₓₒ) model from BKT-Y16-20260622-v10. 2, extends the three-level relational non-closure estimator apparatus from BKT-43 USC-RA1 20260619 v1. 3, and organizes earlier Zenodo records related to the (K^ₐ₌) estimator, relational geometry, and response tomography: 10. 5281/zenodo. 19893953, 10. 5281/zenodo. 20798037, 10. 5281/zenodo. 20797198, and 10. 5281/zenodo. 19824700. The response-tomography record is used as methodological context, not as validation evidence for the quantum calculations presented in the present article. The package contains the Polish version, the English mirror version, LaTeX source files, figures, MasterData tables, auxiliary scripts, bibliography, and editorial-technical audit reports. The purpose of the record is to provide a complete, reproducible, and citable formalization package for the estimator family before further editorial assessment and possible experimental validation.