What question did this study set out to answer?

This work aims to provide a criterion for evaluating the transition from quantum to classical behavior.

June 20, 2026Open Access

Unified Residual Classicality Criterion for the Quantum-to-Classical Transition

Key Points

This work aims to provide a criterion for evaluating the transition from quantum to classical behavior.
Proposes a residual-vector criterion for quantum-to-classical transition assessment.
Defines predeclared residual channels and their tolerances for various parameters.
Includes validation reports and supplementary materials for reproducibility.
Classicality is only certified when all residual channels meet their specified tolerances.
Offers a finite-time certification framework with stringent error-control conditions.
Provides benchmarks for validating the proposed criterion.

Abstract

This record archives version v1.3 of the manuscript “Unified Residual Classicality Criterion for the Quantum-to-Classical Transition” and its full reproducibility package. This version is the repository companion to the journal-submission version prepared for Quantum Studies: Mathematics and Foundations. It includes the main manuscript, supplementary mathematical notes, supplementary validation report, figure source archive, LaTeX/source archive, benchmark CSV files, Python scripts, manifest files, citation metadata, license file, checksums, and author declarations. The work proposes a falsifiable, comparator-dependent residual-vector criterion for assessing quantum-to-classical behaviour. Classicality is certified only when predeclared residual channels — dynamical, semiclassical, operational, coarse-graining, and open-system — simultaneously pass their declared tolerances for a specified comparator, observable class, resolution, norm, and finite time interval. The work does not claim a universal solution to the measurement problem or a universal proof of quantum-to-classical emergence; it provides a finite-time certification framework with sufficient error-control conditions and controlled benchmark validation. Version-specific DOI: 10.5281/zenodo.20750070Previous version DOI: 10.5281/zenodo.20682081

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