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Access-scale selection of public quantum records in critical and gapped environments

Samuele Garbati, Simona Garbati

Published Jun 6, 2026• 0 citations
Publisher

Abstract

This record contains the post-PRA rebuilt preprint and source package for the working paper “Access-scale selection of public quantum records in critical and gapped environments”. The manuscript introduces a context-indexed selector for finite public quantum records and centers on a critical-versus-gapped selector theorem. The main result is that critical environmental correlations can create a scale-growing public-record selector advantage, whereas gapped correlations do not generically produce that advantage. The package includes the main manuscript, supplementary material, LaTeX sources, bibliography, citation metadata, licenses, and manifest files.

DOI
10.5281/zenodo.20569123

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This record contains the post-PRA rebuilt preprint and source package for the working paper “Access-scale selection of public quantum records in critical and gapped environments”. The manuscript introduces a context-indexed selector for finite public quantum records and centers on a critical-versus-gapped selector theorem. The main result is that critical environmental correlations can create a scale-growing public-record selector advantage, whereas gapped correlations do not generically produce that advantage. The package includes the main manuscript, supplementary material, LaTeX sources, bibliography, citation metadata, licenses, and manifest files.
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Quantum Darwinism identifies objectivity with redundant environmental records of system information. A complementary question arises when more than one finite-strength diagnostic record is available to an observer with a declared access rule: which record is selected at a given fragment size? We formulate this question as a context-indexed public-record selector and derive a microscopic asymptotic mechanism for access-scale inversion. The model contains a central qubit coupled simultaneously to a local spin-meter bath that records a σz diagnostic and to a critical transverse-field Ising bath that records a σx diagnostic through the Ising order parameter. For contiguous fragments of length ℓ, the local meter gives trace-distance evidence Fz(ℓ,t)=Cz(t)ℓ+o(ℓ), whereas the critical bath gives Fx(ℓ,t)=Cx(t)ℓ^{7/4}+o(ℓ^{7/4}) in the Ising scaling regime. With public amplitude A_i^pub(ℓ)=[R(ℓ)F_i(ℓ)]^{1/2} and block redundancy R(ℓ)=N/ℓ, the local record is selected at small access scales but the critical record is selected for ℓ>ℓc, with ℓc=[Cz(t)/Cx(t)]^{4/3} up to sector-size and scaling corrections. The crossover is not simultaneous perfect broadcasting of incompatible observables; it is a context-indexed finite-record selection rule. An exact free-fermion/Toeplitz scaling check of the critical bath gives a block-susceptibility exponent consistent with 7/4, while exact diagonalization of a small noncommuting Hamiltonian and parameter scans are included as finite-size pilots of the selector mechanism. This record is a public preprint/manuscript version and has not been peer-reviewed as a journal publication.
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