Full-Curve Non-Identifiability of Pointer Information under Fragment-Size Averaging: A Certified N=4 Witness

Fragment-size averages of the pointer Holevo information summarize how quantum environmental records are accessed without specifying their microscopic locations. We give a focused N=4 non-identifiability result: assuming the previously archived interval-certified root for a four-qubit two-branch witness, a second, two-carrier pure-branch ensemble exists with exactly the same complete size-averaged Holevo curve (A1, A2, A3, A4). The key additional step is a rational-interval verification of g(c) < 4A1 < 2g(sqrt(c)), where g(t) = h2((1+t)/2) and c is the overlap of the original branches. Continuity then provides the matching two-carrier ensemble, and the support-projection identity forces agreement at the remaining fragment sizes. Independent 16-dimensional state-vector calculations reproduce the matching averaged curves to floating-point precision; these diagnostics are not used as a substitute for the existence proof. The result concerns one certified curve in an equiprobable two-branch pure-state model, not equality of every individual fragment's information, an open family of curves, or arbitrary environment sizes. The original Krawczyk certificate is a documented imported premise and was not rerun in the present extension audit. Unrefereed preprint. Scientific claims are conditional on the archived original OBS01 certified-root premise. Supporting files provide numerical and interval checks, recorded base certificates and their hashes. Base Krawczyk/Arb computations were not rerun in this extension. This is not a claim of global priority or experimental realization. Manuscript, original notes and data are CC BY 4.0; original Python code is MIT; embedded archived materials retain their applicable component notices and rights. AI-assisted work is disclosed in the manuscript.

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-14
DOI
https://doi.org/10.5281/zenodo.23365301
Primary Topic
Quantum Mechanics and Applications
Type
preprint
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preprint

Full-Curve Non-Identifiability of Pointer Information under Fragment-Size Averaging: A Certified N=4 Witness

Yoichi Tsujisawa
Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
preprint

Full-Curve Non-Identifiability of Pointer Information under Fragment-Size Averaging: A Certified N=4 Witness

Yoichi Tsujisawa
preprint en

Abstract

Fragment-size averages of the pointer Holevo information summarize how quantum environmental records are accessed without specifying their microscopic locations. We give a focused N=4 non-identifiability result: assuming the previously archived interval-certified root for a four-qubit two-branch witness, a second, two-carrier pure-branch ensemble exists with exactly the same complete size-averaged Holevo curve (A1, A2, A3, A4). The key additional step is a rational-interval verification of g(c) < 4A1 < 2g(sqrt(c)), where g(t) = h2((1+t)/2) and c is the overlap of the original branches. Continuity then provides the matching two-carrier ensemble, and the support-projection identity forces agreement at the remaining fragment sizes. Independent 16-dimensional state-vector calculations reproduce the matching averaged curves to floating-point precision; these diagnostics are not used as a substitute for the existence proof. The result concerns one certified curve in an equiprobable two-branch pure-state model, not equality of every individual fragment's information, an open family of curves, or arbitrary environment sizes. The original Krawczyk certificate is a documented imported premise and was not rerun in the present extension audit. Unrefereed preprint. Scientific claims are conditional on the archived original OBS01 certified-root premise. Supporting files provide numerical and interval checks, recorded base certificates and their hashes. Base Krawczyk/Arb computations were not rerun in this extension. This is not a claim of global priority or experimental realization. Manuscript, original notes and data are CC BY 4.0; original Python code is MIT; embedded archived materials retain their applicable component notices and rights. AI-assisted work is disclosed in the manuscript.

Zenodo (CERN European Organization for Nuclear Research)
Quantum Mechanics and Applications
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