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[WITHDRAWN] The Hartmann Time Source Density Operator: A Generalized Framework for Temporal Information Extraction

Christoph Hartmann

Published Nov 16, 2025• 0 citations
Publisher

Abstract

Withdrawn by the author. This document was produced in an exploratory project with AI language models (2025–2026). An independent check in September 2026 found that it contains mathematical errors and novelty claims that cannot be upheld. Its correct mathematical content is either standard theory or is covered, with complete proofs, in:C. Hartmann, Second-order generators with quadratic Leibniz defect on M_n: a self-contained study of ½[H,[H,·]] + [K,·], Zenodo (2026), DOI: [https://doi.org/10.5281/zenodo.22967633].Please cite that text instead. This version is kept for the record only.

DOI
10.5281/zenodo.17632987

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•Apr 2, 2026•0 citations
Withdrawn by the author. This document was produced in an exploratory project with AI language models (2025–2026). An independent check in September 2026 found that it contains mathematical errors and novelty claims that cannot be upheld. Its correct mathematical content is either standard theory or is covered, with complete proofs, in:C. Hartmann, Second-order generators with quadratic Leibniz defect on M_n: a self-contained study of ½[H,[H,·]] + [K,·], Zenodo (2026), DOI: [https://doi.org/10.5281/zenodo.22967633].Please cite that text instead. This version is kept for the record only.
Withdrawn by the author. This document was produced in an exploratory project with AI language models (2025–2026). An independent check in September 2026 found that it contains mathematical errors and novelty claims that cannot be upheld. Its correct mathematical content is either standard theory or is covered, with complete proofs, in:C. Hartmann, Second-order generators with quadratic Leibniz defect on M_n: a self-contained study of ½[H,[H,·]] + [K,·], Zenodo (2026), DOI: [https://doi.org/10.5281/zenodo.22967633].Please cite that text instead. This version is kept for the record only.
Withdrawn by the author. This document was produced in an exploratory project with AI language models (2025–2026). An independent check in September 2026 found that it contains mathematical errors and novelty claims that cannot be upheld. Its correct mathematical content is either standard theory or is covered, with complete proofs, in:C. Hartmann, Second-order generators with quadratic Leibniz defect on M_n: a self-contained study of ½[H,[H,·]] + [K,·], Zenodo (2026), DOI: [https://doi.org/10.5281/zenodo.22967633].Please cite that text instead. This version is kept for the record only.
After further review and discussions among the authors, we want to do further experiment to improve the existing premature results. Specifically, authors want to add more complex analysis to support the results. Given the importance of maintaining the highest standards of academic integrity, we believe that withdrawal is the most appropriate course of action. All authors are fully aware of this decision and have agreed to the withdrawal. We have had several rounds of correspondence regarding this matter, and all authors have been included in these communications to ensure transparency and prevent any potential disputes in the future.
⚠️ CORRECTION NOTICE (added 2026): The author has since identified serious errors in this work through a systematic adversarial audit. The central claims of this record should not be relied upon. Specific issues found across this research program include implementation errors (e.g., conflation of signed cosine with cos²), circular definitions, proof gaps, results that reduce to known theorems, and effects that vanish under proper null models and direct-influence correction. This record is left online for transparency and as a documented case, not as a valid result. For the author's current, audited methodology, see the later work on classical-baseline auditing of quantum-like contextuality claims: https://doi.org/10.5281/zenodo.20680607 — A. Ogasawara This paper introduces the Order-Projection Principle (OPP), a minimal andmodel-independent framework describing when order-dependent observables becomevisible in systems combining noncommutative operations and irreversibleprojection. This record is provided for archival and priority purposes. This manuscript was prepared by the author, with AI tools used for language drafting and organization. The scientific content and conclusions are the author’s own.
⚠️ CORRECTION NOTICE (added 2026): The author has since identified serious errors in this work through a systematic adversarial audit. The central claims of this record should not be relied upon. Specific issues found across this research program include implementation errors (e.g., conflation of signed cosine with cos²), circular definitions, proof gaps, results that reduce to known theorems, and effects that vanish under proper null models and direct-influence correction. This record is left online for transparency and as a documented case, not as a valid result. For the author's current, audited methodology, see the later work on classical-baseline auditing of quantum-like contextuality claims: https://doi.org/10.5281/zenodo.20680607 — A. Ogasawara This paper proposes a minimal structural origin of temporal asymmetry. The central claim is that an observable arrow of time appears whenever two conditions are jointly present: noncommutative operational order and irreversible projection. The argument is intentionally model-independent and does not assume a specific Hamiltonian, spacetime structure, or thermodynamic postulate. The paper shows that time reversal fails to commute with irreversible projection in the presence of noncommutativity, so projected histories acquire a preferred directional ordering at the level of observable records. Temporal asymmetry is therefore treated as a structural consequence of order plus information-reducing observation, rather than as a separate dynamical assumption. A decoder-independent numerical illustration is provided in a linear-Gaussian setting using the MMSE gap as an irreversibility measure. The results confirm that the asymmetry vanishes exactly in both control limits: the commutative limit and the lossless projection limit. A strictly positive asymmetry appears only when noncommutativity and irreversible projection are combined. The paper is intended as a minimal structural analysis of the arrow of time in observable processes and as a foundation for a companion quantitative treatment. Note: Parts of the manuscript were linguistically and structurally refined with the assistance of AI-based tools.All scientific content, analysis, and conclusions are the author's own. Note: This work represents Version 1.0 of an ongoing research program on the Order-Projection Principle (OPP). Minor typographical corrections and clarifications may appear in later versions. The core conceptual claims remain unchanged.