Author's Note (August 24, 2026): This exploratory preprint is currently being re-evaluated as part of a methodological audit of the transformation framework used in this research program. In particular, I am reassessing whether the reported Bell-type → uniform → anti-type inversion should be interpreted as a distinctive consequence of the previously defined “zero-operation” framework or as behavior arising within a broader class of transformations on probability distributions. The numerical observations, their dependence on the chosen transformation class, and the generality of the structural interpretation are therefore being re-audited. Any necessary corrections, reclassification of claims, or revisions will be documented transparently in a subsequent version. This exploratory preprint develops a minimal distributional transition model in which a Bell-type correlation distribution is continuously transformed into an anti-type correlation distribution through a uniform neutral point. The paper distinguishes terminal uniformization from transitional uniformization and connects this distinction to the zero-operation framework.
Author's Note (August 24, 2026): This exploratory preprint is currently being re-evaluated as part of a methodological audit of the transformation framework used in this research program. In particular, I am reassessing whether the reported Bell-type → uniform → anti-type inversion should be interpreted as a distinctive consequence of the previously defined “zero-operation” framework or as behavior arising within a broader class of transformations on probability distributions. The numerical observations, their dependence on the chosen transformation class, and the generality of the structural interpretation are therefore being re-audited. Any necessary corrections, reclassification of claims, or revisions will be documented transparently in a subsequent version. This exploratory preprint develops a minimal distributional transition model in which a Bell-type correlation distribution is continuously transformed into an anti-type correlation distribution through a uniform neutral point. The paper distinguishes terminal uniformization from transitional uniformization and connects this distinction to the zero-operation framework.
Author's Note (August 24, 2026): This exploratory preprint is currently undergoing methodological re-evaluation. The “zero-operation” framework used here as the basis for target-based control is being reassessed, including whether these transformations constitute a distinct operator class or are better understood within a broader class of transformations on probability distributions. Consequently, the interpretation and generality of the reported control results, including their dependence on the chosen candidate transformation set, are under re-audit. This notice does not by itself imply that the numerical results are incorrect; rather, the claims concerning zero-operations as a control framework should be regarded as provisional. Any necessary corrections, reclassification of claims, or revisions will be documented transparently in a subsequent version. This exploratory preprint formulates zero-operation selection as an inverse problem over probability distributions. Starting from a Bell-type four-state distribution, it searches over operation types, redistribution rules, and parameters to identify operations that approach or reach specified target distributions. Basic targets are reached by corresponding simple operations, while the soft-00 target requires a composite rule combining fixation and off-diagonal redistribution. This is the fourth manuscript in a preprint series on zero-operation-based quantum computer theory.
Author's Note (August 24, 2026): This exploratory preprint is currently being re-evaluated as part of a broader methodological audit of the subsequent research program. In particular, the structural interpretation of the reported results and its relationship to later abstract transformation models are being reassessed. This notice does not indicate that the numerical results reported in this preprint have been shown to be incorrect; rather, their interpretation and scope are under review. Any necessary corrections or revisions will be documented transparently in a subsequent version. This exploratory preprint examines whether representative quantum noise channels can be interpreted as distinct modes of structural reconfiguration in observable quantum correlation distributions. Using Bell-state-based simulations, the study compares depolarizing noise, phase damping, and amplitude damping across Z, X, and Y measurement bases. The results suggest that noise-channel type and measurement basis jointly determine whether the observed distribution tends toward preservation, uniformization, fixation, or observation-dependent deformation.
Author's Note (August 24, 2026): This exploratory preprint is currently undergoing methodological re-evaluation. The “zero-operation” bases used to define and expand the reachable sets in this study are being reassessed, including whether these transformations constitute a distinct operator class or are better situated within a broader class of transformations on probability distributions. In particular, I am re-auditing which features of the reported reachable-set expansion are specific to the proposed zero-operation bases and which may instead follow more generally from the choice and enlargement of the available transformation set. The numerical results, their dependence on the chosen operation basis, and the generality of their interpretation are therefore under review. Any necessary corrections, reclassification of claims, or revisions will be documented transparently in a subsequent version. This exploratory preprint analyzes how reachable regions in a four-state probability-distribution space depend on the available zero-operation rule basis. Starting from a Bell-type distribution, it compares symmetric and asymmetric operation bases, showing that mixed rules expand one-dimensional trajectories into higher-dimensional reachable regions, while symmetry constraints can prevent exact reachability of asymmetric targets. This is the fifth manuscript in a preprint series on zero-operation-based quantum computer theory.
⚠️ 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 work reports a system-spanning numerical investigation of order-dependenteffects arising from noncommutative operational histories under irreversibleprojection. Using several representative systems with distinct dynamics—including theIsing model, neural networks, and simulated annealing—we analyze history-dependentdifferences through a minimal, model-agnostic framework based on projection andlow-mode decomposition. We show that a low-dimensional geometric structureconsistently emerges across systems, dominated by a small number of modes, andthat this structure is preserved only when represented in a vector (complex)form rather than by scalar amplitudes alone. The observed phase variability across realizations is interpreted as a gaugedegree of freedom, while directional overlap provides a robust invariant forcross-system comparison. Differences between systems are found not in theexistence of the geometric core itself, but in the visibility of its rotationalresponse under changing conditions. This record is intended as a technical preprint to establish precedence anddocument the numerical and geometric findings. Broader theoretical connectionsand applications are deliberately left outside the scope of the present work.Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, 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 manuscript explores structural aspects of irreversible projection and sequential operations under minimal assumptions.Rather than introducing new physical postulates, it examines how order dependence and relational representations arise in systems subject to information deletion. The analysis focuses on the structural consequences of projection processes and discusses connections to phase-like representations, interference-type effects, and approximate reversibility in weak-projection regimes. The work is intended as a formal and conceptual contribution to the study of order-dependent dynamics across physical and computational systems.No modification of standard quantum theory is proposed.Note: Parts of the manuscript were linguistically and structurally refinedwith the assistance of AI-based tools.All scientific content, analysis, 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 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.