This preprint defines the classical candidate-geometry baselines that should be compared before any claim of non-classicality in the quantum-like contextual non-additivity, order effects, and Bell-type indicators reported for large language models (LLMs) and masked language models (MLMs), and quantifies their explanatory power and limits. It does not claim physical quantum coherence in AI, nor a full explanation of AI quantum-like behavior. The revised edition adds four components. (i) Detection-power certification: the detector's condition is ICC < S_odd - 2, and Tsirelson-level injection tests certify that genuine contextuality of that magnitude would be detectable at the empirical signaling levels; the 312 Experiment-4 tables all satisfy S_odd < 2 with zero corrected excess, so the negative result is not attributable to ICC-induced blindness. (ii) A product-distribution theorem establishing that the zero excess of independent scoring is a mathematical necessity, not an empirical finding. (iii) A structural reproduction of the Lo et al. construction with a no-model null: uniformly random marginals without any language model already reach a CbD-contextual rate of 0.667 (vs. 0.711 reported), and the real BERT/RoBERTa rates are largely indistinguishable from a marginal-matched sign-randomized null at substantive effect sizes. (iv) A multi-model audit across six models from four families: raw S_odd > 2 appears (max 2.773) but is entirely explained by direct influence, with zero corrected excess across all 144 tables and on the powered subset. The package includes the manuscript (LaTeX source and PDF), figures, reproduction code, and data (including the raw joint probabilities from which the per-table metrics are regenerated and cross-checked). Central thesis: reading AI quantum-like behavior as non-classicality requires exceeding not the raw score but the combination of classical candidate-geometry baselines, direct-influence correction, detector-power certification, and a no-model null. This work is neither a full reproduction nor a refutation of Lo et al.; it audits the interpretation of raw contextual-instance counts. Manuscript language: English. Code is released under the MIT License; text and figures under CC BY 4.0. 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.
This preprint defines the classical candidate-geometry baselines that should be compared before any claim of non-classicality in the quantum-like contextual non-additivity, order effects, and Bell-type indicators reported for large language models (LLMs) and masked language models (MLMs), and quantifies their explanatory power and limits. It does not claim physical quantum coherence in AI, nor a full explanation of AI quantum-like behavior. The revised edition adds four components. (i) Detection-power certification: the detector's condition is ICC < S_odd - 2, and Tsirelson-level injection tests certify that genuine contextuality of that magnitude would be detectable at the empirical signaling levels; the 312 Experiment-4 tables all satisfy S_odd < 2 with zero corrected excess, so the negative result is not attributable to ICC-induced blindness. (ii) A product-distribution theorem establishing that the zero excess of independent scoring is a mathematical necessity, not an empirical finding. (iii) A structural reproduction of the Lo et al. construction with a no-model null: uniformly random marginals without any language model already reach a CbD-contextual rate of 0.667 (vs. 0.711 reported), and the real BERT/RoBERTa rates are largely indistinguishable from a marginal-matched sign-randomized null at substantive effect sizes. (iv) A multi-model audit across six models from four families: raw S_odd > 2 appears (max 2.773) but is entirely explained by direct influence, with zero corrected excess across all 144 tables and on the powered subset. The package includes the manuscript (LaTeX source and PDF), figures, reproduction code, and data (including the raw joint probabilities from which the per-table metrics are regenerated and cross-checked). Central thesis: reading AI quantum-like behavior as non-classicality requires exceeding not the raw score but the combination of classical candidate-geometry baselines, direct-influence correction, detector-power certification, and a no-model null. This work is neither a full reproduction nor a refutation of Lo et al.; it audits the interpretation of raw contextual-instance counts. Manuscript language: English. Code is released under the MIT License; text and figures under CC BY 4.0. 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.
⚠️ 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 short report investigates order-dependent geometric structurearising from noncommutative histories in a classical statistical system.Using the two-dimensional Ising model as a concrete physical setting,we show that history-induced structure is not directly observablein conventional scalar projections, but can be detected througha gauge-invariant low-order complex-mode representation. The analysis demonstrates that noncommutative update historiesgive rise to a reproducible low-dimensional geometry,which remains hidden under phase-dependent scalar observables.This work provides a minimal physical realization of theorder-projection framework introduced in earlier theoretical studies,without invoking quantum dynamics or wavefunction-based assumptions.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.
Contextuality is a distinguishing feature of quantum mechanics, and there is evidence that it is a necessary condition for quantum advantage in the context of magic state distillation. To harness it, researchers have been asking whether similar phenomena arise in other domains. The answer has been affirmative, e.g. in behavioural sciences. However, one has to adopt frameworks that take some degree of signalling into account. Two such frameworks exist: (i) a signalling-corrected sheaf-theoretic model and (ii) the Contextuality-by-Default (CbD) framework. This paper provides the first large-scale experimental evidence for contextuality in the large language model BERT. We constructed a linguistic schema modelled over a contextual quantum scenario, instantiated it in the Simple English Wikipedia, and extracted probability distributions for the instances. This led to the discovery of 77 118 sheaf-contextual and 36 938 948 CbD contextual instances. We prove that these contextual instances arise from semantically similar words by deriving an equation that relates degrees of contextuality to the Euclidean distance of BERT’s embedding vectors. Our linguistic schema is a variant of the coreference resolution challenge. These results suggest that quantum methods may be advantageous in the field of natural language processing.
Question-order effects in human survey data have been reported to approximately satisfy the QQ (quantum question) equality, a parameter-free prediction of the standard projective quantum question-order model. We develop this equality into an audit framework for sequential binary judgments of autoregressive large language models (LLMs). Theoretically, we characterize mechanism families that satisfy QQ robustly, show that classical repetition can reproduce the equality exactly, and combine QQ with the rank-2 Contextuality-by-Default criterion through ∣qQQ∣≤OSS. This separates order sensitivity, QQ imbalance, and residual contextuality rather than treating them as interchangeable signatures. Methodologically, we introduce a committed multi-turn forced-branch protocol that reconstructs order-conditioned joint distributions from next-token log-probabilities under counterbalanced label mappings and pre-specified health gates. A first-signal pilot on an open-weight instruction-tuned model reveals the central measurement problem. Although all pre-specified health gates passed, the binary-conditioned distributions were near-deterministic for 17 of 18 item pairs under the direct-evaluation framing and 7 of 8 under the persona framing. Label assignment materially changed several mapping-specific QQ verdicts, and no item was certified as residually contextual. Thus, under the tested conditions, the observed QQ outcomes did not uniquely identify a response mechanism in the presence of a saturated and label-sensitive measurement interface. The main implication is methodological: next-token probabilities should not be interpreted as survey-response distributions without first establishing adequate dispersion. We therefore argue that saturation screening and label counterbalancing should precede structural interpretation in distribution-level audits of LLM judgments.
⚠️ 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.
A Kernel-Role Determinacy Theorem for Bell-Witness Fixation, No-Signaling, and Tensor-Level Compatibility This manuscript develops a fixed-domain AASC analysis of Bell-nonlocal quantum entanglement as a theorem of reusable witness determinacy. It does not introduce hidden variables, modify quantum mechanics, derive Hilbert-space formalism from below, or propose a new signaling mechanism. Instead, it asks a prior structural question: once a Bell-type operational family is used as the same non-degenerate witness across settings, lawful transformations, retained records, comparison, and later classification, what admissible same-domain standing form is forced? The governing claim is that AASC is not an optional interpretive overlay on physics. Once an operational Bell family is asserted as a determinate reusable witness, admissibility, standing, reference, and irreversibility are already active as minimal necessity conditions of same-witness objecthood. Target instantiation therefore carries governance occupancy: an alleged determinate Bell witness with no admissible governance realization is not an empty alternative, but a refusal or retyping of the target. The manuscript defines finite operational Bell objects with explicit setting carriers, outcome families, channel/interface data, standing-token valuations, continuation and report/reuse structure, comparison profiles, and act-time status. It then defines object-indexed query sorts, dependent response families, exactly recoverable operational simulations, lawful Bell groupoids, six governance-effect functors, and target-active extensional governance equivalence. The result is a typed interface in which arbitrary native formalisms can be compared by their target-bearing governance effects rather than by their internal syntax. The central Bell-specific theorem states that every same-target candidate-admissible Bell-governance construction is forced component by component into the certified boundary-compatible standing form on the complete target-active practice. Candidate admissibility does not assume the canonical form at the outset. Instead, target occupancy, lawful transport, standing-flow exclusion, compatibility certification, coordinate-deviation exhaustion, and componentwise closure force exact target-bearing realization and governance equivalence to the canonical representative CP∗C^{*}_{P}CP∗. The target-induced governance quotient therefore has exactly one element. The Bell carrier is treated as a compatible empirical model on a finite measurement cover. Bell-local completion is identified with the existence of a global section, and Bell nonlocality is the obstruction to such a section. The manuscript separates operational marginal invariance, absence of controllable communication, and exclusion of same-domain standing transport. No-signaling is therefore preserved without retyping Bell nonlocality as superluminal communication, metric transport, distant repair, or hidden standing transfer. The finite-dimensional quantum specialization uses the standard bipartite tensor-product and local-POVM carrier. Every separable realization in that carrier is Bell-local; therefore, if the fixed Bell-nonlocal empirical model has such a finite-dimensional quantum realization, every realizing state in that carrier is entangled. Post-quantum Bell-nonlocal no-signaling models remain within the general witness theorem but outside the quantum-entanglement corollary. The accompanying Lean 4 development, release v0.8.0, directly verifies the finite Bell-side witness carrier: denominator-32 vector/Born weights, structural no-signaling, CHSH numerator 808080, all sixteen deterministic local extrema, finite denominator-32 Bell-local-envelope exclusion, and conditional endpoint routing. Its direct witness certificate is vectorBorn_flagship_spine, and its deepest released endpoint is reasonableDeepestFiniteEntanglement_spine. The manuscript-level typed governance interface, empirical lawful groupoid, compatibility equivalence, coordinate-deviation exhaustion, completed role collapse, candidate-to-canonical derivation, and finite-dimensional quantum specialization are not attributed to the released Lean layer. This paper is the Bell-witness member of the paired AASC quantum determinacy arc. The record-side manuscript, Admissible Record Construction in Physically Non-Selective Quantum Regimes, fixes when local physical record occurrences stand as the same evidential record objects. The present manuscript fixes when the Bell operational family sampled by such records stands as the same reusable witness. The paired endpoint is therefore: record-role fixation+Bell-witness compatibility.\text{record-role fixation} + \text{Bell-witness compatibility}.record-role fixation+Bell-witness compatibility. The manuscript is classificatory and eliminative rather than mechanistic. It does not claim that AASC generates the Bell probabilities or supplies a hidden physical influence. Its claim is that reusable Bell-witness determinacy strongly constrains how Bell-nonlocal correlations may be coherently classified on a fixed domain: not as independently complete local states later connected by a mechanism, not as Bell-local hidden-variable value assignments, not as superluminal signaling, and not as same-act repair, but as boundary-level compatibility carried by one standing-preserving Bell witness.