CORRECTION NOTICE — This version supersedes v1 (DOI: 10.5281/zenodo.20499330), which used misleading certificate names BELL-PASS and BELL-CLASSICAL. See ERRATA.md for full details. NOT A PHYSICAL BELL TEST: The CHSH framework in this paper is repurposed as a mathematical correlation classifier for AI feature matrices — NOT as a test of quantum mechanics in AI systems. AI systems do not satisfy the locality and measurement independence conditions required for genuine Bell tests. The CHSH-INSPIRED-CORRELATION-AUDIT certificates are correlation pattern labels only, not evidence of quantum entanglement. Certificate naming correction (v1 → v2): BELL-PASS → CHSH-INSPIRED-CORRELATION-AUDIT: PASS BELL-CLASSICAL → CHSH-INSPIRED-CORRELATION-AUDIT: CLASSICAL We introduce the EPR-Bell Entanglement Validator (EBEV), applying CHSH-inequality-inspired statistics to AI model correlation matrices. Physics of EPR (1935), Bell (1964), and CHSH (1969) is correctly cited. Sacred Geometry Coherence Engine (SGCE) uses geometric constants as culturally meaningful organizational constants, not physical observables. This paper is part of the SZL Holdings Ouroboros Thesis corpus (umbrella DOI 10.5281/zenodo.20490218, v21). Honest disclosure: Conjecture 1 (Λ-uniqueness) is NOT a theorem. 163 sorries remain outstanding. Doctrine v11 LOCKED 749/14/163 c7c0ba17. SLSA L1 honest.
CORRECTION NOTICE — This version supersedes v1 (DOI: 10.5281/zenodo.20499330), which used misleading certificate names BELL-PASS and BELL-CLASSICAL. See ERRATA.md for full details. NOT A PHYSICAL BELL TEST: The CHSH framework in this paper is repurposed as a mathematical correlation classifier for AI feature matrices — NOT as a test of quantum mechanics in AI systems. AI systems do not satisfy the locality and measurement independence conditions required for genuine Bell tests. The CHSH-INSPIRED-CORRELATION-AUDIT certificates are correlation pattern labels only, not evidence of quantum entanglement. Certificate naming correction (v1 → v2): BELL-PASS → CHSH-INSPIRED-CORRELATION-AUDIT: PASS BELL-CLASSICAL → CHSH-INSPIRED-CORRELATION-AUDIT: CLASSICAL We introduce the EPR-Bell Entanglement Validator (EBEV), applying CHSH-inequality-inspired statistics to AI model correlation matrices. Physics of EPR (1935), Bell (1964), and CHSH (1969) is correctly cited. Sacred Geometry Coherence Engine (SGCE) uses geometric constants as culturally meaningful organizational constants, not physical observables. This paper is part of the SZL Holdings Ouroboros Thesis corpus (umbrella DOI 10.5281/zenodo.20490218, v21). Honest disclosure: Conjecture 1 (Λ-uniqueness) is NOT a theorem. 163 sorries remain outstanding. Doctrine v11 LOCKED 749/14/163 c7c0ba17. SLSA L1 honest.
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.
Abstract Einstein’s “spooky action at a distance” names a correlation that no local mechanism can produce. This article turns that observation into an audit instrument for artificial intelligence. Two AI agents that share training data, weights or random seeds but cannot communicate are local systems in Bell’s sense, so their behaviour in a Clauser–Horne–Shimony–Holt (CHSH) game is bounded by S ≤ 2 whatever their architecture; a significant excess identifies a covert channel without modelling the agents. The instrument is tested in three computational experiments with known ground truth. First, 135 trained pairs of neural agents (three widths, three latent dimensions, two objectives) never exceed the bound (maximum S = 2.0000), including pairs trained to imitate the correlations of an entangled singlet. Second, opening a one-bit channel with probability p moves the learned CHSH value onto the theoretical optimum 2 + 2 p (mean absolute deviation 0.0016 across 220 runs); any leak below p ≈ 0.414 produces values indistinguishable in S from quantum entanglement. Third, as a finite-sample test the audit keeps its nominal size against honest but strongly correlated agents (rejection 4.4% and 4.3%), whereas a conventional dependence test flags the same agents in 100.0% of audits; detecting a 5% leak with 80% power needs about 7,375 rounds and a 1% leak about 185,120. The decisive weakness lies with the auditor: with predictable settings (a low-order bit of a linear congruential generator, a fixed rotation or a reused seed), agents with zero communication reach S ≈ 4 and trigger false alarms in 100% of audits, while cryptographic and freshly seeded generators restore the nominal error rate. The bridge to algorithmic collusion and multi-agent AI governance is stated as a formal analogy and a hypothesis for field testing, not as a finding about deployed systems. JEL classification: C12, C63, D43, L41, O33
We derive the Bell–CHSH inequality as a conditional theorem inside Charlton Geometry (CG), rather than as an independent axiom about “local realism”. The key CG primitive is non-invertibility, η(ω) = η(−ω), which forces an observational quotient and produces irrecoverable “lost state” carried by polarity and intrinsic phase. In a bipartite experiment, Bell’s bound is recovered exactly when one adds an additional factorization condition asserting that outcomes depend only on local settings and a local lift choice, i.e. that the lost-state fiber decomposes into independent local fibers. Within CG, the natural geometric coupling of two regions through shared lift and holonomy generically violates that factorization while preserving operational no-signaling, so the Bell inequality becomes a theorem about a restricted subclass of quotients rather than a universal constraint. Using the Born brick as an upstream theorem that fixes the unique binary law cos2(θ/2) on the spin-lifted setting space, we recover the standard singlet correlation E(a, b) = −a °§ b and the Tsirelson bound 2√2 as the sharp CG-compatible CHSH maximum. In this framing, Bell violation is not an ontic miracle but the expected signature of a globally shared, non-invertible geometric substate whose reversal cannot be represented Original DOI: 10.5281/zenodo.18216032 Version: 0.9.0
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.
This article presents a systematic account of the EPR argument and Bell tests, focusing on rigorously established mathematical results and experimental evidence published up to the cut-off date of October 28, 2026. The assumptions of local factorization and measurement-setting independence are stated explicitly. The CHSH bound of 2 is proved, and the quantum bound of 2√2 is derived using operator methods and semidefinite certificates. The joint outcome probabilities for the singlet state are derived, and the no-signalling theorem is proved for completely positive, trace-preserving local operations. Separability is shown to imply Bell locality, and entanglement is carefully distinguished from the violation of a particular Bell inequality. For noisy two-qubit states, spin measurements are explicitly distinguished from binary strategies that allow constant outcomes. The account also includes explicit constructions of local distributions, Fine’s theorem, and self-testing bounds. Experimental evidence is examined together with the statistical assumptions underlying its analysis; historical interpretations and unconfirmed proposals are clearly identified as such. The 1930 photon box is also analysed, with a distinction drawn between a semiclassical reconstruction of the apparatus and an exact relation between energy and time evolution. These results do not, in themselves, constitute particle detections, enable superluminal communication, or single out a unique ontology.
The empirical evidence tends to confirm the quantum - mechanically (QM) predicted violation of Bell's - type inequalities. The latter are widely accepted to be correct representation of the objective reality (OR) underlying EPR's gedankenexperiment. Contrariwise, we argue here that the starting premises leading to Bell's and CHSH's inequalities are not appropriate formulations of OR in the EPR context. Indeed, the essence of EPR argument is the correlation between pair of particles travelling with some well defined orientations. To measure such correlation, one requires detectors with high resolution, and some appropriately defined relative orientations. On the contrary, experimental tests of Bell's inequalities typically involve counting the number of particles with some value of spin (or polarisation) using low-resolution detectors and completely arbitrary orientations. Depending upon the relative orientation of good-resolution detectors, we obtain two families of CHSH-type inequalities. One of these families is the most often used version of CHSH inequality, that was derived by Clauser and Horne with the supplementary no - enhancement assumption: here, it is obtained without special provisions. The other family is completely new and refers to coincidence counts from multiple events. Experimental test to distinguish between the QM and OR descriptions of nature should take into account these new constraints.