This is the data set for the published, peer reviewed paper: https://ijqf.org/archives/8027 "Phenomenological Velocity and Bell–CHSH: Exceptional-Locus Semantics, Selection Simulations of − cos, and a Microcausal Realization:" https://ijqf.org/wp-content/uploads/2026/02/IJQF2026v12n2p10.pdf Bell--CHSH is often read as a universal prohibition on \emph{local hidden variables}. Mathematically, however, the CHSH bound $S\le 2$ is a theorem about a particular hypothesis class: a \emph{single} Kolmogorov probability space carrying all counterfactual outcomes, together with measurement independence, Bell locality (factorized response functions), and bounded outputs. On that class the proof is pointwise and unconditional, so no algebraic reformulation of a parameter (including a ``phenomenological velocity'' (PV)) can yield Tsirelson-scale singlet correlations $E(a,b)=-\cos(a-b)$ on a Tsirelson quartet. We then make precise two distinct ways in which PV can remain meaningful as a \emph{local} and in that sense ``hidden'' parameter while coexisting with Tsirelson-scale correlations, without contradicting Bell's theorem. First, we formalize ``exceptional-locus/defined-only'' conventions as setting-dependent acceptance (post-selection): reported correlators are conditional expectations under a setting-indexed family of accepted laws $\{\nu_{ab}\}$. Within this rung-1 semantics we give an explicit Bell-local deterministic base model whose accepted-sample joint law exactly matches the singlet law (unbiased marginals and correlator $-\cos(a-b)$) for all $a,b$, via an explicit acceptance rule $\gamma(a,b,\lambda)\in[0,1]$. Second, we give a PV-indexed microcausal (operator-algebraic) realization: PV parameterizes a canonical $SU(2)$ unitary that conjugates local observables inside commuting Alice/Bob subalgebras, and in the singlet state the unconditional correlator equals $-\cos(a-b)$ and attains Tsirelson's value $2\sqrt2$. The results clarify a semantic and structural trichotomy: any ``PV-to-Tsirelson'' account must (i) change the effective ensemble by selection/context, or (ii) leave the Kolmogorov (commutative) model class (e.g.\ via noncommutativity or quasi-probability), or (iii) relax a Bell premise such as measurement independence or Bell locality. In this sense, Bell--CHSH constrains a specific formalization of hidden variables rather than ownership of the terms ``local'', ``real'', or ``hidden'' in physics discourse.
This is the data set for the published, peer reviewed paper: https://ijqf.org/archives/8027 "Phenomenological Velocity and Bell–CHSH: Exceptional-Locus Semantics, Selection Simulations of − cos, and a Microcausal Realization:" https://ijqf.org/wp-content/uploads/2026/02/IJQF2026v12n2p10.pdf Bell--CHSH is often read as a universal prohibition on \emph{local hidden variables}. Mathematically, however, the CHSH bound S≤2 is a theorem about a particular hypothesis class: a \emph{single} Kolmogorov probability space carrying all counterfactual outcomes, together with measurement independence, Bell locality (factorized response functions), and bounded outputs. On that class the proof is pointwise and unconditional, so no algebraic reformulation of a parameter (including a phenomenological velocity'' (PV)) can yield Tsirelson-scale singlet correlations $E(a,b)=-\cos(a-b)$ on a Tsirelson quartet. We then make precise two distinct ways in which PV can remain meaningful as a \emph{local} and in that sense hidden'' parameter while coexisting with Tsirelson-scale correlations, without contradicting Bell's theorem. First, we formalize exceptional-locus/defined-only'' conventions as setting-dependent acceptance (post-selection): reported correlators are conditional expectations under a setting-indexed family of accepted laws $\{\nu_{ab}\}$. Within this rung-1 semantics we give an explicit Bell-local deterministic base model whose accepted-sample joint law exactly matches the singlet law (unbiased marginals and correlator $-\cos(a-b)$) for all $a,b$, via an explicit acceptance rule $\gamma(a,b,\lambda)\in[0,1]$. Second, we give a PV-indexed microcausal (operator-algebraic) realization: PV parameterizes a canonical $SU(2)$ unitary that conjugates local observables inside commuting Alice/Bob subalgebras, and in the singlet state the unconditional correlator equals $-\cos(a-b)$ and attains Tsirelson's value $2\sqrt2$. The results clarify a semantic and structural trichotomy: any PV-to-Tsirelson'' account must (i) change the effective ensemble by selection/context, or (ii) leave the Kolmogorov (commutative) model class (e.g.\ via noncommutativity or quasi-probability), or (iii) relax a Bell premise such as measurement independence or Bell locality. In this sense, Bell--CHSH constrains a specific formalization of hidden variables rather than ownership of the terms local'', real'', or ``hidden'' in physics discourse.
Bell--CHSH is frequently paraphrased as ``local realism is impossible'' after experimental violations of CHSH. The theorem is correct, but the paraphrase hides a structural assumption: \emph{selection centrality} (fair sampling), i.e.\ that the detected sample is not a setting- and hidden-variable--dependent reweighting of the hidden prior. We give a precise measure-theoretic separation between (i) the \emph{central} sector, where Eobs=Efull and CHSH≤2 holds under measurement independence and locality, and (ii) the \emph{noncentral} sector, where the observed correlations are computed under a reweighted measure dνa,b=w(a,b,λ)dρ. We prove a sharp CHSH inflation bound Sobs≤2+4δ,δ:=supa,b∫∣w(a,b,λ)−1∣ρ(dλ), so reproducing Tsirelson's 22 by strictly local measurement-independent models via selection requires δ≥(22−2)/4≈0.2071. We provide (A) a canonical Radon--Nikod\'ym construction (piecewise constants on sign regions plus a small positive remainder), (B) an explicit local factorized detection-loophole construction that reproduces arbitrary finite correlation tables, and (C) an implementable optics protocol to estimate or upper-bound δ from time-tag data via window dithering, threshold and spectral sweeps, and auxiliary-tag binning. This paper critiques not the validity of Bell's theorem, but the common overstatement of what CHSH violations imply without an explicit, quantitative centrality audit.
Bell--CHSH is frequently paraphrased as ``local realism is impossible'' after experimentalviolations of CHSH. The theorem is correct, but the paraphrase hides a structural assumption:\emph{selection centrality} (fair sampling), i.e.\ that the detected sample is not asetting- and hidden-variable--dependent reweighting of the hidden prior.We give a precise measure-theoretic separation between (i) the \emph{central} sector, whereEobs=Efull and CHSH≤2 holds under measurement independence and locality,and (ii) the \emph{noncentral} sector, where the observed correlations are computed under areweighted measure dνa,b=w(a,b,λ)dρ.We prove a sharp CHSH inflation boundSobs≤2+4δ,δ:=supa,b∫∣w(a,b,λ)−1∣ρ(dλ),so reproducing Tsirelson's 22 by strictly local measurement-independent models via selectionrequires δ≥(22−2)/4≈0.2071.We provide (A) a canonical Radon--Nikod\'ym construction (piecewise constants on sign regions plusa small positive remainder), (B) an explicit local factorized detection-loophole construction thatreproduces arbitrary finite correlation tables, and (C) an implementable optics protocol to estimateor upper-bound δ from time-tag data via window dithering, threshold and spectral sweeps, andauxiliary-tag binning.This paper critiques not the validity of Bell's theorem, but the common overstatement of what CHSHviolations imply without an explicit, quantitative centrality audit.
Bell-CHSH is frequently paraphrased as "local realism is impossible" after experimental violations of CHSH. The theorem is correct, but the paraphrase hides a structural assumption: selection centrality (fair sampling), i.e. that the detected sample is not a setting-and hiddenvariable-dependent reweighting of the hidden prior. We give a precise measure-theoretic separation between (i) the central sector, where E obs = E full and CHSH≤ 2 holds under measurement independence and locality, and (ii) the noncentral sector, where the observed correlations are computed under a reweighted measure dν a,b = w(a, b, λ) dρ. We prove a sharp CHSH inflation bound
We revisit the Bell--CHSH scenario for two spin-21 particles and isolate the precise algebraic origin of the Bell contradiction. On the quantum side, spin-21 is described by a noncommutative spinor (Clifford) algebra acting on the Hilbert space of two spin-21 particles, with the singlet state yielding the usual correlation E(a,b)=−a⋅b and Tsirelson's bound 22. On the classical side, the standard Bell assumptions amount to describing all measurement outcomes as {±1}-valued random variables on a single Kolmogorov probability space, i.e.\ elements of a commutative algebra C(Λ).
We show that there is no representation of the spinor algebra of spin-21 (with its singlet state and locality structure) into any such commutative Kolmogorov algebra that preserves the {±1} spectra of local spin components and the singlet correlations entering the CHSH expression, under the standard Bell assumptions of locality (factorization) and measurement independence. In this sense, the Bell--CHSH contradiction is exhibited as an algebraic mismatch between a noncommutative spinor/Clifford description of spin and the classical assumption of a single global Kolmogorov space supporting all outcomes. In the language of quantum probability, this is a C∗-algebraic reformulation of the known fact that the singlet correlations admit no local hidden-variable model with jointly distributed outcomes on one probability space.
We also give an explicit realization of the same spinor structure within the author's Quantum Index Algebra (QIA) framework, where locality appears as disjoint index slots and the singlet state as a simple index cocycle.
ON THE VERSION NUMBER. "v3" is the version of the NOTE, not of this Zenodo deposit. Versions 1 (February 2026) and 2 were circulated privately and never deposited; v1 contained four errors of substance, which are stated with their repairs in the "What changed" section rather than quietly removed. This is the first Zenodo deposit, so if you see a deposit counter it will not match the document version. The document version is the one that matters for citation. Preprint, version 3 (complete rewrite). This note is the synthesis of the contextuality-obstructions program; the proofs live in the companion papers. The proposal is that the Copenhagen viewpoint, stripped of its rhetoric, is a set of structural statements about one geometric object: the transformation groupoid of measurement contexts (maximal abelian subalgebras) with its canonical U(1) 2-cocycle. In that formulation: local validity, the exact classicality of every single context, is a theorem with an explicit witness; complementarity is the nonvanishing holonomy of the cocycle along closed context loops, which detects exactly the all-versus-nothing sector of contextuality; collapse is pinned by statistics, repeatability and covariance to a one-parameter family per degenerate block whose unique efficient member is the Lueders rule, with a classical twin theorem identifying the same axioms' classical solution as Bayesian conditioning; observer-relativity of facts and the movable cut are theorems of an enlarged observer-context category; and the Frauchiger-Renner argument localizes to an ordinary state-dependent violation, with contextual fraction exactly 1/6, carried by a single CHSH facet, the loop holonomy of the observer switch being provably trivial. ATTRIBUTION. The classification of achievable state-independent values, the even/odd dichotomy and the fixed value d/2, is due to Abramsky, Cercelescu and Constantin (FSCD 2024). It is recast here in certificate language; the priority is theirs and is stated in the text. HARDWARE CAVEAT, STATED UP FRONT. Two signatures were measured on superconducting hardware. The quoted significances, about 56 sigma for the triangle holonomy and 35.4 sigma for the Peres-Mermin witness above the deterministic bound 4, are shot-noise statistical only, computed under the implemented model. They are not systematics-aware, and neither experiment is loophole-free. Read them as consistency checks on real hardware, not as precision measurements. ERRATA. Version 1 of this note contained four errors of substance. Section "What changed" states each of them and its repair. They are recorded rather than quietly removed. STATUS AND SCOPE. This is a preprint, not a peer-reviewed article. Each tenet is either a theorem of the companion papers, a machine-verified certificate in the public suite, or is explicitly labeled a conjecture. The paper offers structural characterizations within its stated axioms; it is not an interpretation-free derivation of Copenhagen and it does not claim to resolve the measurement problem. AI-ASSISTANCE DISCLOSURE. This work was carried out with substantial AI assistance. Every load-bearing claim is machine-verified by scripts that ship with the papers, and the author takes full responsibility for the contents. COMPANIONS. Paper A: https://doi.org/10.5281/zenodo.21630431 . Paper B: https://doi.org/10.5281/zenodo.21630630 . Paper D: https://doi.org/10.5281/zenodo.21630697 . Paper C: https://doi.org/10.5281/zenodo.21633744 (posted 2026-07-28, after three adversarial review passes; it carries a labelled retraction of an earlier sqrt(2) reading). VERIFICATION CODE. https://github.com/manuflog/contextuality-obstructions
Following the operative pattern of the absorption of E₀ = m₀c² as basal rest sector of the Sistema Vectorial SV (Lloret Egea, 2026g), this document proposes and proves the absorption of Bell's local bound CHSH ≤ 2 and the quantum bound of Tsirelson 2√2 as two operative manifestations of one and the same coupled angular factual apparatus of the Sistema Vectorial SV. The construction articulates the CHSH regime in three structurally distinct sub-regimes (R₀ uncoupled, R₁ weakly coupled, R₂ strongly coupled) parametrized by the structural coupling coefficient χ_c. On R₀, the Bell bound holds as exact algebraic invariant T ≡ 0 (mod 2) on the finite field 𝔽₂, with exact compliance verified on 78 772 cases without a single counterexample. On R₂ at full saturation (χ_c = 1), the Tsirelson bound 2√2 emerges as structural saturation of the unique coupled angular correlator admitted by the SV, with numerical verification at machine precision. The technical core of the document is the introduction of the Coupled Angular Factual Calculus of the Sistema Vectorial SV as a new mathematical apparatus, whose central result is the Theorem of Uniqueness of the Coupled Factual Cosine: under nine structural axioms of the SV apparatus — angular dependence, full anticorrelation in basis coincidence, full correlation in opposite basis, parity, polar complementarity, normalized factual conjugate component, standard SO(2) composition law on the auxiliary function C̃ = −C_SV, structural continuity, and minimal angular fidelity of the CHSH-SV apparatus — the only admissible coupled angular correlator is C_SV(δ) = −cos δ. The Tsirelson bound 2√2 emerges from this theorem as canonical saturation of the unique angular factual representation admitted by the apparatus, without invocation of Hilbert formalism, complex probabilistic amplitudes, or probability as truth criterion. The construction is compatible with operational compatibility with the experimental record, measurement freedom, and the experimental record cited herein. The Sistema Vectorial SV is positioned as a fourth technical reading of the Bell apparatus, complementary to and distinct from superdeterminism, post-quantum boxes, and generalized probabilistic theories, with three differentiating properties: deterministic discipline without grounding probability, structural derivation of the Tsirelson bound without Hilbert importation, and simultaneous compatibility with structural non-locality, operational compatibility with the experimental record, and measurement freedom. --- Note: Canonical material source on GitHub: https://github.com/juantoniolloretegea/SV-matematica-semantica/tree/main/documentos/adendas/matematica-fisica-factual-contemporanea-sv/de-bell-a-tsirelson-sin-formalismo-hilbert. Supplementary reproducible laboratory deposit on Zenodo: https://doi.org/10.5281/zenodo.20020201. These canonical sources are provided to facilitate direct consultation of the living textual record, reproducible laboratory verification and reader-side translation through standard browser translation tools when required.