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Machine-checked falsification of quantum foundations: Bell, Tsirelson, no-cloning, and Kochen-Specker in Lean 4

Year: 2026

Type: preprint

Abstract: Machine-checked (Lean 4 / Mathlib) certificates for the main falsification results of quantum foundations. Bell's theorem: the CHSH correlation satisfies S <= 2 for local hidden variables, in both the deterministic +/-1 form and the general local-realism form |a|,|b| <= 1. The Tsirelson bound: QM saturates S = 2*sqrt(2), so locality is violated. No-cloning: v -> v tensor v is not linear. Kochen-Specker: no non-contextual 0/1 value assignment in dimension >= 3 (the no_dispersion_free corollary of Gleason). Zero sorry/axiom; #print axioms = propext, Classical.choice, Quot.sound only.

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.24027301

Author: Mitchell, Rob

Language: English

Topic: Quantum Mechanics and Applications

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7225461525

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