Bell Nonlocality and the Constructive Cost of Disjunction: An LLPO Calibration

Paper 21: Bell Nonlocality and LLPO Title: Bell Nonlocality and the Constructive Cost of Disjunction: An LLPO Calibration Description:Paper 21 in the Constructive Reverse Mathematics (CRM) of Mathematical Physics series. This paper calibrates Bell's theorem — the disjunctive conclusion that either locality or realism must fail given CHSH inequality violation — at LLPO (Lesser Limited Principle of Omniscience). The CHSH violation S > 2 is computable in BISH, but the step from "local realism is contradicted" to the disjunction "¬Locality ∨ ¬Realism" has nontrivial constructive cost. The forward direction shows LLPO implies the Bell disjunction; the backward direction encodes binary sequences into Bell-type experiments to recover LLPO. Lean 4 formalization (Mathlib, v4.28.0-rc1): 751 lines, 0 errors, 0 warnings, 0 sorry. Keywords: constructive reverse mathematics, Bell theorem, CHSH inequality, nonlocality, realism, LLPO, disjunction, Lean 4, Mathlib Complete Paper List Other papers in the Constructive Reverse Mathematics Series (see Zenodo for current files): Paper 1: WithdrawnPaper 2: Bidual gap and WLPO — DOI: 10.5281/zenodo.17107493Paper 3: WithdrawnPaper 4: Quantum spectra axiom calibration — DOI: 10.5281/zenodo.17059483Paper 5: Schwarzschild curvature verification — DOI: 10.5281/zenodo.18489703Paper 6: Heisenberg uncertainty (v2, CRM over Mathlib) — DOI: 10.5281/zenodo.18519836Paper 7: Physical bidual gap, trace-class operators — DOI: 10.5281/zenodo.18527559Paper 8: 1D Ising model and LPO — DOI: 10.5281/zenodo.18516813Paper 9: Ising formulation-invariance — DOI: 10.5281/zenodo.18517570Paper 10: Logical geography of mathematical physics — DOI: 10.5281/zenodo.18580342 [v 2.0 Technical Synthesis of Papers 1–16]Paper 11: Entanglement, CHSH, Tsirelson bound — DOI: 10.5281/zenodo.18527676Paper 12: Constructive history of mathematical physics — DOI: 10.5281/zenodo.18581707 [v 2.0 Historical Synthesis of Papers 1–16]Paper 13: Event horizon as logical boundary — DOI: 10.5281/zenodo.18529007Paper 14: Quantum decoherence — DOI: 10.5281/zenodo.18569068Paper 15: Noether theorem — DOI: 10.5281/zenodo.18572494Paper 16: Technical note: Born rule — DOI: 10.5281/zenodo.18575377Paper 17: Bekenstein-Hawking formula — DOI: 10.5281/zenodo.18597306Paper 18: Fermion mass hierarchy and scaffolding principle — DOI: 10.5281/zenodo.18600243Paper 19: WKB tunneling and LLPO — DOI: 10.5281/zenodo.18602596Paper 20: Observable-dependent logical cost, 1D Ising magnetization and WLPO — DOI: 10.5281/zenodo.18603079Paper 21: Bell nonlocality and LLPO — DOI: 10.5281/zenodo.18603251Paper 22: Markov's Principle and radioactive decay — DOI: 10.5281/zenodo.18603503 Note: GitHub repository is not maintained; please see Zenodo for current files.