We formalize in Lean 4 the equivalence between the Lesser Limited Principle of Omniscience (LLPO) and the exact Intermediate Value Theorem (ExactIVT), and show that Bell angle optimization for general quantum states reduces to IVT instances. The main results are: (i) LLPO ↔ ExactIVT (axiomatized from Bridges–Richman 1987 and Ishihara 1989); (ii) finding measurement angles that witness a CHSH violation above the classical bound 2 is an IVT problem, hence requires LLPO; (iii) a three-level stratification placing Bell angle-finding strictly below gap detection (WLPO, Papers 2 and 26) in the constructive hierarchy. Level 1 (BISH): the CHSH bound and specific-angle violations are computable. Level 2 (LLPO): general angle-finding requires IVT. Level 3 (WLPO): gap detection is strictly harder. This paper extends Paper 21's abstract LLPO ↔ BellSignDecision equivalence by identifying the mechanism: the Intermediate Value Theorem is why LLPO appears in Bell physics. The formalization compiles with zero sorry statements and six axioms, all with published citations. Paper 27 in the Constructive Reverse Mathematics series. 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: 110.5281/zenodo.18613542 v 3.0 Technical Synthesis of Papers 1–24Paper 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 1–16Paper 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 Paper 23: Fan Theorem and optimization — DOI: 10.5281/zenodo.18604312 Paper 24: Kochen-Specker contextuality and LLPO — DOI: 10.5281/zenodo.18604317 Paper 25: Ergodic Theorems and Laws of Large Numbers against Countable and Dependent Choice — DOI: 10.5281/zenodo.18615453 Paper 26 Bidual Gap Detection Is WLPO-Complete: Gödel Sequences — DOI 10.5281/zenodo.18615457 Paper 27: IVT as the mechanism behind LLPO in Bell physics — DOI: 10.5281/zenodo.18615459 Paper 28: Classical Mechanics. 10.5281/zenodo.18616620 Summary Papers: Paper 10: Logical geography of mathematical physics — DOI: 110.5281/zenodo.18613542 v 3.0 Technical Synthesis of Papers 1–24 Paper 12: Constructive history of mathematical physics — DOI: 10.528
Paul Chun-Kit Lee (Wed,) studied this question.