LLPO Equivalence via Kochen-Specker Contextuality: The Constructive Cost of Single-System No-Go Theorems (Paper 24, Constructive Reverse Mathematics Series)

Paper 24 (DOI: 10.5281/zenodo.18604317) Title: LLPO Equivalence via Kochen-Specker Contextuality: The Constructive Cost of Single-System No-Go Theorems (Paper 24, Constructive Reverse Mathematics Series) Description: Paper 24 in the Constructive Reverse Mathematics Series. Lean 4 formalization establishing that Kochen-Specker (KS) contextuality has the same constructive cost (LLPO) as Bell nonlocality (Paper 21), despite being a physically distinct phenomenon. The KS sign decision — the assertion that at least one measurement context lacks predetermined values — is proved equivalent to LLPO over BISH. The CEGA 18-vector KS set in R^4 (Cabello, Estebaranz, Garcia-Alcaine 1996) is verified KS-uncolorable by exhaustive search over 2^18 = 262,144 candidate colorings via native_decide. The LLPO calibration uses the same geometric series encoding as Paper 21, confirming that two physically distinct quantum no-go theorems — Bell nonlocality (spatially separated systems) and KS contextuality (single-system incompatible measurements) — are the same logical phenomenon: "disjunction without constructive witness." Main results: cega_uncolorable (BISH), llpo_iff_ks_sign (LLPO ↔ KSSignDecision), ks_stratification (three-level theorem). Axiom audit: ONE custom axiom (llpo_real_of_llpo), identical to Paper 21 — confirming the structural identity of Bell and KS logical costs. Bundle contains: LaTeX source and compiled PDF (~20 pages), Lean 4 formalization (16 files, ~887 lines, 0 errors/0 warnings/0 sorry), proof specification, bibliography, and README. Built with Lean 4.28.0-rc1 + Mathlib. Complete Paper List (Papers 1–24) Paper 1: Withdrawn Paper 2: Bidual gap and WLPO — DOI: 10.5281/zenodo.17107493 Paper 3: Withdrawn Paper 4: Quantum spectra axiom calibration — DOI: 10.5281/zenodo.17059483 Paper 5: Schwarzschild curvature verification — DOI: 10.5281/zenodo.18489703 Paper 6: Heisenberg uncertainty (v2, CRM over Mathlib) — DOI: 10.5281/zenodo.18519836 Paper 7: Physical bidual gap, trace-class operators — DOI: 10.5281/zenodo.18527559 Paper 8: 1D Ising model and LPO — DOI: 10.5281/zenodo.18516813 Paper 9: Ising formulation-invariance — DOI: 10.5281/zenodo.18517570 Paper 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.18527676 Paper 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.18529007 Paper 14: Quantum decoherence — DOI: 10.5281/zenodo.18569068 Paper 15: Noether theorem — DOI: 10.5281/zenodo.18572494 Paper 16: Technical note: Born rule — DOI: 10.5281/zenodo.18575377 Paper 17: Bekenstein-Hawking formula — DOI: 10.5281/zenodo.18597306 Paper 18: Fermion mass hierarchy and scaffolding principle — DOI: 10.5281/zenodo.18600243 Paper 19: WKB tunneling and LLPO — DOI: 10.5281/zenodo.18602596 Paper 20: Observable-dependent logical cost, 1D Ising magnetization and WLPO — DOI: 10.5281/zenodo.18603079 Paper 21: Bell nonlocality and LLPO — DOI: 10.5281/zenodo.18603251 Paper 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