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 R⁴ (Cabello, Estebaranz, Garcia-Alcaine 1996) is verified KS-uncolorable by exhaustive search over 2¹8 = 262, 144 candidate colorings via nativedecide. 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: cegaᵤncolorable (BISH), llpoᵢffₖsₛign (LLPO ↔ KSSignDecision), ksₛtratification (three-level theorem). Axiom audit: ONE custom axiom (llpoᵣealₒfₗlpo), 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 Complete Paper List (Papers 1–24) Paper 1: Withdrawn Paper 2: Bidual gap and WLPO — DOI: 10. 5281/zenodo. 17107493 Paper 3: Withdrawn Paper 4: Quantum spectra axiom calibration — DOI: 10. 5281/zenodo. 17059483 Paper 5: Schwarzschild curvature verification — DOI: 10. 5281/zenodo. 18489703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