The Worst Prediction in Physics Is Not a Prediction: Axiom Calibration of the Cosmological Constant Problem (Paper 42, Constructive Reverse Mathematics Series)

Paper 42 in the Constructive Reverse Mathematics (CRM) of Mathematical Physics series. This paper applies the axiom calibration framework to the cosmological constant problem -- the alleged 10¹20 discrepancy between quantum field theory's "prediction" of vacuum energy and the observed value. The problem decomposes into three logically distinct claims with different constructive status. Claim I (Dissolved): The 10¹20 ultraviolet discrepancy is a regulator-dependent artifact. The unregularized vacuum energy does not converge to a real number at any level of the constructive hierarchy. Different regularization schemes (cutoff, dimensional, zeta-function) produce different finite values. A regulator-dependent quantity has no empirical content within the framework. The CRM analysis provides a formal, machine-checked expression of the post-naturalness position articulated by Martin (2012), Bianchi-Rovelli (2010), and Hossenfelder (2019): the 10¹20 is a property of a calculational choice, not of quantum field theory. Claim II (Reclassified): The "naturalness" argument is a Bayesian prior, not a mathematical derivation. The Hollands-Wald axioms prove that the cosmological constant is a free parameter of the renormalized theory. Naturalness resides outside the BISH/LPO deductive hierarchy. Claim III (Identified, LPO): The genuine constraint is the 55-decimal-place cancellation between the bare cosmological constant and the electroweak/QCD vacuum condensates. Computing the exact interacting condensates requires the thermodynamic limit (Fekete's subadditive lemma, Paper 29), showing that LPO suffices for the fine-tuning equation. The residual fine-tuning is an LPO equality -- logically mundane, at the same level as every thermodynamic limit in physics. The Casimir effect proves the scaffolding diagnostic works: energy differences are BISH-computable and experimentally verified; absolute vacuum energies are regulator-dependent and physically meaningless. Main formalized results: - vacuumₑnergydivergent: Unregularized vacuum energy is unbounded (BISH) - predictionᵣegulatordependent: Two valid schemes yield different values (BISH) - lambdafreeₚarameter: Wald ambiguity -- Lambda is a free parameter (BISH) - casimirbish: Casimir energy difference has computable Cauchy modulus (BISH) - condensateₗpo: Exact interacting condensate exists given LPO (LPO) - rgᵣunningbish: Perturbative RG running via Picard-Lindelof (BISH) - fineₜuningₗpo: Fine-tuning equation holds given LPO (LPO) - cccalibration: 7-part assembly theorem (BISH + LPO) - ccₘaster: Master theorem with full axiom audit Axiom profile (#print axioms ccₘaster): 11 physics bridge axioms + 1 CRM axiom (bmcfromₛubadditive = Fekete equiv LPO, Paper 29) + 3 Lean infrastructure (propext, Classical. choice, Quot. sound). Zero sorry. Zero warnings. Technical details: - Lean 4: leanprover/lean4: v4. 28. 0-rc1- Mathlib4 (pinned via lake-manifest. json) - Build: cd P42CosmologicalConstant && lake build- Status: 0 errors, 0 warnings, 0 sorry- Size: 10 modules, ~830 lines