Null Engine: Empirical null calibration for dark energy Δχ² tests (8 parameterizations, 10,000 ΛCDM mocks each, Pantheon+ / DESI / Planck)

Empirical null Δχ² distributions and calibration engine for eight dark energy parameterizations in active post-DESI use: Λ_sCDM, w†CDM, CPL-wb (control), Gaussian EoS, GDE, Padé, 4pDE, and BellDE. Each distribution comprises 10,000 ΛCDM null mocks generated with the full Pantheon+ Type Ia supernova covariance (1701 SNe; Scolnic et al. 2022), DESI DR2 BAO data, and Chen, Huang, and Wuang's compressed 2018 Planck CMB distance priors. No signal injected. Production optimizer: 24-start Nelder-Mead with boundary retry. The polynomial control (CPL-wb) recovers Wilks' theorem to three significant figures (empirical mean 2.99 vs χ²(3) = 3.0), validating the pipeline. The deposit includes the null engine code with a plugin interface for user-defined parameterizations (supply an H(z) or w(z) function and run), optimizer convergence diagnostics across five configurations, earlier 12-start runs for comparison, and a validation mode for quick sanity checks before committing to full runs. Accompanies Yates (2026), 'Parameter counting fails in post-DESI dark-energy inference.' Code: Python 3.8+, numpy, scipy. License: CC-BY 4.0.