Conditioning the Dark Energy Equation of State in Planck 2018 + BAO

Conditioning the Dark Energy Equation of State in Planck 2018 + BAO A Reproducible Late-Time Robustness Diagnostic in w₀CDM This paper presents a controlled cosmological inference analysis testing the numerical compatibility of a Relational-Gravity–motivated late-time deviation in the dark-energy equation of state when confronted with real observational data. The analysis compares a standard w₀CDM control model (CTRL2) against a Relational-Gravity–conditioned variant (RG) in which the equation-of-state parameter is restricted to the non-phantom domain (w₀ > −1). The goal is not model selection or discovery, but a robustness test: whether such conditioning remains admissible once late-time geometric information is included. The study combines: The full Planck 2018 likelihood (TTTEEE_lite + low-ℓ TT + low-ℓ EE + lensing) BAO distance measurements (SDSS DR12, 6dFGS, SDSS DR7 MGS) The results show that: A quintessence-like deviation (δw ≈ +0.05–0.10) remains numerically admissible under Planck + BAO Early-universe parameters remain statistically stable Parameter shifts follow an existing degeneracy manifold rather than introducing a new likelihood-preferred mode The total goodness-of-fit difference relative to the control model is modest No statistical preference over ΛCDM is claimed. Reproducibility A separate Platinum-level reproduction archive is provided as a supplement to this paper and is linked via the “Is supplement to” relation. That reproduction archive contains all material required to independently reproduce the reported results, including: Fully specified Cobaya configuration files MCMC chains for both CTRL2 and RG runs Analysis notebooks used to generate reported tables and figures Environment specifications (Conda exports and system information) Execution scripts and documented run commands A detailed README describing the reproduction workflow Epistemic Role This work upgrades Planck-only admissibility tests to Planck + BAO robustness, strengthening empirical plausibility while remaining strictly observational. All results are derived from real data. No mock likelihoods, forecasts, or future-survey assumptions are used.