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

This paper presents a controlled cosmological inference analysis testing the numerical admissibility of a Relational-Gravity–motivated late-time conditioning of the dark-energy equation of state when confronted with real observational data. The analysis compares a standard w_0CDM control model against a conditioned variant in which the equation-of-state parameter is restricted to the non-phantom domain (w_0 > -1). The purpose is not model selection or discovery, but a robustness diagnostic: whether such conditioning remains admissible once late-time geometric information is included. The study combines the full Planck 2018 likelihood (TTTEEE_lite, low-\ell TT, low-\ell EE, and lensing) with baryon acoustic oscillation distance measurements from SDSS DR12, 6dFGS, and SDSS DR7 MGS. The results show that a quintessence-like deviation (\delta w \approx +0.05\text{–}0.10) remains numerically admissible under Planck + BAO constraints, that early-universe parameters remain statistically stable, and that parameter shifts follow existing degeneracy manifolds rather than introducing new likelihood-preferred modes. No statistical preference over \LambdaCDM is claimed. A fully reproducible “Platinum-level” archive is provided as a supplement, containing configuration files, MCMC chains, analysis notebooks, and environment specifications sufficient to independently reproduce all reported results. N.b! This paper extends earlier Planck-only admissibility analyses by incorporating BAO data within the same controlled methodology. It is intended as an observational robustness test rather than a model-selection or discovery claim.