Relational Capacity Dynamics and Gravitational Realizations: Consistency Tests of RFG and a Covariant KGB Cosmology

Relational Capacity Dynamics (RCD) is developed as a non-geometric macroscopic scalar continuum and connected to several distinct gravitational realizations within the R-Universe research programme. The manuscript derives the classical RCD scalar sector, constructs and audits preferred-foliation RFG and regularized RFG-R/RFG-RΞ realizations, and develops a separate covariant luminal Kinetic Gravity Braiding (KGB) cosmology. The KGB realization is evolved directly through H-EFTCAMB with photons, baryons, cold dark matter and neutrinos and is tested against Planck 2018 CMB and lensing, Pantheon+, DESI DR2 BAO and cosmic-chronometer data. Four independent direct chains yield a converged posterior. Dynamic nested sampling gives log Z_KGB = −1250.3771730 ± 0.4241604 and log Z_ΛCDM = −1250.9013480 ± 0.4135692, corresponding to Δlog Z = +0.5241750 ± 0.5924116 and B_KGB,ΛCDM = 1.6891. The central evidence estimate is slightly higher for KGB, while the difference remains below the numerical integration uncertainty and is not interpreted as decisive evidence for replacement of ΛCDM. This version supersedes and substantially extends the earlier R-Universe preprint. The manuscript explicitly distinguishes derived results, model assumptions, finite-domain viability tests and open completion gates.