A Fixed-Background Residual Fractal Tension Deformation in Pantheon+, DESI DR2, BAO and Cosmic Chronometer Data

This paper presents a background-only empirical diagnostic of a fixed Residual Fractal Tension (RFT) deformation, formulated within the Fractal Consistency Law (FCL) program, against the standard flat Lambda Cold Dark Matter (ΛCDM) expansion model. The study deliberately restricts its scope to the homogeneous background expansion channel and does not claim validation of the growth sector, dark-matter phenomenology, perturbation theory, or the full FCL framework. The tested deformation replaces the constant late-time residual term in flat ΛCDM with a fixed scaling factor governed by Bexp = −1.73, yielding E²(z) = Ωm(1 + z)³ + (1 − Ωm)(1 + z)²+Bexp. The analysis uses Pantheon+ Type Ia supernovae with full STAT+SYS covariance, DESI DR2 baryon acoustic oscillation measurements, and a compilation of cosmic-chronometer H(z) points. A sequence of increasingly stringent audits is reported: information-criterion fits, MCMC posterior sampling, full-covariance MCMC, and nested-sampling Bayesian evidence. The final full-covariance nested-sampling run gives Δlog Z = 1.586 ± 0.282 in favor of RFT-fixedB over ΛCDM, corresponding to a Bayes factor of approximately 4.88. A diagnostic RFT-freeB model recovers Bexp = −1.773 (+0.122, −0.127), consistent with the fixed value. These results constitute positive but moderate Bayesian evidence for the RFT background-expansion submodule under the specified priors and compressed likelihood implementation. The evidence is not presented as a definitive cosmological discovery; rather, it motivates full likelihood replication, prior-sensitivity studies, official DESI/Pantheon+ likelihood comparisons, and a future perturbation-level treatment.