Return Theory (RT): Empirical - Cosmology, A Late-Time Sector Connection Reference-conditioned temporal reconstruction from cosmic chronometers, with frozen transfer to BAO and supernova likelihoods

Return Theory (RT) — Empirical: Cosmology: A Late-Time Sector Connection provides a standalone cosmological implementation of the RT observer–reference architecture. A declared 38-record cosmic-chronometer likelihood fixes one joint reference-conditioned coordinate state. The RT reconstruction map then produces an observable expansion-rate history that is frozen before transfer to baryon acoustic oscillation (BAO) and supernova likelihoods. No target-side history coordinate is refitted. The primary implementation uses the affine-scale-factor Reference Card H_R⁠ = H_b(1+z), three source-supported coordinate nodes, bounded PCHIP interpolation, and two-sided continuation in the reconstruction coordinate log(Gamma). The primary RT branch contains one reference scale and three geometric coordinates, without fitting explicit Lambda, Omega_Lambda, w_0, or w_a parameters. The cosmic-chronometer fit gives chi-square/dof = 24.596/34 = 0.723; the independently fitted flat LambdaCDM comparison gives 23.329/36 = 0.648, so both histories are compatible with the source record. On the 11 DESI observables inside the chronometer-supported coordinate domain, frozen RT transfer gives 9.371/10 = 0.937, compared with 22.536/10 = 2.254 for the independently chronometer-fitted flat LambdaCDM history. On the declared BAO composite, the corresponding values are 11.132/13 = 0.856 and 24.279/13 = 1.868. Profiling one common BAO ruler gives r_d = 144.650 Mpc at the frozen point. Propagation of the full chronometer posterior gives a median of 145.629 Mpc and a 16th–84th percentile interval of [140.943, 150.702] Mpc. This calibration is explicitly covariance-sensitive: the 2.510 Mpc shift induced by the primary chronometer covariance treatment is comparable to the 2.573 Mpc RT-to-flat ruler-profile separation and is not presented as milliparsec-scale precision. The record includes the 112-page A4 publication PDF, LaTeX source, figures, compact frozen result objects, code-and-text reproducibility archive, machine audits, and SHA-256 manifests. Complete raw-input reproduction additionally requires separately obtained third-party survey vectors, covariances, the derived chronometer likelihood object, and the posterior archive listed in DATA_INPUTS.md. Text, figures, and author-owned compact data are CC BY 4.0; author-written code is MIT. Bundled Lora fonts remain under OFL 1.1, and included third-party likelihood adapters retain their upstream BSD terms.