RLDS VI: What the Expansion History Tests in a Regime-Limited Interacting Dark Sector — A Closing Analysis against DESI DR2

We confront the Regime-Limited Dynamical Systems (RLDS) model of an interacting dark sector with the Planck 2018 compressed CMB distance priors, DESI DR2 baryon acoustic oscillations and Pantheon+ supernovae. The rebuilt likelihood reproduces the published DESI DR2 constraints on ΛCDM, wCDM and w₀wₐCDM to within 1.1σ for all compared parameters. With the pre-registered priors, the self-consistent (shooting) version improves on ΛCDM by Δχ² = −4.8 for three additional parameters, and the version with a free matter density by Δχ² = −6.36 for four. The nominal information criteria favour ΛCDM (ΔBIC = +17 and +23, respectively). The Δχ² = +36 reported in Papers III–IV required both the earlier simplified likelihood and priors that excluded the ΛCDM limit of the shooting closure. The coupling strength K remains degenerate with the slope α and the activation threshold R_c. Along the shooting profile likelihoods, the fit depends on the matter created by the coupling after recombination, ΔΩₘ ≡ Ωₘ,₀ − ωₘ,early/h². The expansion-history data provide no upper bound on ΔΩₘ within the explored prior ranges. In the effective w₀–wₐ plane, the shooting profile minima follow a short track from ΛCDM to (w₀, wₐ) ≈ (−0.91, −0.20). With widened priors, the free version reaches the 68% region of our CPL posterior for the same data. It achieves Δχ² = −7.97, comparable to CPL (−7.7), at ΔΩₘ = 0.14 with parameters at prior edges. Conditional on the cluster gas-fraction calibration applying to RLDS, a Gaussian prior on Ωₘ based on the low-redshift cluster constraint gives ΔΩₘ = 0.018 ± 0.028 for the shooting version and 0.010 ± 0.035 for the free version. The upper ends of the approximate two-sided 95% profile intervals are 0.074 and 0.080, respectively. Every free-version solution we found inside the 68% CPL region lies above the corresponding conditional bound. Re-optimising the free version with the cluster prior gives Δχ² = −0.80 relative to ΛCDM fitted with the same prior. These results revise the observational conclusions of Papers III–IV.