Causal Israel–Stewart viscosity and background scaling with a geometric dark-sector proxy in a model-independent effective-fluid framework

We investigate a thermodynamically consistent unification of the late-time dark sector in a model-independent effective-fluid framework endowed with causal Israel–Stewart (IS) bulk viscosity. On a flat FLRW background, we recast the dynamics into a closed autonomous system, identify stable scaling solutions that alleviate the coincidence problem, and recover a smooth [Formula: see text]CDM limit. We compute background observables [Formula: see text], [Formula: see text] and [Formula: see text] and adopt a phenomenological quasi-static closure for linear growth via [Formula: see text] without committing to a specific modified-gravity microphysics. Physical consistency is ensured by positive entropy production and IS causality bounds [Formula: see text]. The validity of the truncated-IS regime is quantified through [Formula: see text] over the redshift range considered, and we display [Formula: see text] along fiducial trajectories. We also document a prospective SN[Formula: see text]Ia/BAO/RSD/cosmic-chronometer pipeline (priors, likelihood structure, AIC/BIC) intended for follow-up work; no posterior constraints are claimed here. The framework yields falsifiable background signatures mild deviations in [Formula: see text] and characteristic trends in [Formula: see text] and [Formula: see text] and remains compatible with luminal gravitational-wave propagation constraints. It provides a clean baseline for subsequent data-driven tests and for embedding explicit geometric models should one wish to move beyond the effective-fluid level.