We introduce an effective, information-motivated parametrisation of late-time cosmology, which we refer to as the PURS framework (Principle of Universal Regulation by Saturation). The framework is built around a scalar saturation variable Ω(z) defined as the ratio between an effective information content and the holographic entropy associated with the cosmological horizon. Its amplitude is set by the background curvature scale, so that no new fundamental energy scale is introduced. We first establish a structural no-go result on the dynamical coupling of Ω(z) to the expansion: through systematic numerical exploration of a broad class of smooth couplings between Ω(z) and the effective equation of state in a modified Raychaudhuri equation, we find that in the perturbative regime (α ≲ 1), any such coupling generically produces ΔH₀ < 0, in contradiction with observations. The no-go holds across monotonic, non-monotonic, and sign-reversed evolutions of Ω(z) and rules out the most natural dynamical realisation of the framework. This obstruction motivates an epistemic reformulation in which Ω(z) does not modify the background expansion, but instead modulates the astrophysical and statistical processes entering the reconstruction of cosmological observables. In this formulation, each probe acquires a deviation from ΛCDM of the form δOᵢ(z) = εᵢ ln Ω(z)Wᵢ(z), with Ω(z) = σ²(R, z)/σ²(R, 0) computed within ΛCDM linear growth and Wᵢ(z) fixed by the physical construction of each probe. The primary contribution of this paper is a set of four distinct empirical tests of the framework, each accessible to current or near-term data and each capable, on its own, of refuting the proposal: (i) a specific redshift-dependent modulation of Type Ia supernova residuals, testable directly on public Pantheon+ binned residuals through a one-parameter fit; (ii) a predicted hierarchy of probe-dependent shifts in inferred cosmological parameters arising from the differing redshift kernels Wᵢ(z); (iii) a characteristic structure in weak-lensing observables consistent in sign and order of magnitude with the observed σ₈ tension; and (iv) percent-level convergence of high-statistics standard-siren measurements toward the CMB-inferred value of H₀ rather than the local distance-ladder value, accessible to forthcoming gravitational-wave observing runs.
Antoine Druilhe (2026) studied this question.