A Falsifiable Relaxative Consistency Bound for Cosmic Expansion

We introduce and test a model–independent relaxative consistency bound for the cosmic background expansion, formulated as a probabilistic inequality on the deceleration parameter. The bound is interpreted as the macroscopic signature of horizon–induced coarse–graining in quantum f ield theory on curved spacetime, which renders the cosmological background an effective open system [1–4]. Using non–parametric reconstructions of H(z) from cosmic chronometers [5, 6], Type Ia supernovae, and baryon acoustic oscillations with full covariance, we evaluate the statistic Idyn ≡ q(zmax) −q(zt), where zt denotes the transition redshift. For the full CC+SN+BAO data combination, we find P(Idyn ≤ 0) = 0.9667, satisfying the HURB criterion and indicating consistency with an averaged relaxative behavior of the cosmic background. Control tests based on anti–relaxation mock realizations explicitly violate the bound when highredshift information is properly anchored, yielding a FAIL–hard outcome (P(Idyn ≤ 0) = 0.0083) and demonstrating that the hypothesis is operationally falsifiable. A block–jackknife [7] universality test (B3) is also performed; its failure is traced to severe effective–sample–size collapse rather than to observational inconsistency, and is therefore classified as inconclusive.