Is Cosmic Acceleration Relaxation?

A model-independent operational invariance hypothesis is tested for the late-time cosmic deceleration parameter q(z) using only low-redshift kinematic probes (Cosmic Chronometers, Pantheon+SH0ES supernovae, and DESI DR1 BAO). The proposed law is formulated as a minimal stochastic relaxation dynamics in lna around the de Sitter fixed point q = −1, dq = −Γ(1+q)dlna+σξdW, and is constrained by a hierarchical path-likelihood built from reconstructed q(z) ensembles. Across all validated configurations, the relaxative drift is strongly preferred (P(Γ > 0) ≃ 1), and the dimensionless ratio κ ≡ Γ/σξ is found to be numerically stable under reconstructor substitution (squaredexponential vs Matérn-3/2 Gaussian-process kernels) and dataset substitution (DESI DR1 BAO vs a compressed alternative BAO variant). The central claim is explicitly operational: it is an invariance audit of κ under controlled reconstructor and dataset substitutions, rather than a claim of a fundamental microphysical constant. This work does not perform Bayesian model selection against ΛCDM and does not claim exclusion of ΛCDM; it reports an auditable PASS/FAIL/INCONCLUSIVE verdict under a pre-registered 14-gate protocol.