From Galaxies to Clusters: Four Observational Signatures of Spacetime Geometric Relaxation

General Relativity assumes that spacetime responds instantaneously to matter. We relax this assumption: the effective gravitational field obeys a constitutive Maxwell–Debye relaxation equation, τ Dg/Dt + g = gbar, with a single vacuum timescale τvac = 36.6 Myr calibrated on the SPARC galactic database. From this one equation, four distinct observational regimes emerge as limiting cases:(i) the quasi-static galactic regime, where delayed response recovers the Radial Acceleration Relation across 175 disk galaxies (RMS = 0.205 dex); (ii) the large-scale flow regime, where regions of lower dynamical complexity retain larger non-equilibrium velocity dispersions, producing a factor-oftwo contrast σ(Q1)/σ(Q4) = 1.93 ± 0.10 in the Cosmicflows-4 catalogue; (iii) the cluster-merger regime, where finite relaxation time generates a gas–potential spatial offset, improving lensing fits over NFW in four independent merging clusters (∆χ2 > 0 in all cases, τ ≈ 30 Myr); and(iv) the post-collision trail regime, where dark-matter-free galaxies in the NGC 1052 trail have velocity dispersions consistent with stellar mass alone (χ2 TIDE = 0.76 versus χ2 ΛCDM = 139 for DF2/DF4/DF9, computed with identical inputs; see companion analyses for likelihood definitions).Across these cases, the inferred relaxation scale remains of order τ ∼ 30–50 Myr, with internal system-specific relaxation times entering where appropriate. We derive concrete, falsifiable predictions for five unmeasured trail members and for upcoming surveys (Euclid, JWST, LISA). Taken together, these results are consistent with a unified phenomenological pattern that may admit a geometric interpretation, in which some phenomena often attributed to an independent dark sector reflect the inertial response of geometry to matter.