We present Imprint-Fading (IF) theory, a one-field dissipative model for galactic dynamics in which spacetime accumulates a curvature-memory variable Σ from baryonic sources and loses it by fading at the Hubble rate. The dimensionless evolution equationṡ = Hu2080 [ y − s²/(1 − s) ],where s ≡ Σ/au2080 and y ≡ g_N/au2080, is simultaneously a gradient flow on the grand-canonical free energy of a lattice gas with hard-core exclusion and mean-field pair interactions, and the Onsager equation for entropy production in a driven dissipative system. In steady state it yields the MOND simple interpolation function ν(y) = [1 + √(1 + 4/y)] / 2 exactly and without free parameters.Global asymptotic stability is proved by a Lyapunov functional. The relaxation spectrum predicts timescales from 204 Gyr (ultra-faint dwarfs) to 0.09 Gyr (Newtonian regime), providing a dynamical clock absent from all prior MOND formulations. Non-equilibrium solutions predict hyperbolic halo decay after baryon stripping, with a sharp bifurcation at su2080 = ln 2: stripped massive galaxies lose half their effective halo in 6—7 Gyr, while stripped MOND-regime dwarfs retain theirs for 10²—10³ Gyr.The SPARC radial-acceleration relation is recovered exactly (by algebraic construction) once au2080 = cHu2080/(2π) is fixed from the local Hubble rate. Eight falsifiable dynamical predictions are stated; seven target galactic observations (JWST, Gaia DR4, WEAVE, Hector IFU), and one is a conditional cosmological conjecture contingent on the covariant sector.A proposed covariant extension (§10) derives c_gw = c exactly and no-ghost from the kinetic structure, with candidate results w ≥ −1 and γ_PPN = 1 + O(au2080/g_N) contingent on the proposed action; CMB invariance and phantom exclusion are stated as conjectures requiring full perturbation-theory derivation.