Viscous Emergent Spacetime (VES)

We present Viscous Emergent Spacetime (VES) as a derivation-constrained effective framework that connects microscopic phase-retention dynamics with emergent infrared gravitational response. The construction proceeds through explicitly separated layers: axiomatic foundations, coarsegrained phase dynamics, conditional Fokker–Planck reduction, single-band phase-slip response, statistical ensemble averaging over heterogeneous couplings, and macroscopic modified acceleration. A key result is the restoration of the statistical ensemble: under a lognormal distribution of coupling strengths, the macroscopic interpolating function µ(y) is derived as a specific oneparameter family controlled by the coupling heterogeneity σK. The deep-MOND asymptotics µ(y) ∼ y emerges automatically from the finiteness of ⟨K−1⟩. The modified acceleration equation µ(a/a0)a = aN yields the infrared scaling a ≃ √ a0aN . The acceleration scale a0 is tied to a retention length through dimensional analysis. The stiffness scaling index βstiff = 1 follows from the quadratic expansion of the retention  energy under a minimal equal-weight assumption. All statements are classified by epistemic status. The framework predicts a characteristic intrinsic scatter in the radial acceleration relation (RAR) that is controlled by σK, providing a falsifiable, VES-specific signature.