Spacetime Memory and Emergent Galactic Dynamics(SM&EGD): A Field-Theoretic Origin of the Observed Acceleration Law

The Spacetime Memory and Emergent Galactic Dynamics (SM&EGD) framework introducesa scalar memory field ϕ that accumulates curvature history through a non-minimalcoupling ξϕR. In the weak-field limit, the field equations yield a universal accelerationrelation a + αa3/2 = aN. Using the SPARC galaxy sample, I obtain α = (1.20 ± 0.06) ×10−10 m−1/2s, corresponding to a0 = (0.69 ± 0.07) × 10−10 ms−2. The model fits rotationcurves across five orders of magnitude in luminosity, outperforming both ΛCDM andMOND. Adding a small mass term to the potential generates a late-time dark energycomponent, and consistency between galactic and cosmological scales forces a0 ∼ cH0with a numerical coefficient matching observations. A non-local memory kernel providesa first-principles foundation, while screening mechanisms ensure Solar System compatibility.The framework resolves the cluster-scale failures of MOND through merger-inducedtidal memory. Distinctive predictions include declining outer rotation curves (vc ∝ r−1/6),anomalous weak lensing, and a scalar gravitational-wave polarisation, all testable with upcomingfacilities.