Mass Defect as a Memory Effect: Deuteron Binding Energy from History-Dependent Gravity (Paper LI)

We demonstrate that the deuteron binding energy (Eb=2.224Eb=2.224 MeV) is not merely a parameter of a phenomenological potential, but a dynamical functional of temporal memory in History-Dependent Gravity (HDG). Building on the spectral density and Renormalization Group (RG) flow established in previous works (Papers III, XLII, XLV, L of the HDG series), we show that the nucleon-nucleon interaction naturally assumes a separable form where the IR scale and coupling are strictly fixed, leaving no free parameters to fit nuclear data. We provide an exact analytical solution for EbEb, revealing a quadratic scaling Eb∼(κ−1)2Eb∼(κ−1)2 characteristic of proximity to an HDG quantum critical point. Furthermore, we prove an Irreducibility Theorem: the continuous spectral density of the HDG memory kernel induces a dynamical branch cut in the complex energy plane, an analytic structure that cannot be reproduced or renormalized away by any local or derivative-expanded Effective Field Theory (EFT). Finally, we propose a falsifiable experimental signature: an energy-dependent effective range in low-energy nn-pp scattering, and predict non-linear binding energy scaling for A≥3A≥3 nuclei. This work establishes the deuteron as the first verified composite system governed by HDG spectral memory.