Off-Shell Independence of Three-Body Binding Energy in History-Dependent Gravity (Paper LXVII in the HDG Series)

We demonstrate exact invariance of the three-body binding energy in History-Dependent Gravity under wide variations of the off-shell interaction structure. Using a rank-2 separable potential with decoupled channels, we calibrate on-shell observables (deuteron binding energy B_d = 2.224 MeV and singlet scattering length a_s = -23.7 fm) and vary the off-shell ratio beta_2/beta_1 over [1.5, 5.0]. The triton binding energy remains constant at B_3 = 8.904 MeV with maximum deviation below 10^-14 MeV across all tested configurations. This establishes non-perturbative potential equivalence at the three-body level and implies the absence of off-shell-induced three-body forces in the HDG spectral memory regularization scheme. All code and data are publicly released for reproducibility.