Neutron--Deuteron Doublet Scattering Length as a Probe of Temporal Memory in History-Dependent Gravity (Paper LIV)

The neutron--deuteron (ndnd) doublet scattering length (2and2and) is a classic probe of three-nucleon forces (3NF) in low-energy nuclear physics. Standard high-precision nucleon--nucleon (NN) potentials systematically underpredict the experimental value (0.65±0.020.65±0.02 fm), typically requiring the introduction of phenomenological 3NF corrections with additional free parameters. In this work (Paper LIV of the History-Dependent Gravity series), we demonstrate that this longstanding discrepancy is resolved without introducing new forces or free parameters. Instead, we employ the History-Dependent Gravity (HDG) framework, where a universal spectral memory density ρ(μ)ρ(μ)—previously fixed exclusively by two-body (deuteron) and three-body (triton) binding energies in earlier works—generates a nonlocal, irreducible correction to the three-body scattering amplitude within the standard Faddeev formalism. We derive an analytic expression for the memory-induced shift and show that it naturally yields Δ2and≃0.11Δ2and≃0.11 fm. This brings the NN-only baseline (0.550.55--0.580.58 fm) to 0.660.66 fm, in excellent agreement with experimental data. Furthermore, we prove a non-reducibility theorem, demonstrating that this memory-induced effect cannot be absorbed into a renormalization of standard two-body effective-range parameters. Beyond the scattering length, the same spectral function ρ(μ)ρ(μ) consistently governs the two-body mass defect, three-body binding shifts, and predicts a distinct, non-polynomial energy dependence of the effective range r0(E)r0(E), offering a falsifiable signature for future phase-shift analyses. These results establish a unified, parameter-free description of few-nucleon observables, suggesting that temporal memory is the fundamental origin of effects traditionally attributed to independent many-body forces.