Spectral Branch-Cut Signatures in Low-Energy Nuclear Scattering: An Energy-Dependent Phase-Shift Test of History-Dependent Gravity (Paper LXII)

Abstract

This paper represents the first controlled, observable-level test of temporal nonlocality in nucleon-nucleon scattering within the History-Dependent Gravity (HDG) framework. Key contributions: Observable-level framework: We construct the spectral curvature observable C(k)C(k) and derive its relation to the vacuum memory density ρ(μ)ρ(μ) through the distorted-wave Born approximation. Quantitative null test: Using real Nijmegen PWA93 data (not illustrative values), we perform the first extraction of r0eff(k)r0eff(k) with a fully reproducible pipeline, finding that the observed energy dependence is fully accounted for by standard analytic shape parameters. Identifiability analysis: Design-matrix analysis demonstrates that the spectral shape is nearly collinear with the polynomial basis, rendering the amplitude unidentifiable at current precision (σs∼104σs∼104 fm). Coupled-channel extension: Multi-channel analysis of (1S0,3S1,ε1)(1S0,3S1,ε1) yields a structural gain factor of 1.95, insufficient to overcome collinearity but establishing a universal-consistency framework for future tests. Experimental-design roadmap: Sensitivity forecast identifies extended kinematic reach, multi-channel universality, and alternative observables as decisive levers for future high-precision PWA. Methodological transparency: All numerical results generated by released Python scripts (hdg_pwa_pipeline_v7.py, hdg_sensitivity_forecast.py, make_figures_LXII.py) No hand-typed numerical entries Full covariance propagation in nested-model tests Robustness verified across systematic floor scans and kmax⁡kmax variations Relation to HDG series: Paper LXI established why local EFT has a convergence limit (breakdown of locality before breakdown of EFT). Paper LXII establishes how—and how not yet—this limit is observable in the S-matrix, converting the spectral signature into a quantitative experimental-design problem. Falsification criterion: Branch (i) of the falsification criterion is realized: current data are insensitive to the HDG-predicted amplitude. This does not falsify HDG; it establishes the sensitivity threshold and identifies the experimental upgrades required for a decisive test.