Volume XV (N): Nadir of the Strong Force and the Death of Space

The strong force presents a fundamental challenge to any discrete causal-graph theory of physics. The observed low-energy 1S0 nucleon-nucleon scattering length, a_s = -23.74 fm, requires a nearly-bound virtual state, while the potential well must remain finite and shallow. We show that the standard point-particle double Yukawa picture, with or without uniform-sphere or vertex form factors, cannot reproduce this scattering length. The resolution comes from the N.E.A. bandwidth constraint itself: when two K4 defects approach, their combined bandwidth deficit approaches the horizon threshold phi = 0.5, and the interaction channel fades into darkness. A phenomenological window W(r) = 1 - exp[-(r/r_c)^n] encodes this fading. With four parameters (V_pi, V_rho, r_c, n), the model reproduces a_s = -23.66 fm and r_min = 1.07 fm, in excellent agreement with experiment. The same mechanism yields a corrected rho-meson mass m_rho = hbar c / (2 Delta - 3/4 Delta^2) = 775.39 MeV, deviating from the PDG value by only +0.017%. We then extend the fading mechanism from K4 to the C8 scaffold itself: at phi = 0.5, space dies. This suggests a natural framework for singularity resolution and emergent cosmology, to be developed in subsequent volumes. The strong force is thus not an isolated sector but the first experimental confirmation of the Nadir: the point where bandwidth exhaustion extinguishes interaction and, at the deepest level, space itself. This is Volume XV of the N.E.A. main paper sequence. Its principal subject is the strong force at low energy, where the bandwidth-fading window is shown to resolve the long-standing conflict between the nucleon-nucleon scattering length and the potential well shape. The same mechanism is then extended from the K4 tetrahedron to the C8 spatial scaffold, leading to the death of space at the horizon condition phi = 0.5, singularity resolution, and a candidate framework for emergent cosmology. All key numerical scripts are publicly available in the Nadir repository:https://github.com/hzhangy/Nadir The relevant scripts include:- nea_rho_mass.py: rho-meson mass correction.- nea_strong_force_fading_into_darkness.py: bandwidth-fading window model.- nea_strong_force_optimize.py: low-energy 1S0 scattering fit.- nea_strong_force_shape_factor_v2.py: uniform-sphere form factor.- nea_strong_force_time_bandwidth.py: time-bandwidth hard core.- nea_strong_force_fit_to_scattering.py: point-particle coupling inversion.- nea_strong_force_k_topology_test.py: coupling-ratio topology test. The three-form-factor and hard-core attempts are phenomenological failures recorded here because they lead to the central insight: the strong force fades rather than repels at short distances.