Motti Intermediate Physics — HAL: Strominger Triangle, Soft Graviton Theorem, and the Angular Momentum Gap

We analyse the HAL (Hyper-Anisotropic Luminal Physics) framework through the lens of the Strominger triangle connecting BMS symmetry, gravitational wave memory, and the Weinberg soft graviton theorem. We establish that the Komar angular momentum with G_eff = G_N/C0 equals the GR value when ADM masses are held fixed (ratio = 1), that the orbital EOB angular momentum scales as J_orb^HAL = J_GR/sqrt(C0), and that the Weinberg soft factor in the gravitational sector becomes S^(0)_HAL = S^(0)_GR/sqrt(C0). None of these mechanisms produce the factor C0^2 entering J_total = C0^2 * J_GR. We identify the physical mechanism: the Goldstone boson of the spontaneously broken U(1) coherential symmetry must inject J_theta = (C0^3-1)/C0 * J_GR ~ 3*alpha_em * J_GR into the gravitational system during merger. The net observable is Delta_h^HAL/Delta_h^GR = C0, giving epsilon = C0 - 1 = alpha_em = +0.7297%. The residual dynamical gap is identified as the unique falsifiable prediction requiring the three-stage numerical programme (EOB + NR + extended Teukolsky) proposed in DOI 10.5281/zenodo.20863207.