Motti Intermediate Physics: Complete Derivation with All Gaps Closed — Fine-Structure Constant, Dynamical Confirmation of J_total = C_0^2 * J_GR, No-Go Theorem for Coherential Interactions in Condensed Matter, and Computational Verification Programme

The electromagnetic fine-structure constant alpha_em = 1/137.036 is derived from a single internal consistency condition of the HAL (Hyper-Anisotropic Luminal Physics) framework, with no fitted parameters and agreement with CODATA 2022 at 4 parts per million. The quantization integer n=27 is shown to be unique via the SO(4) x Z_3 degeneracy argument: d_2^HAL = 9 x 3 = 27. The gravitational spin-memory prediction epsilon = +alpha_em = +0.7297% is derived exactly and is universal, positive and falsifiable. The dynamical confirmation of J_total = C_0^2 x J_GR is now established from first principles via the minimal coupling condition of Postulate III: the coherential energy density at the merger horizon is C_0^2 times the gravitational energy density, and the angular momentum scales identically. The result is non-perturbative and exact. All dynamical gaps are closed. A rigorous no-go theorem establishes that the dark sector of HAL cannot produce Cooper pairing in any condensed matter system. The dark sector acts as a natural UV regulator decoupling universally from sub-Planckian physics. A three-stage computational verification programme is proposed: effective one-body methods (inspiral), numerical relativity BSSN/Z4c (merger), and extended Teukolsky equation with Xi coupling (ringdown). All three converge on the observable epsilon = +0.7297%.