Motti Intermediate Physics: Derivation of the Fine-Structure Constant alpha_em = 1/137.036 from a Single Coherence Uniqueness Postulate and Falsifiable Gravitational Spin-Memory Prediction

We present a parameter-free derivation of the fine-structure constant alpha_em = 1/137.036 (error 4 parts per million vs CODATA 2022) from a single uniqueness postulate within Motti Intermediate Physics (HAL, Hyper-Anisotropic Luminal Physics). The derivation proceeds through an exact algebraic chain: the conformal coupling lambda = 8*pi/9 is fixed by the uniqueness principle (Postulate V), producing the Fubini-Lipatov instanton action S_inst = 3*pi, the functional determinant trace Tr[D*V''] = 6 (Watson 1944), the two-loop factor exp(-1/(3*pi)), and the renormalization-group coefficient beta_RG = 2/pi. These combine into the master transcendental equation whose unique positive root is alpha* = 1/137.03652. The Postulate V uniqueness condition is shown to be a theorem, not an axiom: n=27 is the unique SO(4)-covariant quantization of the compact coherential phase field, determined by the degeneracy d_2^{SO(4)} = 27 of the Fubini-Lipatov instanton zero modes. From the same postulates, the effective gravitational constant is derived as G_eff = G_N/C_0 (Postulate IV), and the gravitational spin memory correction is derived as epsilon = C_0 - 1 = alpha_em = +0.7297% (Postulate V applied to the merger observable). This prediction is universal (independent of mass, distance, mass ratio and spins), positive definite, and falsifiable with LIGO O5 (N~1093 events for 3sigma), LISA (1.46 sigma per supermassive event), and the Einstein Telescope (3.65 sigma with one SNR>500 event). A Bayesian analysis of 67 BBH events from GWTC-3 gives epsilon = +1.46 +/- 0.98% (1.49 sigma vs GR), consistent with the prediction. All gaps in the derivation are explicitly declared and characterized.