Motti Intermediate Physics — HAL: Closing Three Open Problems — P-hat as BMS Generator, Gap 1 Internal Sufficiency, and the Candidate Unified Lagrangian L_unif

Three open HAL problems resolved: (1) P-hat^HAL = C_0 x Q_BMS^GR (not Q_BMS): factor C_0 is the origin of epsilon=alpha_em. (2) Gap 1 closed algebraically: n=27 unique integer satisfying Postulates II+V without tachyons, forcing alpha_em uniquely and hence J_total = C_0^2 J_GR. (3) L_unif written explicitly: L_HAL + L_SM[g_i, y_f/C_0, lambda_H] + (alpha_em/2C_0)|Q_theta|^2. Three items remain for complete proof.