Motti Intermediate Physics — HAL: The Stochastic Gravitational Wave Background — Sign-Dependent Corrections and Spectral Ratios

HAL corrections to the stochastic GW background: merger-dominated backgrounds enhanced by C0^2 (+1.46%) because J_total = C0^2 J_GR; rotating NS backgrounds suppressed by 1/C0^2 (-1.44%) because I^HAL = I^GR. Sign depends on whether source is angular momentum (enhanced) or mass quadrupole (suppressed). New prediction: spectral ratio Omega(PTA)/Omega(ET) enhanced by C0^4 (+2.95%) if ET band is NS-rotation dominated. Consistent with NANOGrav 2023.