Four-loop electron EDM matching and timelike $\tau$ electric dipole form factor

We compute the four-loop matching of a CP-odd four-$\tau$ interaction onto the electron electric dipole moment (EDM), together with the leading timelike $\tau$ dipole form factor generated by the same source. Both results are scale independent at this order. Without a local electron dipole, exact electron-EDM cancellation still leaves a timelike $\tau$ signal proportional to the four-$\tau$ coefficient. Its absorptive part cannot be canceled by a real local dipole, allowing collider limits to constrain the cancellation direction and complement static electron-EDM searches.