A general formula is given for the Hopf transversality condition associated with characteristic equations of the form $R(z)=H(z,\tau)$, where $R$ is analytic and $H(\cdot,\tau)$ is the Laplace transform of a distributed-delay kernel. Our main result expresses the crossing direction of a simple purely imaginary characteristic root and provides a geometric interpretation of the transversality condition. We obtain as special cases the classical discrete-delay formula and explicit criteria for self-similar kernels, including the exponential and Erlang families. Several consequences for stability switching are also discussed, and examples are given.