(speculative) continuous spectrum + discrete spectrum + and now let me go out on a limb: there's an analogue of a power series here, and there are more terms.. but they're all precisely 0 when there's no change of state.
If you've ever played around with fractals/functions with the conjugate operation, you know of phenomena where a curve splitting the plane into two regions can just kind of /condense/. Again, this is completely speculative.