Plane with an object shadow isn't creating mixed shader transparency

I've got a shader that I need to use as a transparent shadow for a character. It shows the shadow just fine when I use a diffuse > shader to rgb > color ramp setup, but when I plug that into a mix shader with transparency, it shows nothing at all.

I've tried adjusting the color ramp, switching it, switching the order of transparent and emission in the mix shader, and nothing makes it appear transparent.

I've also tried plugging a regular voronoi into the mix shader, and the transparency works fine with that