Except that's exactly what Plato said. If one were to grant the possibility of some other realm where numbers are real or archetypes, then one is not an nominal

Except that's exactly what Plato said. If one were to grant the possibility of some other realm where numbers are real or archetypes, then one is not an nominalist at all, as the author of this paper seems to be (although he may actually be a conceptualist). A nominalist would never grant that such a realm exists or he would be a realist/platonist.