I just had an idea. I'll throw it at you and see if it sticks. What do you think of splitting the word to exist and give it a companion maybe "to besist"? Besist would mean mathematical existence, and the existence of rules. So Numbers besist and Newtons Laws besist, but cake, elephants and electrons exist. Besistence only applies to the "world" of logic. Platos ideas would thus not be real but simply besisting.