If they are of the same type then a point (A,0,0,B,0,0) would result in the same state as (B,0,0,A,0,0) I would understand this as those points mapping to a same R^3->C function. I thought there was no billiard balls and that the wavefunction has ontological priority? If I had two separate particles of different kinds in the same position I could tell from the R^3->C undulations on which kind of particle it is. I can understand it might be handy to order the undulations by their centers point-like shorthands. I thought that the real mechanics happen on the R^3->C and if there are mechanics on the higher dimensional structure they are an emergent consequence of that level.

Like I can index me throwing a rock on the lake by where my rock lands. However this kind of description can not describe any two simultanoues throws or things like throwing a stick sideways into the water. The wierder throws I make the more things I need to spesify. However if I somehow manage convey the shape of the water there is no way it can be inadeqaute picture of the wave (such as if I make a topographical map). And in no way of splashing can I add or remove water or make it do anything but go up or down. The quantum field takes on value of C so it has "more room" than simply going up or down. However in no way of taking on those C values does the lake change in volume or dimensionality.