I was actually quite glad while reading this when I realized it wasn't trying to make-time-a-dimension! Sometimes it seems to me that ppl are cool with just making a float4 out of x,y,z,t and still think everything will work out fine!? (obviously fine in coding projects I'm more talking about a physical interpretation of an idea of 'coordinates' of a reference-frame).

Granted there's some clear ties and relationships between time and space, the classic x,y,z - well I would argue that the dimensionality of space probably amounts to more like approximately 3 integers-worth of connectivity-along-separable-axes in general (on average) but probably can and does fluctuate down nearer to 2 and beyond 3 in places!? Woo maybe slightly fringe way of thinking about space? But in my opinion time fundamentally doesn't (and probably cannot) work like that at all: Space is mostly symmetrical (in that +x is the same as -x, ignoring gravity for a sec) and can be moved-through by objects, especially those that control their own velocity. Time is not symmetrical (it seems, at all?!) and there is no control over the 'motion' of anything in time - causality is the engine making it 'tick' or 'go forward' (personal opinion of course).

I am not qualified to understand the paper but it does seem to me that given one could connect bits of string or wires (in our mostly-3d universe) into topologically-4d-networks.. maybe that is what this is more about? In this case the claim is that the material can do 4d wave-transmission IIUC which is a fair-bit more complicated than bits of string/wire. I don't think it's unclear thinking though, just a very complex topic!