The paper is here https://www.science.org/doi/10.1126/sciadv.adh4310

more supporting material. https://en.wikipedia.org/wiki/Phason

I don't understand anything about this field but I did used to know what "adiabatic" meant so forgive my lay interpretation... it seems the effects of a synthetic 4D are achieved, by varying these slices of the "periodic crystal of higher dimensions (up to 6)"... whatever that is... which is done changing the phase of "space modulation" in the material.

I think it's like: if you witness a 3D wave and you live in 2D flatland, you can still characterize the wave in 3D. And maybe you can even frob some knobs in flatland which change how that 3D wave behaves, e.g. by shifting its phase; changes in behavior in 3D which are observable in flatland's 2D "slices" also.

Phasons being on Wikipedia with no sniff of scam warnings there or in related articles, I'm inclined to believe the paper isn't a scam, whatever it's saying.

As you point out, combining special dimensions with 1 time dimension is often very sensible.

And a situation where the temporal behavior of waves are controlled across a 3D object would seem to be a sensible place to do it.

But the article doesn’t seem to be equating the “4th D” with time

It is just very unclear writing, or perhaps thinking.

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!