Those theories were quite interesting.
Interesting to see some theories popping up here, String theory, parallel multiverses, and higher dimensions.
@quagzlor explained it really nicely on how higher dimensions work from a perspective of a being that can only perceive the 2D plane. Since they can't perceive higher dimensions, anything you present to the 2D world will only appear as 2D even if you force a 3D object into that world. In the same vein forcing a 4D or 5D would appear 3D on our perception. If a 4D object that looks like a square partially intersects our 3D world on it's corner we would see a triangle, we would never see what it's full shape is as there's another dimension that we can't perceive. The map explanation was pretty nice on tackling this as well, since the Earth is round but we needed to describe that into a flat surface (e.g. Map) which is why flight routes are curved when drawn on maps to compensate for this.
If I'm getting this right it seems that the fundamentals of magic here is just knowing how to actually manipulate the higher dimensions and interfere with the 3D's laws (in which a higher dimension overrides the 3rd dimension's laws or something similar). I really like this type of explanation of magic, it's like tying magic into a scientific foundation (albeit using unproven theories). And maybe the reason why magic can work on GATE's world as the intercepting dimensions make it possible than on the our world. This would be more likely if Leilei cannot use magic when she's on our world as the intercepting dimensions there might be different.
Also from that string measurement experiment they did, it looked like light was distorted there. I'm pretty sure they actually did put that string on a straight line but since light was distorted, it looked like it was bent. Maybe that black mist is some kind of gravitational anomaly (like some higher forces clashing with the current 3D plane's laws) in the same vein where Leilei explained that by using higher dimensions it can make a string float despite gravity existing.
Though I do somewhat see Rory making glances on the discussion, I wonder what she thinks about this. She is an arbiter of what people are allowed to know and not like Gisselle, seems she's listening carefully on Leilei not actually learning things that isn't allowed in their world. On another note, Leilei plainly announced that she's Itami's wife lol oddly enough there wasn't any blowback from the other harem members xD.