If we place x4 on top of x2, the distance between x2 and x4 becomes zero violating the constraints that distance between x2 and x4 needs to be 'd* sqrt(2)'. It is not possible to satisfy all the constraints for every pair of points in this case.
we are only preserving the neighbourhood distances. You said you are preserving only the four d's not others. Even the distance between x1 and x3 is 2*d in 1D. So we can place x4 on top of x2 so that it preserves the d's.
I will make a video eloborating further. I understand the point you made. It's a good point. I am currently traveling. I will respond back with a follow up video by tomorrow. Thank you once again for asking a good question.
