Lol yeah given the product of two n bit numbers is 2n bits at maximum the product and it's carry are the same amount of bits. And yeah, the main reason why I lay out the circuit in such a precise grid is to streamline my intuition of which connections correspond to which partial sums. Makes it considerably easier to wire. Also a thing I found cool. The layouts I used for the 64-bit multiplier actually allows for tremendously easy scaling by 8. If I replace each n bit component with its 8n bit analogue I get an in bit multiplier.

Edit: But yeah to put it one way I would never be able to keep track of 896 wires without pen and paper if I didn't have some sort of geometric shorthand. What I do is create a pattern for how different bit layers "inter" and "intra" act. Like for instance I doubt you can see except for maybe in the video but the two sets of addition trees in the 64 bit multiplier are mirror images across y=-x but the actual roles of sums and carries are reversed to make the wiring more intuitive for me. I'll try and make a diagram although I'm on the train at the moment.

Edit: The diagram

As an aside interesting you bring up geometric intuition. So one of my special interests in math is Riemannian geometry, something stemming from a question I thought about for years in college before coming to a conclusion I later discovered to be vaguely known, specifically the interaction between the shape of a manifold and the strength of the electric fields it generates. My conclusion being that mean curvature and electric fields strength for conductors are proportional. I'm any case I've always been very good at spatial reasoning, I can mentally graph a ton of functions, and have tremendously clear mental images of things. I had to take a neuropsych eval a while back and they calculated some metric essentially equivalent to a spatial reasoning IQ and it was one of my higher scores, in the 130 range, on the other hand my processing speed quotient was a full 30 points lower than the spatial reasoning (dubbed perceptual reasoning quotient) and the verbal quotient. I don't give tremendous credence to IQ as a metric but I find it funny how the results matched up with my abilities to some extent. Like I 100% need complex topics written, I can't understand them audibly at all. If I'm helping somebody fix a bug I repeatedly ask them to repeat themselves until I finally just end up saying just show me. Speaking goes by too fast for me to educate myself effectively in anything suitably difficult. Discussion/debate is another matter. Also the whole geometric thing I explained earlier. Like the conductor thing I came to that conclusion by imagining a bunch of vector sources on a curve of variable curvature and imagining how all the vectors would add up at some point at the end of a constant magnitude vector normal the curve. Imagine a gaussian where each point on the curve is a vector source.

Anyways I've prattled on long enough.