This is correct, as I understand it. Most complexity measures are defined in terms of asymptotic behavior, so any specific finite algorithm has 'constant' comp

This is correct, as I understand it. Most complexity measures are defined in terms of asymptotic behavior, so any specific finite algorithm has 'constant' complexity. This is an obviously unhelpful bit of pedantry in the theory side. In fact, it's as you say; we can compute a 'raw' complexity for a finite operation (eg, raw count of arithmetic ops), and then use that operation as a primitive to create an algorithm with an asymptotic complexity which depends directly on the finite operation's 'raw' complexity. (complexity theory, and specifically for matrix multiplication, is a great example of metrics becoming targets becoming bad incentives, a la Goodhart's Law. The so-called best algorithms are 'galactic' and therefore of no use to anyone. There's some fuzzy-headed hope that one day the people chasing the big-O exponent metric will come up with something practically useful, buuuuuut... you actually gotta work practical problem to solve the practical problem, and that requires different metrics. This seems to be what's motivating the work under discussion here.)