capability to match or surpass human intelligence across all conceivable cognitive tasks

What human intelligence do you mean? Genius? Professional? Educated? Random person? “Dumb” person?

I think the distinction between these options probably doesn’t matter alll that much if the threshold you’re using is either “random person” or higher? Maybe bump it up to “random educated person”?

They are still different concepts of course, but I imagine that once one is achieved, the others aren’t far off.

“General”.