Earlier quoted context omitted.
You won't find a specific link, but at some point if you generate millions of urls the 1024 bits will start to return values pretty quick through bruteforce. The one link won't be found quickly, but a bunch of links will. You just need to fetch all possibilities and you'll get data.
1024 bits seems a bit too much for the birthday problem to be a thing. I looked at [1] to do the calculation but (2^1024)! is a number too large for any of my tools. If someone has a math shortcut to test this idea properly... [1] https://en.wikipedia.org/wiki/Birthday_problem#Calculating_t...
(Well, before you apply the logistic taper to it. So you wanted an approximation? There you go. Until you get the chance of a hit to be quite high, it's basically equal to guesses * valid links / 2^1024.)