> Google could look at a page and give you the smallest query that would have returned exactly this page as a first result

Maybe like a decade ago this was a student project that Google sponsored (maybe as either Summer of Code or some precursor to that). A student group developed a system for “tagging” a page with a series of “random” but memorable words that could be used to identify a page. Kinda like how imgur and other other sites generate URLs now. Like “glittery hamster bananas” or something like that.