Hmm, what is "the google[...].html authentication file" ?
We roped off all of /.well-known/ and it is after all under a dot directory which ought to have been caught by a lot of existing software anyway, it seems like if people have things they want treated this way they ought to live in /.well-known/ too, it's not as though the registration process is onerous, you just need to write a specification for your thing.
Google lets you prove ownership of a website by hosting a specific file with a unique name they provide. When you’re the owner, Google lets you see search analytics for your site.