Is locate/mlocate some obscure command? It works pretty well for this sort of thing (and has the advantage that you wouldn't need to put git repos everywhere, or something silly like that).
I often forget what I've named a pdf that I've downloaded, but usually I'll put something related to the topic of a paper in the file name, so a command like:
locate -i "*svd*.pdf"
will have a decent chance of finding any papers about svd's that I have, and is more or less instantaneous.Although -- I think I did come across the locate command because I was searching for alternatives to 'find.' I can not for the life of me remember the correct order for the path to start searching, and the filename.