[Finnucane]

>if archive.org scans in a hardback with its ISBN, what do I use for the scanned pdf?

The scanned pdf just doesn't have an ISBN. ISBNs are assigned by publishers to products for inventory management. That's it. If archive.org scans a book, it's not a product that needs inventory control.

[NoMoreNicksLeft]

I need unique identifiers. And I disagree. For me, the scan of a book keeps the same ISBN as the printed book that was scanned (when it has an ISBN at all). No other sensible alternative really exists. I also believe Open Library catalogs them the same (since they are archive.org too, and doing much of the scanning).

[Finnucane]

You may need a unique identifier. You may use the isbn if you like. No one will stop you from doing that. But no isbn-issuing entity has applied an isbn to that file.