Copyright law & space shifting?

I have a little situation at work, and I think I have a way to solve it, but it requires doing something that would have to fall under copyright fair use, and I’m not sure if it does.

If I have a book with a copyright, and no other license granted from the publisher, and I scan that book into a pdf and then archive the book in the basement, have I now violated the publisher’s copyright?

To me, this is space shifting (which is a little legally dubious ), but is at least arguable. We’re certainly not letting the pdf off our local network.