Hi Karl,
Sorry to post another thumbnail thread but I've tried all the troubleshooting found on the forums but I can't seem to get thumbnail generation to work when I'm using nginx. I have the config file set up with the rewrite rules from your github/gist and the diagnostics page says everything is okay but thumbnails result in a 404 error.
I'm not seeing any php errors or nginx errors in the logs so I'm having some trouble tracking down where the rewrite is failing or if it's some other setting that is preventing the thumbnail generation. It's a fresh install with minimal content and I'm trying to test it out on a centminmod install running Centos 7. If you want to pm me a public key I can give you access to the server if needed.
Site: beta.tekphotos.org