It is looking like Thingiverse has gotten rid of the Zip files. If you click on the "Download All Files" button, it now opens a listing of all the project files, with each file having its own download button. Not sure if this is a permanent thing or something temporary.

Thingiverse was having issues where if you loaded a new project you would get hundreds of downloads the first hour. The work-around was to save the project and then wait a day before publishing. I had two projects that I uploaded and published on the same day. The analytics show the massive downloads, then back to the usual one or two downloads per day (see attached image).

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