The core is a modestly enhanced 486, meaning it has nothing to do with Clairemont (unless we were lied to about that). Compare the block diagram here:

https://communities.intel.com/servlet/JiveServlet/previewBody/21825-102-2-25117/Intel%20Quark%20Core%20HWRefMan_001.pdf

With the traditional 486 block diagram here:

http://intel-vintage-developer.eu5.org/DESIGN/INTARCH/PIX/272713_1.GIF

You can also confirm it in the cycle timings here:

https://communities.intel.com/servlet/JiveServlet/previewBody/21826-102-2-25118/Intel%20Quark%20Core_DevMan_001.pdf

And I want on a lengthy rant about the processor that I don't feel like repeating, if you want you can read that here: http://forums.anandtech.com/showpost.php?p=35564891&postcount=78 :P