Slimjet Browser by company Flashpeak
Wikipedia info: https://en.wikipedia.org/wiki/SlimBrowser
Threads:
http://www.murga-linux.com/puppy/viewtopic.php?t=97172
http://murga-linux.com/puppy/viewtopic.php?t=111442
http://www.murga-linux.com/puppy/viewtopic.php?t=106957
You will find .pets links from the links above.