Does a fasting person licking his saliva that reached outside the lip and swallowing it harm the fast?

Swallowing normal saliva that has not left the mouth does not invalidate the fast by scholarly consensus. However, if saliva exits the mouth and is then returned and swallowed, it invalidates the fast. Also, the fast is invalidated by swallowing saliva that has mixed with something else and changed its color, or by swallowing saliva that reached the outer part of the lip and was then drawn back. As for intentionally gathering saliva and then swallowing it, there are two views on this, and the soundest of them is that it does not invalidate the fast.