144 hours or 72 hours in Beijing Capital?

Hello,

I am traveling USA-Beijing (PEK)-Seoul, US Passport. Arriving into PEK on 11th April at 14:00, and departing to Seoul (ICN) from PEK Airport at 18:10 on 14th April. I read here and in other places that there is 144 hours for PEK, and in others 72 hours. I did see an official website of the Chinese Government state 144th Hours. I believe my stay is 76 hours with that itinerary. Am I ok to transit? Also, does one require a valid Chinese visa to use the transit (as in, we say we don't want to use it) or is having no entry permit ok? Final Destination is Seoul but I wanted to take advantage of the transit and see the Great Wall.