Where are the rules of the 144 hour free transit officially written by a Chinese authority?

Can you confirm that I (as a US citizen) qualify for free transit with this itinerary: Fly from Chicago to Shanghai, stay in Shanghai for 3 days, then fly to Ho Chi Minh City for a 5 day stay, then return to Shanghai and stay again in Shanghai for another 5 days before flying back to Chicago. I am an independent traveller and not with a group, and I have confirmed flight information for all flights to show authorities.

I am just nervous that there does not seem to be anything about this, at least with the latest rules, appearing on the websites of the Chicago or New York Consulates under visa information. Please help--only two weeks to go before my departure. THANK YOU!!!