San Francisco -> Beijing -> Singapore -> San Francisco?

Hi All,

I am a US citizen living in San Francisco.

I am flying from San Francisco to Beijing on Sept 2, arriving at 14:40. I leave Beijing for Singapore at 13:00 on Sept 5 and then leave Singapore for San Francisco on Sept 7. While in Beijing I will be in the city and staying at a hotel sightseeing. Is this something that is covered under the 72-hour Visa-free Transit rule in China? I.e. Can I enter Beijing (and leave) without a visa?

Thank you for your guidance here!