This gymnastic maneuver is mind-blowing, especially the last 45 seconds:

While she very well might be defying whatever laws we thought governed the limits of human grace and athleticism, she is not in fact defying any laws of physics. She is actually using them:

From the paper:

To perform the ‘Biles', Simone needs to travel and spin. Her take-off energy therefore needs to incorporate these two elements:

[1] 𝐸𝑘𝑡𝑎𝑘𝑒-𝑜𝑓𝑓=𝐸𝑘𝑙𝑖𝑛𝑒𝑎𝑟+𝐸𝑘𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙

We can break this equation down a bit by considering that she moves up and forward:

[2]𝐸𝑘𝑡𝑎𝑘𝑒-𝑜𝑓𝑓=𝐸𝑘𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙+𝐸𝑘ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙+𝐸𝑘𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙

Can we perhaps simplify the problem?

To simplify the problem, we assume that the gymnast is a point mass, i.e. the gymnast is just a point particle.

Yes, of course. I was just about to say that.

In all seriousness, the paper is reasonably accessible. However, I find it fascinating to try to figure out how she physically does it.

Think in terms of flexion of muscles (shortening) and extension (lengthening) as in a bicep curl where the biceps shorten as you curl up while the triceps simultaneously lengthen.

It is the shortening phase where force and direction is being applied. Then just watch as her joints flex and extend all throughout the complicated move in perfect harmony to produce the "Biles."

Or, you can just marvel at the accomplishment of it all.