Hi I am an author of the paper. We believed that a simple formula should exist but had not been able to find it despite significant effort. It was a collaborative effort but GPT definitely solved the problem for us.
Oh that's really cool, I am not versed in physics by any means, can you explain how you believed there to be a simple formula but were unable to find it? What would lead you to believe that instead of just accepting it at face value?
There are closely related "MHV amplitudes" which naively obey a really complicated formula, but for which there famously also exists a much simpler "Parke-Taylor formula". Alfredo had derived a complicated expression for these new "single-minus amplitudes" and we were hoping we could find an analogue of the simpler "Parke-Taylor formula" for them.