In TFA itself!

The multiplication they call an "alternating [skew-symmetric?] invariant form": Q0 in symbols I think?

Basically a polynomial function in the components of the "superoctonions" that go into the product.that how I'd vibesplain to a fellow non-pro, anyways

P10, sec 2.4 Lemma 2.8

The complex structure itself is much more complicated.. or else alpoge would have posted a one line verification of the result? But a summary that excites everybody can only be done by a pro...

The next relevant thing in the paper though, that I might be able to attempt to vibesplain using my uh consumer knowhow, is "integrability" (starting in the section labelled "Context")

Or one could just ask Fable/ChatGPT to ELI10