Assembly theory explains and quantifies selection and evolution
nature.com
nature.com
It sounds like "all" they've done is develop a formalism that is (1) mathematically precise, (2) testable and (3) useful for describing evolutionary processes.
That is, they haven't actually showed how selection can overcome the constraints of physics and randomness; they've just developed a useful framework so that hopefully a future breakthrough can be found more easily.
Do I have that right?
The idea is that the possibility-space of molecules is combinatorially vast, even for nature itself. If you can identify a sort of kolmolgorov complexity for molecules (assembly index), the ones with high complexity are indicative of intentional, non-random processes like life.
One of the key differences here from prior approaches is that the definitions they've chosen are computable and universal, though I haven't gotten the same impression of universality and utility from their papers.
The project seems to have a slight case of Wolframesque overreach
https://arxiv.org/abs/2210.00901
The 8 Fallacies of Assembly Theory
"The more complex a given object, the less likely an identical copy can exist without selection of some information-driven mechanism that generates that object."
In other words, tweaking definitions to fit a pre-defined narrative.