One of the models for associating individual wealth with productive output in an economy that is predominantly (if not completely) post-labor is to apportion ownership of companies across the population. This could be a matter of distributing shares of existing companies or granting shares or exclusive ownership to new companies.
The ideal fit would be with self-starting startups. As a dedicated AI system (or many such systems) launch profitable companies, their ownership is distributed throughout the population according to whatever criteria make the most sense. It could be random or tied to consumer behavior or other interests / aptitudes.
Or possibly one could gain ownership in businesses by expressing an early interest in them or contributing to the original idea from which they are launched. You might think of it as the auto-pilot of entrepreneurship. The machine does all the hard stuff while we reap the benefits.
For a related idea, see Wealth Robots.
For a road map of how we get from here to there, check out Melanie Swan’s recent piece on Blockchain Thinkers and Smart Contracts.