Synthesis capability: When the system is capable of deriving established knowledge from first principles (similar to theorem proving from axioms)

Gap detection: The system is able to identify gaps in established knowledge

Path/problem decomposition: The system is able to decompose a problem (i.e., an identified gap) and break down the solution into a set of subproblems that can be independently solved.

Improvement/Optimization: Given a known solution, the system is able to discover objectively better approaches to solution.

There are probably other dimensions, but I would start with these.