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.
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.