Once again, you're trying to analogize your way into something you haven't studied.

What exactly is your purpose here? You still can't even articulate the fundamental flaws LLMs have with tasks not fully within the training data. Right now, today, there is no frontier model that can operate on tasks without resorting to reward hacking once its outside the small class of problems its training data covers. The solution for this is to invest significant time from domain experts to meticulously define how to solve tasks in other domains.

Here's a trivial example: Try getting Claude to generate coherent COBOL. Or TCL. Or even Powershell. Any language that has low representation on StackOverflow is a language that Claude can't speak until someone teaches it how. Even the Python it generates has limited expressiveness or extensibility.

Everywhere you look, the AI is limited by the fact that it can't generate its own new information. Navier-Stokes and statements in pure mathematics like it are the absolute best case scenario for agentic work against rigorous specification. The theorem statement itself is already a rigorous specification. It has undergone decades of auditing by the mathematical community and its rendering in Lean is a straightforward translation defined in terms of battle-tested mathematical objects from mathlib. The verifier, the Lean theorem prover, has been extensively audited and specifically designed to avoid the types of unsoundness that would make it vulnerable to reward hacks.

No other domains outside of mathematics have such rigorous specifications. Yet, somehow, you believe there's magic pixie dust somewhere within the LLM that will help it achieve something without human interventions and that, somehow, we're "close" to that accomplishment. Don't quit your day job.