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Your understanding is basically correct. "how applicable the search controller is when applied to new problems". We need meta-agent thinking pattern. Self-evolving agent has been very popular and we want to use agent to design a perfect agent. This is the problem that the "search" controller employed in this paper aims to solve.
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Great explanation.

Do you think this could be extrapolated to areas with no objectively verifiable results / outcomes?

(Outside of math & science)

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Could use the shorthand of 85%, 10%, and 5% as the way to divide the workload; 850/1000 computes, 100/1000, and 50/1000. Brute sprint, clean up & revaluation runs, then checksum and presentation.
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Intuitively I wouldn't readjust how many steps they each do, but instead add another run afterwards, that get the same amount of steps as the previous, but now also with a concise description of what the previous attempts did and what they achieved, and ask it to improve. The amount of compute you have available, would dictate how many full iterations of this "fan out search > consolidate" workflow you can do.
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In the paper (section 5.1), they actually tried to abstract high level directional insights into the prompt in order to see if that helped, and they basically found it underperformed a prompt that didn't have those insights at all, implying that directional guidance perhaps over-constrains things.
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Isn't that a challenge with RL anyway that for a lot of problems its hard to even know accuracy continuously for each step
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