How to decide a level of reasoning?

Codex
1

I am finishing writing a formal description of what I call “pointfree funcoids” (it’s not relevant what they are) between partially ordered sets.

Now I want Codex to produce for every theorem about pointfree funcoids, a special case of the theorem, when the partially ordered sets are necessarily the sets of filters on a set. In simple words, I want to automatically produce for every theorem its certain special case.

What level of reasoning (Low…Extra High) should I set for this task? At one hand, the task involves many theorems, so the level should probably be high. At the other hand, specializing each theorem is expected to be relatively easy, so the level should probably be not very high.

Is the level about total amount of reasoning after a prompt, or is is about how meticulously each subtask is done?

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2

I would test all and go with the lowest thinking one that worked?

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3

But I want to know the principle: Is the level about total amount of reasoning after a prompt, or is is about how meticulously each subtask is done?

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4

It’s a bit more low level than that - the level of reasoning controls max number of reasoning tokens the model will consume before attempting a response - generated during its “reasoning cycles” - essentially a structured period of talking to itself.

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