Take a look at the harmony repo which specifies the internal OpenAI format - the effort level is specified in the context after the <start> tag - https://github.com/openai/harmony

Note that inference libs also have parsers that put hard limits on reasoning tokens with separate counters (similar to how you can put a limit on token generation per completion versus waiting for an <eos>).

Different models do slight variants.

Usually it’s done in post training to enforce behavior based on prompt. Ie. System prompt with thinking:max or low or wtv.

Enforcement then goes via constrained decoding, checking for think token start and end with max lengths, or other variations

At a guess. May be associated with token length context window. Down selecting is consistent with warning message, forcing cutoff to context window. The technical term cache being a synonym. Increasing the headroom for more "thinking" should allow the implementation to access more resources without warning about the cache breaking.

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