I wish I could link it, but I had also read another strategy for reasoning effort, perhaps the most naive implementation, described as whether or not you ignored or accepted the end of sequence token, n-times, n being some count of subsequent ignores.

Now how true that is, I don't know. You could reasonably implement this locally with an inference provider, but I don't know any that do, or I haven't used them at least.

I may also have the technical detail incorrect, but it did come down to essentially "continuing inference beyond a natural termination."

Sounds similar to Qwen3 but the exact opposite: "stopping thinking before a natural termination"

https://arxiv.org/pdf/2505.09388

> Thinking Budget. An additional advantage of Thinking Mode Fusion is that, once the model learns to respond in both non-thinking and thinking modes, it naturally develops the ability to handle intermediate cases—generating responses based on incomplete thinking. This capability lays the foundation for implementing budget control over the model’s thinking process. Specifically, when the length of the model’s thinking reaches a user-defined threshold, we manually halt the thinking process and insert the stop-thinking instruction: “Considering the limited time by the user, I have to give the solution based on the thinking directly now.\n</think>.\n\n”.

^-^