Then I can't explain why it's producing the results that it does. If you have more information to share, I'm happy to update my knowledge...

Doing a web search on the topic just comes up with marketing materials. Even Wikipedia's "Reasoning language model" article is mostly a list of release dates and model names, with as only relevant-sounding remark as to how these models are different: "[LLMs] can be fine-tuned on a dataset of reasoning tasks paired with example solutions and step-by-step (reasoning) traces. The fine-tuned model can then produce its own reasoning traces for new problems." It sounds like just another dataset: more examples, more training, in particular on worked examples where this "think step by step" method is being demonstrated with known-good steps and values. I don't see how that fundamentally changes how it works; you're saying such models do not predict the most likely token for a given context anymore, that there is some fundamentally different reasoning process going on somewhere?

I'm saying adding "think step by step" does not get you close to actual reasoning, it just produces marginally self-consistent linguistic reasoning.

Actual reasoning requires training on diverse data sources, as you noted, but also coached experimentation (supervised fine-tuning) not just adding "think step by step" instruction to a model trained on typical textual datasets. "Think step by step" came first and produced increased performance on a variety of tasks, but was overhyped in its approximation of reasoning.