Where a model's reasoning lives now, and what you get to see of it

We read both vendors' documentation and the recent work on looped transformers with three questions: what does a model's reasoning cost, what can you steer, and what can anyone read afterwards. The answers sort into three places.

On the page, as visible text. You pay the output rate, you steer it with the prompt, and you can read it, though studies show these visible traces are often unreliable.

Off the page, as hidden tokens. The example in OpenAI's own guide shows 1,186 output tokens charged, 1,024 of them reasoning; you pay for every one and the text stays with the vendor. Anthropic's docs show the same: you're billed for full thinking tokens whether shown or not. The rate is the same, the steering is an effort knob in place of a prompt, and what you can read is at most a summary. The exact count is in the usage object, and on the newer models earlier turns' hidden reasoning stays in context and is billed again as input.

Inside the network, as extra passes through the same layers, which is what recurrent depth means. Compute rises per token, the token count does not move, and there is no text for anyone to read, the vendor included.

Whether Astra uses this is unconfirmed. The plainer explanation for shorter traces is just that more capable models write less. Both fit.

Of the three places, the middle one is the one whose count you can still read. Log it per turn, and treat the visible trace as the summary the documentation calls it. That count is the only exact thing a response gives you about its own reasoning.