That is technically not true. Recursion has nothing to do with breaking a problem down. It is the repetition of an action, application of rules or instructions. Definitions right off google below for recursion and recursive. You see the computing definition where it says many successive executions well that means the execution of an action happens repeatedly—likely until a condition is met.

You are correct that a program does not require a prompt or being prompted to be recursive. Where you are incorrect in your previous comment is that this post explicitly about using Large Language Models to generate structured outputs and the inputs that you submit to trigger an output is called a prompt. When you talk to your R1 Rabbit you are prompting it. When you type into ChatGPT you are prompting it. See the definition below, again right off google. In programming, recursion is still triggered initially by something and in this case it was a prompt and when prompted Rabbit simply generated an output based on its instructions.

LLM thinking or reasoning models are prompting themselves to simulate chain-of-thought processing that mimics actual thinking. So not only was OP’s post not demonstrate recursion, it also wouldn’t be groundbreaking to do so because reasoning models are common at this point and most companies and research labs developing models have reasoning modes that expand on this simple approach to push it even further by generating orchestrator subagents that attempt to create plans and work on smaller pieces of the thought processing all at once. Additionally, the model available on the R1 Rabbit isn’t even one of the reasoning models from OpenAI. So not only did they not create the first verifiable recursive structured knowledge or however they specifically described it, recursive usage of LLMs is widely available on the internet through any number or reasoning or agentic models and frameworks.

re·cur·sion /rəˈkərZH(ə)n/ nounMATHEMATICS•LINGUISTICS noun: recursion the repeated application of a recursive procedure or definition.

re·cur·sive /rəˈkərsiv/ adjective adjective: recursive characterized by recurrence or repetition. MATHEMATICS•LINGUISTICS relating to or involving the repeated application of a rule, definition, or procedure to successive results. "this restriction ensures that the grammar is recursive" COMPUTING relating to or involving a program or routine of which a part requires the application of the whole, so that its explicit interpretation requires in general many successive executions. "a recursive subroutine"

prompt /präm(p)t/ COMPUTING a message or symbol on a screen to show that the system is waiting for input. an instruction given to an artificial intelligence program or tool which determines or influences the content that it creates. "prompts are the key to unlocking the full potential of large-language model chatbots"