Meta$^n$: Recursive Self-Improvement through Emergent Depth· Meta$^n$：通过递归深度实现自我改进

Self-improving LLM agents refine answers, not the process that produces those answers. Systems that add a meta-level hold that level fixed, and those that edit themselves must leave part of their own editing machinery untouched to stay stable, capping the meta-depth they realize at roughly two. We present Meta$^n$, which keeps the meta-operation fixed and recurses on its input instead. That operation, $Ω$, is applied repeatedly to its own products, reading the traces of the solver stack below together with the code that produced them, then writing the next layer as a strategic pre-process and a library of callable helpers. Because $Ω$ never changes, it cannot destabilize the system, and because its input strictly grows, each layer reasons from a higher vantage than the last. Depth is set b