Synthesize, Recurse, or Infer: Data-Adaptive Program Synthesis at Runtime AI Breakpoints

We introduce the recursive AI breakpoint, a single execution primitive that lets aprogram be written as a seed -- one generic instruction with no implementation -- andgrow its own code at runtime, shaping itself to the data it encounters. At a breakpointthe program pauses, shows a language model (LLM) a sample of its live runtime state, andthe model chooses among three actions: infer the answer directly, synthesize guarded codethat computes it locally, or recurse -- emit code that handles the part of the data itrecognizes and re-invokes the breakpoint on the residual it does not. We show that thesethree actions form a single operator, Solve, of which "call the LLM per item" and "ask theLLM to write one function" are the two degenerate endpoints. Our central result is a costlaw: when a dataset of size n decomposes into k internally-regular sub-populations plus anirreducible tail of size t, Solve incurs an LLM cost of Theta(k*c_synth + t*c_infer) --additive in the data's heterogeneity rather than multiplicative in its size. Across livecontrolled experiments on a current LLM we observe exactly this: guarded synthesis matchesper-item inference accuracy (0.99) at 40x less data; a validate-and-escalate step closesthe robustness gap that pure synthesis suffers on unseen formats; and full recursion drivesthe data sent to the model from 100 rows to 8 at identical accuracy, by discovering thedata's cluster structure on its own. On a real, standard data-cleaning benchmark the samemechanism cleans hundreds of records at near-perfect accuracy while sending an order ofmagnitude fewer rows, confirming the cost law outside synthetic data. We are equallyexplicit about the boundary: the benefit is contingent on data being clustered, and westate where the mechanism degrades on messier, less systematic heterogeneity.