Recursive Criticality in AI Research-Agent Ecosystems

Research agents can accelerate the development of their successors without making the development process self-amplifying. We develop a dynamical criterion for distinguishing these regimes in AI-enabled R\&D systems that include models, tools, human oversight, evaluations, training infrastructure, and deployment. A delayed capability model yields a recursive reproduction number $\RAI$, given by realized recursive gain divided by research-frontier hardening. Small improvements decay relative to the reference trajectory when $\RAI<1$ and reproduce when $\RAI>1$. Baseline research speed does not move this local threshold in the minimal model, while successor-cycle delay controls how quickly supercritical amplification becomes visible and bounds its high-throughput rate by $\ln \RAI/\tau$. A finite effective frontier can terminate a supercritical episode. Extending the analysis to interacting research actors replaces the scalar criterion with the spectral radius of a transfer matrix, allowing an ecosystem to become supercritical even when each participant remains individually subcritical. The resulting framework treats recursive self-improvement as a property of an open development system rather than a capability label attached to a model.