Recursive Language Models Through the Admissibility-Dynamics Framework: A Principled Theory of When Recursive Scaffolding Succeeds

The Recursive Language Models (RLM) architecture (Zhang, Kraska, and Khattab, MIT CSAIL, 2026) extends standard language model inference by allowing a root model to spawn recursive sub-calls, each operating in its own REPL environment with access to the same tools and query functions. This paper applies the constraint-requirement framework developed in the companion papers (PIT, NEO, IA) to formally characterize when the RLM architecture can and cannot satisfy given admissibility structures. The central results establish sufficient and insufficient conditions for the RLM architecture under the framework. A quantitative accumulation bound is derived showing that residual failure rates scale with the number of sub-call invocations actually exercised rather than the maximum depth parameter allowed — a distinction with direct empirical consequences, as the root model chooses whether to recurse and frequently processes tasks at depth zero regardless of the depth allowance. The paper further characterizes when recursive sub-calls provide structural benefit versus when they inherit the fundamental limits established by the impossibility results of the prior papers, identifying faithful summary transmission across the sub-call boundary as the specific condition separating architecturally beneficial recursion from recursion that merely propagates failure. Applications to retrieval-augmented generation, the OOLONG-Pairs benchmark residual failure rate, and the relationship between certification depth and sub-call task decomposition are discussed. The paper is the fifth in a sequence developing a unified constraint-based framework for bounded-context AI systems. Foundational results are in: Projection Insufficiency and Trajectory Realization (DOI: 10.5281/zenodo.19633241), The Non-Locality of Extendability (DOI: 10.5281/zenodo.19688367), Inconsistency Accumulation in Forward-Local Sequential Policies (DOI: 10.5281/zenodo.19688628), and Language Model Hallucinations: An Impossibility Theorem (DOI: 10.5281/zenodo.19715059). ORCID: 0009-0003-9208-1556