From Recursive Scaffolding to Admissibility-First Construction: Mechanism, Stability, and Failure-Mode Decomposition on OOLONG-Pairs

This paper reports an empirical decomposition of Recursive Language Models (RLMs) on OOLONG-Pairs, testing whether RLM's reported gains arise from recursive scaffolding per se or from the construction of an admissibility-relevant summary state. The hypothesis tested: if RLM's advantage arises from admissibility-relevant summary construction, then direct Global Admissibility Filtering (GAF) construction should recover comparable performance without requiring the recursive scaffold. In the canonical 20-query seed-7700 run at approximately 32K context tokens, direct GPT-5 collapsed (micro-F1 ≈ 0.0019), while RLM(GPT-5) recovered global pair structure (micro-F1 = 0.9064, macro-F1 = 0.8400). Model-based GAF filtering over RLM output improved precision (micro-F1 = 0.9107). Critically, model-based admissibility-first GAF construction without RLM achieved the highest non-oracle micro-F1 (0.9212), demonstrating that the structural benefit can be recovered without recursive scaffolding. A three-seed robustness subset (7701, 7702, 7703) over five queries reveals an important separation between filter-mode GAF and construction-mode GAF. On seed 7702, RLM suffered catastrophic recall collapse (micro-F1 = 0.1379) driven by candidate under-generation; filter-mode GAF inherited the collapse. Construction-mode GAF remained robust across all three seeds (Z1G-S-mini: 0.9035-0.9244 micro-F1), demonstrating that construction is robust to candidate-generation failure where filtering is not. Direct output-structure comparison on q15 seed 7702 provides mechanism-level evidence: RLM and direct admissibility construction produced identical aggregate counts but differed by symmetric single-endpoint false-positive substitution, indicating both routes converged to the same admissibility-summary form with disagreement isolated to endpoint-level classification noise. The central conclusion is mechanism-level: on OOLONG-Pairs, recursive scaffolding is not the essential mechanism. The essential mechanism is the construction or approximation of an admissibility-relevant state. RLM is one route; GAF-style admissibility-first construction states the mechanism directly. Companion machine-checked Lean 4 results are available at 10.5281/zenodo.20062396