Endogenous Method Transfer in AI-Assisted Research Systems: Capability Escalation and the Governance Bottleneck

This paper examines endogenous method transfer in AI-assisted research systems through a bounded reconstruction of recent mathematical episodes involving large language models and additive combinatorics. The paper argues that the most important methodological signal is not merely fluent generation or retrieval, but the apparent production of candidate transfer objects in which technical methods are adapted across problem contexts inside a bounded research episode. To analyze this possibility rigorously, the paper introduces a conservative conceptual framework distinguishing local generation, retrieval, analogy, assisted transfer, endogenous method transfer, and governance-stabilized transfer. It then reconstructs the Gowers/Nathanson episode as a candidate transfer case while explicitly avoiding claims of canonical mathematical validity or autonomous scientific agency. The paper’s broader contribution is governance-theoretic. Once AI-assisted systems become capable of generating plausible cross-context technical candidates, the central bottleneck shifts from generation itself to admissibility review, artifact validation, authority assignment, and governance-visible stabilization. Building on the Reflexive Laboratory series, the paper introduces the candidate transfer object model and situates endogenous method transfer within a broader architecture of transcript sufficiency, artifact integrity, executable research objects, and governed research state. This release includes the publication manuscript, source materials, figures, curated transcript-support materials, linked mathematical draft artifacts, manifest and checksum files, and methodological documentation sufficient to preserve reconstructability without requiring full archive export.