From Mathematical Instruments to Reusable Reasoning: A Second Phase of Extraction from AI-Generated Mathematics

Large collections of AI-generated mathematics create a research problem: how can their arguments become a cumulative resource for further mathematics? This paper proposes a methodology for reusable reasoning centered on source-linked reasoning graphs. It links the extraction of mathematical devices in the Math Instruments program to reconstruction of their dependencies and comparison of mechanisms across problems. Investigating transfer obligations, verifying new results, and returning outcomes to the collection form a proposed research protocol. These graphs represent claims and joint-premise inferences as directed hypergraphs, retaining explicit scope and evidence status. We apply the extraction procedure to six manuscripts: four OpenAI papers and two retrospective application papers by the present author. Dependencies are recorded at the level of mathematical argument steps. The records cover 105 proof environments, 158 arguments, 454 inferences, and 1,760 nonblank source blocks. A multiscale viewer connects the collection, a paper's argument map, individual inferences, and exact source passages. Two retrospective case studies show how signed restrictions, cubic-moment optimization, and polynomial certificates transfer only through additional application-specific work. Complete reasoning graphs for selected arguments and a separate query pilot illustrate valid routes, scope obstructions, and obligations that merely restate a target. Author review led to corrections of premises, scope and source anchors; its coverage and remaining limits are reported explicitly. We also propose using the curated collection to suggest hypotheses automatically, each accompanied by a candidate reasoning graph and explicit proof obligations. The proposed methodology treats an argument, its conditions, and its review history as a unit of cumulative mathematical work. Source accounting, mathematical validity, and discovery performance remain distinct; independent annotation accuracy and prospective discovery benefits have not yet been measured.