VALG routes failed proofs by obstruction type — derivation, structure, or the theorem statement itself

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VALG (arXiv 2608.13060, 2026-08-13) organizes ML theory research as an agentic workflow combining multi-level verification, adaptive problem formulation and graph-structured proof development. Within each source-relative theorem branch it holds a fixed mathematical specification, checks theorem-level composition of a typed proof-dependency graph, and builds and reviews local proofs in dependency order. The interesting control-flow idea for agent builders is the failure router: when a proof attempt fails, VALG diagnoses whether the obstruction sits in a derivation, in the proof structure, or in the theorem formulation, and routes the next attempt accordingly — formulation-level obstructions spawn an explicitly related variant or relaxation that preserves the relation to the source problem. Evaluated on nine subproblems.