Theorist Toolbox: Adversarial LLM Methods Verify Economic Proofs, Catch Hallucinations

Economists traditionally start from a blank page, while empiricists have shared packages and replication archives. By 2026, large language models can produce and check nontrivial mathematics, but they also hallucinate convincingly. Moran Koren’s Theorist Toolbox addresses this trust bottleneck by proposing three verification protocols for LLM-assisted economic theory: a single disciplined pass, an adversarial prover-verifier pair (Claude Opus 4.8 proposing, OpenAI Codex refuting), and a structured multi-agent project with a reviewer gate (inspired by Google’s co-mathematician architecture).

The paper demonstrates these protocols on a single open example: designing a Groves/Pigouvian incentive mechanism for the Gans–Kominers eigengrade model of grade inflation. None of the three runs produced the requested strict direct-revelation VCG/Clarke mechanism—possibly because such a mechanism does not exist. However, three recurring phenomena emerged: convergent discovery (two runs deriving the same effective-resistance externality kernel from opposite margins), the load-bearing role of adversarial verification (the pair caught three of its own false claims, and the gate rejected a sub-goal), and the observation that polish is not rigor (the most finished-looking output was the least verified). The methodological takeaway is that external verification, not raw model capability, is the critical design variable for reliable AI-assisted theoretical research.