🤖 AI Summary
This work addresses the challenge of providing auditable, high-assurance verification for AI-generated informal reasoning while maintaining broad coverage. It proposes a structured approach that reformulates solutions as typed state-transition sequences, where every step must be explicitly justified—via citations, computations, or given premises—and enforces a “change completeness” invariant to surface hidden assumptions and fabricated references. By integrating explicit justification licensing, human-readable proof traces, and an adversarial validation framework, the method enables transparent, traceable, and contestable reasoning. Empirical evaluation demonstrates strict certification accuracies of 91.4% on HLE-Verified Gold and 97.1% on GPQA Diamond, significantly outperforming existing monolithic LLM-based evaluators in detecting concealed premises and hallucinated citations.
📝 Abstract
When should an AI system's answer be trusted? Formal proof assistants offer certainty but cannot reach most of the problem distribution; scalar LLM judges offer coverage but produce opaque scores that cannot be audited after the fact and are subject to the same coherence issues as any LLM. We present Theoria, a verification architecture that closes this gap. A candidate solution is rewritten into a sequence of typed state transitions, each licensed by an explicit justification, whether that be a citation, computation, or problem-given fact, and every transition is independently auditable. The foundational invariant is completeness of change: every difference between consecutive proof states must be accounted for, so hidden premises surface as unlicensed mutations rather than passing silently. On HLE-Verified Gold (185 text-only expert problems), Theoria certifies 105 at 91.4% strict precision (Wilson 95% CI [84.5%, 95.4%]). Every certification produces a human readable proof trace in which each step can be independently challenged. Holistic LLM judges achieve comparable precision at matched coverage but fail on different problems (Jaccard 0.14-0.36), making the approaches complementary. On 95 adversarial poisoned proofs across 15 domains, structured judges catch 94.7% versus 83.2% for holistic judging (p= 0.0017). The overall 11.5 pp gap concentrates in hidden premises (90.6% vs. 62.5%, a 28 pp difference) and fabricated citations (100% vs. 90%), the error classes where the formal analysis predicts an advantage; performance is identical on arithmetic and theorem-misapplication errors, where no advantage is predicted. On GPQA Diamond (n= 65), certified precision is 97.1% (Wilson CI [85.1%, 99.5%]).