Theoria: Rewrite-Acceptability Verification over Informal Reasoning States

Computer Science > Artificial Intelligence

arXiv:2607.01223v1 (cs) [Submitted on 1 Jul 2026 (this version), latest version 2 Jul 2026 (v2)]

Title:Theoria: Rewrite-Acceptability Verification over Informal Reasoning States

Authors:Ben Slivinski, Michael Saldivar View a PDF of the paper titled Theoria: Rewrite-Acceptability Verification over Informal Reasoning States, by Ben Slivinski and 1 other authors View PDF HTML (experimental)

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%]).

Subjects:	Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Machine Learning (cs.LG); Logic in Computer Science (cs.LO); Software Engineering (cs.SE)
Cite as:	arXiv:2607.01223 [cs.AI]
	(or arXiv:2607.01223v1 [cs.AI] for this version)
	https://doi.org/10.48550/arXiv.2607.01223 Focus to learn more arXiv-issued DOI via DataCite

Submission history

From: Ben Slivinski [view email]
[v1] Wed, 1 Jul 2026 17:56:42 UTC (24 KB)
[v2] Thu, 2 Jul 2026 02:28:31 UTC (24 KB)
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