6arXiv cs.LG (Machine Learning)·
Theoria: Structured verification architecture for auditable AI reasoning via typed state transitions
Theoria is a verification architecture that rewrites candidate AI solutions into sequences of typed state transitions, each requiring an explicit justification (citation, computation, or given fact), making every reasoning step independently auditable. On HLE-Verified Gold (185 expert problems), Theoria certifies 105 at 91.4% strict precision, and on adversarial poisoned proofs catches 94.7% of errors versus 83.2% for holistic LLM judges — a gap concentrated in hidden premises and fabricated citations. The approach is complementary to scalar LLM judges (Jaccard overlap 0.14–0.36), suggesting ensemble use. On GPQA Diamond, certified precision reaches 97.1%.
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AI-Assisted Theorem Proving in Lean 4: Aristotle API Case Study on IMO 2009 Problem 6
This paper presents a case study of using the Aristotle API for AI-assisted formal theorem proving in Lean 4, targeting the Grasshopper problem (IMO 2009 Problem 6). The generated artifact verifies four helper lemmas but leaves the main theorem unresolved via a 'sorry' placeholder, exposing a key limitation: local proof search can succeed while global combinatorial bookkeeping remains unsolved. The study provides a reproducible Lean artifact and precise analysis distinguishing verified from unverified proof content, offering a concrete benchmark for evaluating AI formalization capabilities.
Neurosymbolic Learning for Inference-Time Argumentation in Claim Verification
This paper introduces Inference-Time Argumentation (ITA), a trainable neurosymbolic framework for ternary claim verification (true/false/uncertain) that integrates formal argumentation semantics with LLM training. The framework uses argumentation semantics both to guide LLM training for argument generation and scoring, and to compute final predictions deterministically from explicit argumentative structures. Unlike conventional reasoning models that rely on potentially unfaithful post-hoc explanations, ITA produces verdicts that are faithful by construction to the underlying arguments. Experiments on two ternary claim verification datasets show ITA outperforms argumentative baselines and competes with non-argumentative direct-prediction approaches.
OpenAI Neural Theorem Prover Solves Formal Math Olympiad Problems in Lean
OpenAI developed a neural theorem prover integrated with the Lean proof assistant that can solve challenging high-school olympiad problems, including problems from AMC12, AIME, and two IMO-adapted problems. The system demonstrates automated formal mathematical reasoning at a level previously requiring human expertise. This represents a significant capability milestone in AI-assisted formal verification and mathematical problem-solving.
Goedel-Architect achieves state-of-the-art formal theorem proving with blueprint-based agentic framework
Goedel-Architect is an agentic framework for formal theorem proving in Lean 4 that uses blueprint generation — a dependency graph of definitions and lemmas — rather than recursive decomposition, enabling parallel lemma closure and global refinement. Built on DeepSeek-V4-Flash (284B-A13B), it achieves 99.2% pass@1 on MiniF2F-test and 75.6% on PutnamBench, scaling to 100% on MiniF2F, 88.8% on PutnamBench, and 4/6 on IMO 2025 when seeded with natural-language proofs. The authors claim state-of-the-art performance for an open-source pipeline at up to 500x lower cost than comparable systems.
Formal theory shows infinite trivial output is provably necessary for AI systems generating valuable mathematics
A new arXiv paper models AI-assisted formal mathematics generation as a nested language-generation-in-the-limit problem, using a proof checker as a membership oracle and an adversarial enumeration of the mathematical literature as the signal for 'valuable' content. The authors prove a sharp dichotomy: generators emitting only finitely many trivial (correct but worthless) statements achieve at most α/2 coverage of unseen valuable mathematics, while allowing an infinite (but asymptotically vanishing) stream of trivia raises the optimum to 1−α/2. The central result is that a perfect verifier cannot substitute for mathematical taste, and the flood of certified-but-trivial output from AI proof systems is a provable mathematical necessity, not an engineering failure. The work formalizes the gap between formal verifiability and mathematical value, which is increasingly the binding constraint as AI-proof-assistant systems scale.
Prover-Verifier Games improve legibility of language model outputs
OpenAI presents research on prover-verifier games as a mechanism to improve the legibility and verifiability of language model outputs. The approach frames output generation as a game between a prover (the model producing solutions) and a verifier (checking correctness), incentivizing clearer, more human-auditable reasoning. The work targets a core alignment challenge: ensuring AI-generated solutions are interpretable and trustworthy to both humans and automated systems.
LLM-as-a-Verifier: Training-free verification framework scales along granularity, repetition, and criteria decomposition
Researchers introduce LLM-as-a-Verifier, a general-purpose verification framework that treats verification as a new scaling axis for LLMs, computing continuous scores from token logit distributions rather than discrete judge outputs. The framework scales along three dimensions—score granularity, repeated evaluation, and criteria decomposition—and achieves state-of-the-art results on Terminal-Bench V2 (86.5%), SWE-Bench Verified (78.2%), RoboRewardBench (87.4%), and MedAgentBench (73.3%) without requiring additional training. The authors also demonstrate that the framework's fine-grained signals can serve as dense RL feedback, improving sample efficiency for SAC and GRPO on robotics and math benchmarks, and build a Claude Code extension for monitoring agentic systems.
VeriTrace: Cognitive-Graph Framework with Explicit Regulatory Loops for Deep Research Agents
VeriTrace introduces a cognitive-graph framework for deep research agents that replaces implicit LLM reasoning over intermediate representations with three explicit regulatory loops: interpretive update, deviation feedback, and schema revision. The system addresses contamination and error propagation in evolving mental models during complex multi-step research tasks. Using Qwen3.5-27B backbones, VeriTrace improves over the strongest matched baseline by 4.22 pp on DeepResearch Bench Insight and 5.9 pp Overall win rate on DeepConsult. With Config-DeepSeek, it achieves the strongest reproducible open-source result on DeepResearch Bench.