FaithSieve: Fine-Grained Evaluation of Math Proofs with Faithful Formal Evidence

arXiv:2608.26310 · cs.AI · Submitted 2026-08-26 · Read on arXiv

cs.AI

Submitted: 2026-08-26

Updated: 2026-08-26

Code: https://github.com/optsuite/lean-tools-mcp

Terminology

• Accuracy — 26× in this paper · explained in 1 episode
• Error Localization — 20× in this paper · explained in 2 episodes
• Fidelity — 19× in this paper · explained in 2 episodes
• Verification — 19× in this paper · explained in 2 episodes
• Ablation — 18× in this paper · explained in 1 episode
• Benchmark — 18× in this paper · explained in 2 episodes
• Alignment — 11× in this paper · explained in 1 episode
• Semantic Alignment — 7× in this paper · explained in 3 episodes
• Calibration — 5× in this paper · explained in 7 episodes
• Consistency — 5× in this paper · explained in 3 episodes
• Provenance — 5× in this paper · explained in 3 episodes
• Semantic Drift — 4× in this paper · explained in 3 episodes
• Ablation study — 3× in this paper · explained in 1 episode
• Chain of Thought — 2× in this paper
• Error Decomposition — 2× in this paper · explained in 3 episodes
• Self-consistency — 2× in this paper · explained in 2 episodes
• Sparsity — 2× in this paper · explained in 4 episodes
• Trace — 2× in this paper · explained in 2 episodes
• Agentic Loop — 1× in this paper · explained in 1 episode
• Aggregation — 1× in this paper · explained in 1 episode
• Failure Modes — 1× in this paper · explained in 3 episodes
• Formal Verification — 1× in this paper · explained in 2 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• Grounding — 1× in this paper · explained in 3 episodes
• Pruning — 1× in this paper · explained in 4 episodes
• Reinforcement Learning — 1× in this paper · explained in 4 episodes

Sources

• Seed-Prover 1.5: Mastering Undergraduate-Level Theorem Proving via Learning from Experience
• Seed-Prover: Deep and Broad Reasoning for Automated Theorem Proving
• Let's Verify Step by Step
• Reliable Fine-Grained Evaluation of Natural Language Math Proofs
• Hard2Verify: A Step-Level Verification Benchmark for Open-Ended Frontier Math
• DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition
• Aria: An Agent For Retrieval and Iterative Auto-Formalization via Dependency Graph
• Self-Consistency Improves Chain of Thought Reasoning in Language Models
• M2F: Automated Formalization of Mathematical Literature at Scale
• Translating Informal Proofs into Formal Proofs Using a Chain of States
• ProcessBench: Identifying Process Errors in Mathematical Reasoning

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