Paper Citation Record · LEDGER

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving

As of 18 August 2026, this Paper Citation Record lists 49 of 49 outbound references and 2 inbound Pith citation observations for arXiv:2505.20869.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2505.20869 v1

Coverage vector

measured 49 of 49 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T13:49:00.179397Z

measured 51 of 51 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-02T12:12:20.879377Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T12:16:56.415778Z

Reference resolution

49 of 49 outbound references displayed

verified exact1
verified fuzzy0
unresolved48
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a52023b5-5a74-4773-878a-73a71ce551ee · outbound

This paper cites GPT-4 Technical Report.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving GPT-4 Technical Report

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:54.372977Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0947fc5-13f6-4487-8db6-ca1b2aa638b7 · outbound

This paper cites ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving ProofNet: Autoformalizing and Formally Proving Undergraduate-Level Mathematics

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:54.550078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1c1ecf9b-0e3a-493c-a769-9ed75b4bf792 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:06.966235Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4152a210-a499-43da-96c1-c6a369275544 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:54.899489Z

Source-reported events for the cited work

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Observation effcdd4c-2ef1-4215-8bb4-3c768c05e118 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:55.073544Z

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Unavailable: canonical work link unavailable.

Observation e4ff89cc-f42a-43a2-a8ed-62bea542d39e · outbound

This paper cites MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving MATHSENSEI: A Tool-Augmented Large Language Model for Mathematical Reasoning

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:55.235032Z

Source-reported events for the cited work

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Observation 73e64946-a81c-45ed-bc8d-f8a4a179743e · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:06.717803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 2d3e91d1-144b-4e59-b05c-9263c51d72c3 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:06.431833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5b3e8ea2-a0f4-4b97-ba7b-3d2b2bcdeb43 · outbound

This paper cites ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:55.651885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c84c1734-ff23-49aa-a98d-b5b5e2fe70f2 · outbound

This paper cites DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:55.798411Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 564198e3-1acf-4fd9-9f13-72aea2109e78 · outbound

This paper cites Measuring Mathematical Problem Solving With the MATH Dataset.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Measuring Mathematical Problem Solving With the MATH Dataset

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:55.887844Z

Source-reported events for the cited work

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Observation bfe04a2b-749b-4553-8f55-9837c83f6799 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:06.246430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7eb095de-8077-487c-96d9-9dc8ab45bcd1 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.130668Z

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Observation 87881562-ac27-4a9b-8bdc-9f8c5da6f455 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:06.028934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e31169b1-fc51-4910-8416-17ee4b0fb9e7 · outbound

This paper cites Let's Verify Step by Step.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Let's Verify Step by Step

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.325154Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a419c50-c06a-4eac-9b93-1900ea188b43 · outbound

This paper cites CriticBench: Benchmarking LLMs for Critique-Correct Reasoning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving CriticBench: Benchmarking LLMs for Critique-Correct Reasoning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.468279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb4a25f0-1dcc-45da-a890-0c3d6216772e · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:05.780532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8d34e31d-b187-40ff-8c3d-f2da2d85c7c5 · outbound

This paper cites DeepSeek-V3 Technical Report.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving DeepSeek-V3 Technical Report

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.652715Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cae42ab4-bf9f-4c02-8636-b263b5b2603b · outbound

This paper cites ProofAug: Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysis.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving ProofAug: Efficient Neural Theorem Proving via Fine-grained Proof Structure Analysis

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.774331Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8cbc7e9d-d74d-4391-8d5a-6727001c91df · outbound

This paper cites Critique Ability of Large Language Models.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Critique Ability of Large Language Models

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:56.880879Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 86977b15-d33a-4a09-808f-d65231109533 · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:57.023034Z

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Unavailable: canonical work link unavailable.

Observation b1d54309-7f37-4ee1-a1a4-4b9865056722 · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:05.508655Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation cb702a3f-b5f8-4b2f-b071-2e781cac1014 · outbound

This paper cites GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:57.250760Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f74da3e-1514-492c-bbf9-b72bc0d7aa77 · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:05.283595Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 373db653-0b20-4826-be62-57d93684b821 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:05.067710Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 34985dc3-0bb2-46d2-b2ee-d5797aec7bc8 · outbound

This paper cites an unresolved cited work.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:04.853590Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 5bd6a367-1f6d-47f3-bb0d-16f6f41c39fd · outbound

This paper cites Learning from Few Examples: A Summary of Approaches to Few-Shot Learning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Learning from Few Examples: A Summary of Approaches to Few-Shot Learning

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:57.689898Z

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Observation 5fd47922-e35c-4bd6-983a-a96bb866fb8d · outbound

This paper cites GFLean: An Autoformalisation Framework for Lean via GF.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving GFLean: An Autoformalisation Framework for Lean via GF

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:57.793460Z

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Observation b08429c0-4a3e-405e-895c-1c5656b425c2 · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:04.641724Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e663a350-2a2e-427f-844d-3cb1ba44e5c0 · outbound

This paper cites Instantiation-based Formalization of Logical Reasoning Tasks using Language Models and Logical Solvers.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Instantiation-based Formalization of Logical Reasoning Tasks using Language Models and Logical Solvers

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:57.988181Z

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Observation 6df9d9de-c16c-4dbd-8d25-60166e877ffc · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:04.424258Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c4fe288e-8194-4497-8688-e4265491cd41 · outbound

This paper cites PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving PRMBench: A Fine-grained and Challenging Benchmark for Process-Level Reward Models

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:58.204424Z

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Unavailable: canonical work link unavailable.

Observation 1fdcb005-33a2-4876-bf4d-834413680968 · outbound

This paper cites Error Classification of Large Language Models on Math Word Problems: A Dynamically Adaptive Framework.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Error Classification of Large Language Models on Math Word Problems: A Dynamically Adaptive Framework

Reference 33

Resolution: verified exact; local_arxiv, observed 2026-08-07T13:49:00.471283Z

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Observation 9d2c7763-e459-47eb-884d-9e64cdffc09b · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 34

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Observation 54b795d1-68df-448b-b344-544e8a03c2ed · outbound

This paper cites Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Not All Votes Count! Programs as Verifiers Improve Self-Consistency of Language Models for Math Reasoning

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:58.532707Z

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Observation 2397eefb-2fb0-45fe-a62b-28641900844b · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:58.653213Z

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Observation 19170fb8-05b9-456b-84de-e2f4496e8b8b · outbound

This paper cites Self-consistency improves chain of thought reasoning in language models.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Self-consistency improves chain of thought reasoning in language models

Reference 37

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 38

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Unavailable: canonical work link unavailable.

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:58.956134Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e88dd56-b72d-4bbb-a544-7ee3bc701ca1 · outbound

This paper cites Enhancing LLM Reasoning via Critique Models with Test-Time and Training-Time Supervision.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Enhancing LLM Reasoning via Critique Models with Test-Time and Training-Time Supervision

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:59.112150Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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This paper cites DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving DeepSeek-Prover: Advancing Theorem Proving in LLMs through Large-Scale Synthetic Data

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:59.169485Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0f8ba24a-76af-410f-8f9d-0bf41e04bb7b · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving DeepSeek-Prover-V1.5: Harnessing Proof Assistant Feedback for Reinforcement Learning and Monte-Carlo Tree Search

Reference 42

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:59.281333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8dea5011-6747-4573-b953-9f4fc3237424 · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 43

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:04.144091Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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This paper cites The Lessons of Developing Process Reward Models in Mathematical Reasoning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving The Lessons of Developing Process Reward Models in Mathematical Reasoning

Reference 44

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:59.544806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b2203d20-f849-49a3-b21b-3af781914e82 · outbound

This paper cites ProcessBench: Identifying Process Errors in Mathematical Reasoning.

Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving ProcessBench: Identifying Process Errors in Mathematical Reasoning

Reference 45

Resolution: unresolved; no resolver link, observed 2026-08-07T13:48:59.682459Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 46

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0786da6c-9df3-405d-969c-885a64fed77d · outbound

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving Unresolved cited work

Reference 47

Resolution: unresolved; raw_fallback, observed 2026-08-07T13:49:00.917383Z

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No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving online" 'onlinestring :=

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Resolution: unresolved; no resolver link, observed 2026-08-07T13:49:00.038201Z

Source-reported events for the cited work

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Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving write newline

Reference 49

Resolution: unresolved; no resolver link, observed 2026-08-07T13:49:00.179397Z

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Unavailable: canonical work link unavailable.

Pith citing papers

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RMA: an Agentic System for Research-Level Mathematical Problems cites this paper.

RMA: an Agentic System for Research-Level Mathematical Problems Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-05-25T06:10:24.148377Z

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Observation 4ff13873-534e-43a7-832e-33f68cc5174a · inbound

Theoria: Rewrite-Acceptability Verification over Informal Reasoning States cites this paper.

Theoria: Rewrite-Acceptability Verification over Informal Reasoning States Step-Wise Formal Verification for LLM-Based Mathematical Problem Solving

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-07-02T12:16:56.417454Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.