Paper Citation Record · LEDGER

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code

As of 7 August 2026, this Paper Citation Record lists 46 of 46 outbound references and 1 inbound Pith citation observation for arXiv:2605.19762.

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

pith.paper-citation-record.v1
2605.19762 v1

Coverage vector

measured 46 of 46 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-20T05:06:46.360174Z

measured 47 of 47 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T22:44:39.024780Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-06-29T22:54:01.573740Z

Reference resolution

46 of 46 outbound references displayed

verified exact4
verified fuzzy30
unresolved3
parse uncertain0
malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d3db041e-5e04-4bee-9eab-46ef65508399 · outbound

This paper cites 2021 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2021 , eprint=

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.898628Z

Source-reported events for the cited work

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Observation 3bf187c7-06b4-4850-8fdb-0340297f0084 · outbound

This paper cites 2022 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2022 , eprint=

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.893588Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4c123530-e486-449c-967e-0a5232c58e65 · outbound

This paper cites Evaluating Large Language Models in Theory of Mind Tasks.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Evaluating Large Language Models in Theory of Mind Tasks

Reference 3

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T05:08:05.084361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b218010c-c49d-415a-89ec-0c4baa903ac5 · outbound

This paper cites OS-Copilot: Towards Generalist Computer Agents with Self-Improvement.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code OS-Copilot: Towards Generalist Computer Agents with Self-Improvement

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T05:08:05.050552Z

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Observation 225e3096-042b-4d89-9c8e-8faa4995535c · outbound

This paper cites Reinforcement Learning for Long-Horizon Interactive LLM Agents.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Reinforcement Learning for Long-Horizon Interactive LLM Agents

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T05:08:05.103512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3888bc65-328b-414f-8067-d78b5de32c7e · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Advances in Neural Information Processing Systems , volume=

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.885295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 455f5e59-2c2c-4c10-9375-2dd7d7b2f9cd · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.827066Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d63e71b9-863c-4911-8dc4-ea42c6007c0c · outbound

This paper cites WebGPT: Browser-assisted question-answering with human feedback.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code WebGPT: Browser-assisted question-answering with human feedback

Reference 8

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T05:08:05.071940Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 47cc0dd9-6e2d-476a-9560-e313005c18be · outbound

This paper cites Transactions on Machine Learning Research , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Transactions on Machine Learning Research , year=

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.917217Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ed5b6a40-3e17-45c0-ad92-49300504e542 · outbound

This paper cites International Conference on Machine Learning , pages=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code International Conference on Machine Learning , pages=

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.933456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 55a5cb3d-33ce-48a3-8b47-8eecfb0c3b88 · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.929073Z

Source-reported events for the cited work

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Observation f1fad733-866d-47c6-9658-f7e4e4484c69 · outbound

This paper cites At Which Training Stage Does Code Data Help LLMs Reasoning?.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code At Which Training Stage Does Code Data Help LLMs Reasoning?

Reference 12

Resolution: verified exact; arxiv_id, observed 2026-05-20T05:08:05.122904Z

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b0ac72d6-f8fe-4f9d-a5b0-3d8578c5492f · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.816853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8a36ecad-6729-4c7d-ba9c-2e55bf41056a · outbound

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What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-05-20T05:08:05.839738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d62fb576-bcd9-46be-835f-194f72bef5a7 · outbound

This paper cites an unresolved cited work.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Unresolved cited work

Reference 15

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No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ac6f77c3-deaa-4baf-aab8-d9050a99ec3a · outbound

This paper cites Journal of Machine Learning Research , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Journal of Machine Learning Research , volume=

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.866842Z

Source-reported events for the cited work

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Observation f9289e24-9827-457c-bf66-2e78fbcb378f · outbound

This paper cites GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding

Reference 17

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T05:08:05.090190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d36f093e-ec65-4551-9677-005adadd9687 · outbound

This paper cites Mixtral of Experts.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Mixtral of Experts

Reference 18

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T05:08:05.077943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 391ca902-fd0a-403f-8f2b-532289625e6a · outbound

This paper cites DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code DeepSeekMoE: Towards Ultimate Expert Specialization in Mixture-of-Experts Language Models

Reference 19

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T05:08:05.110833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c3a36539-7831-4992-b9d8-47f883aab241 · outbound

This paper cites DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model

Reference 20

Resolution: metadata mismatch; local_arxiv, observed 2026-05-20T05:08:05.096201Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 22b35160-4a23-41cf-8825-32cbb2e0269b · outbound

This paper cites 2017 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2017 , eprint=

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.848260Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 8128afb6-f8c1-43df-8303-bf4d5bd555b0 · outbound

This paper cites 2023 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2023 , eprint=

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.871483Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9b3a3b54-82e5-4def-8555-0018ca1ecc93 · outbound

This paper cites Advances in neural information processing systems , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Advances in neural information processing systems , volume=

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.937801Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 894d6a9e-46e6-4c43-905f-1b1494ddec02 · outbound

This paper cites 2022 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2022 , eprint=

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.835930Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6d1236ba-63c2-4cef-873a-afe060fa153c · outbound

This paper cites A Survey on Data Selection for Language Models.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code A Survey on Data Selection for Language Models

Reference 25

Resolution: metadata mismatch; arxiv_id, observed 2026-05-20T05:08:05.065052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d5555e70-5a61-4bd6-98b2-0169e925a5cf · outbound

This paper cites When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code When Less is More: Investigating Data Pruning for Pretraining LLMs at Scale

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-20T05:08:05.057764Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b7e74f4d-f3d3-40e1-8dae-f05314151097 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Advances in Neural Information Processing Systems , volume=

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.821591Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 49c7df5d-f599-465d-b10b-94096774bcee · outbound

This paper cites Advances in neural information processing systems , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Advances in neural information processing systems , volume=

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.831948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a14645a0-31e3-4424-96bc-b941d05c8b9c · outbound

This paper cites Programming Every Example: Lifting Pre-training Data Quality Like Experts at Scale.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Programming Every Example: Lifting Pre-training Data Quality Like Experts at Scale

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-05-20T05:08:05.116809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation aeda7a43-c1c5-473c-8456-c6e586859d54 · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.925154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e8416680-d8e5-455f-9535-f319b6229d5a · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.876017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation eebff848-c45e-4193-b096-b7c0a902970f · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Advances in Neural Information Processing Systems , volume=

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.907306Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ee982acf-9e90-4e4f-bfaf-16c09ddd8a09 · outbound

This paper cites The Thirteenth International Conference on Learning Representations , year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code The Thirteenth International Conference on Learning Representations , year=

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.912235Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 098271e2-bba0-4142-bbad-e18b913a8d68 · outbound

This paper cites Getting structured data from the internet: running web crawlers/scrapers on a big data production scale , pages=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Getting structured data from the internet: running web crawlers/scrapers on a big data production scale , pages=

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.857335Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 58e65125-e217-4276-bd0a-8aaa165f682e · outbound

This paper cites Communications of the ACM , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Communications of the ACM , volume=

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.902917Z

Source-reported events for the cited work

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Observation ce610cfb-1b51-420b-b013-bea688c5a168 · outbound

This paper cites 2019 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2019 , eprint=

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.808296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e516d510-e5f8-4501-843d-f46e7d648aa9 · outbound

This paper cites XRDS: Crossroads, The ACM Magazine for Students , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code XRDS: Crossroads, The ACM Magazine for Students , volume=

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.812304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 78f81e79-a6ac-4b1c-ba5b-0403ab3aeb5e · outbound

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What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Unresolved cited work

Reference 38

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 513d8027-4e22-4310-b4e2-5d20e627e15d · outbound

This paper cites Journal of the Franklin Institute , volume=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Journal of the Franklin Institute , volume=

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.799680Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 01e3aa75-6cf6-4dcc-86ae-a0e0ee9bf4af · outbound

This paper cites 2023 , eprint=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2023 , eprint=

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.795334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 389c1de3-43f1-4211-a059-e3e8cc4520aa · outbound

This paper cites Findings of the Association for Computational Linguistics: ACL 2024 , month=aug, year=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Findings of the Association for Computational Linguistics: ACL 2024 , month=aug, year=

Reference 41

Resolution: verified exact; doi, observed 2026-05-20T05:08:04.168414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 6bcc97f4-ad59-4ec6-abe0-c17a3ddecdb7 · outbound

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What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Semantic-Aligned Code Summarization: Bridging the Gap Between Code and Natural Language Through Data Flow Analysis , year=

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.804251Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 278a8229-060a-4571-b989-251e2e530862 · outbound

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What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2026 , address =

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.852873Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9ae1cadf-43dd-4491-8aa4-d4d8f039853a · outbound

This paper cites Proceedings of the 42nd International Conference on Machine Learning , pages=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code Proceedings of the 42nd International Conference on Machine Learning , pages=

Reference 44

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.880708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 67fc429c-183f-4347-90b1-3e47181cea5f · outbound

This paper cites 2024 , publisher=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2024 , publisher=

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.861786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b084196a-6413-4299-9e0a-181c8ea67993 · outbound

This paper cites 2025 , url=.

What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code 2025 , url=

Reference 46

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T05:08:05.921440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

Observation 6215026e-5034-41bb-b4c3-c83173b5ee06 · inbound

GeoMathCode: Understanding Interleaved Math-Code Reasoning for Geometry Problem Solving cites this paper.

GeoMathCode: Understanding Interleaved Math-Code Reasoning for Geometry Problem Solving What Really Improves Mathematical Reasoning: Structured Reasoning Signals Beyond Pure Code

Reference 50

Resolution: verified exact; local_arxiv, observed 2026-06-29T22:54:01.575039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.