Paper Citation Record · LEDGER

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

As of 21 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 5 inbound Pith citation observations for arXiv:2507.23317.

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

pith.paper-citation-record.v1
2507.23317 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T10:56:16.246899Z

measured 36 of 36 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 5 of 5 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:50:30.556542Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-03T17:28:44.643417Z

Reference resolution

31 of 31 outbound references displayed

verified exact0
verified fuzzy13
unresolved17
parse uncertain0
malformed identifier1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1d101c04-8e82-48bd-b6fc-02b50a0b9798 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.554738Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c225e7c9-0ca5-43a8-b270-932661d0279f · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.544386Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9d679ac0-6b90-49eb-b6cd-a1572b11bdfe · outbound

This paper cites Matching Criteria.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner **Matching Criteria**

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.534465Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation f63f2698-9806-47ce-be2a-c6be4a29b5ff · outbound

This paper cites \n\n" delimiter. However, we observed in practice that the model often generates.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner \n\n" delimiter. However, we observed in practice that the model often generates

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.575974Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a12a5a68-5769-44cb-b045-7d2a0e627873 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.377355Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation e0bcdb32-32c0-4447-bb4d-c03a9593fdb3 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 6

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This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.354838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ea2ce7b2-4231-47cf-a743-8026a14a8178 · outbound

This paper cites Output Format.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner **Output Format**

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.342847Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 201ede07-4d79-45e1-9180-663e75e2d547 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.525113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation db635548-8c61-41e9-9cfc-eda96db656d9 · outbound

This paper cites final answer.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner final answer

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.514475Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 69ded6a6-a37c-433f-9f0d-5dfad764d4f2 · outbound

This paper cites - Only record clear content correspondences.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner - Only record clear content correspondences

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.503977Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b75c7d99-dcb0-44ae-aa84-2dee90c54b1e · outbound

This paper cites Solution_Step_Number.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Solution_Step_Number

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.492704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 0c5a7c8f-b486-4c49-bb0b-d635dd4d5452 · outbound

This paper cites 0": [1, 3],.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner 0": [1, 3],

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.482170Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 21a72cf2-b32f-4299-9ca4-eec7a0bf17a5 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.471395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 210163cf-3a9a-4a0a-a692-153878b8187b · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.460688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 54049b85-bfbf-43ac-ac56-fdefdab6cd9e · outbound

This paper cites Reflection 1.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Reflection 1

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.449999Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 5647d5fc-204c-4215-a568-f7a56c47e1d6 · outbound

This paper cites Specifically, if multiple reflection segments map to the earliest source, we keep the reflection segment with the maximum index.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Specifically, if multiple reflection segments map to the earliest source, we keep the reflection segment with the maximum index

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.565593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 9c4dfe45-523e-4686-983e-0705e1a9bed9 · outbound

This paper cites If this step ONLY involves double-checking a previous calculation to verify its correctness, without finding a specific error, then ignore this step.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner If this step ONLY involves double-checking a previous calculation to verify its correctness, without finding a specific error, then ignore this step

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.439390Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation d8bbc9e5-2fd5-4ae4-9e82-eb6eda105b5b · outbound

This paper cites Earliest Step.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Earliest Step

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.428737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8e352368-8797-4b12-a757-3cf4c4640e9e · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 20

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.417356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 4427de4e-14ef-45d7-b436-15000690c8f6 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.407746Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 22

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Observation d430b73a-1aa3-4470-81a0-9b6fcf58e84c · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.387500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b5bc936a-f210-4021-bf74-aa815d329cd7 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 27

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b88483d7-dce1-40c8-8104-5149821450d9 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.318943Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 184c4c39-6a58-42cf-8718-8577ce497713 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.306083Z

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Observation 856ad6a5-8f00-4d8c-afea-36004b954d85 · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.293259Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

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This paper cites Table 19: The prompt used to decompose answer.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Table 19: The prompt used to decompose answer

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.279943Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation c7d80a63-38bb-4a17-80a1-943cd15a9b3a · outbound

This paper cites a randomly selected subset of A.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner a randomly selected subset of A

Reference 2024

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T10:56:16.607046Z

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No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 81a7cd85-c8d6-42bd-949a-fccb23425cba · outbound

This paper cites an unresolved cited work.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Unresolved cited work

Reference 2048

Resolution: unresolved; raw_fallback, observed 2026-08-06T10:56:16.585690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cabb7412-e827-4a51-946b-b72c6d72268a · outbound

This paper cites Therefore, 32767 = 7 × 31 × 151.

Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner Therefore, 32767 = 7 × 31 × 151

Reference 4681

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 44294502-7b9b-4803-9b52-ac85b4732737 · inbound

A Survey of Reinforcement Learning for Large Reasoning Models cites this paper.

A Survey of Reinforcement Learning for Large Reasoning Models Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-05-18T00:05:31.552356Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 655d1a57-9d47-49ec-a10d-288d54480e52 · inbound

Verifying Meta-Awareness via Predictive Rewards in Reasoning Models cites this paper.

Verifying Meta-Awareness via Predictive Rewards in Reasoning Models Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T15:50:30.556542Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f308673-b459-437a-acf1-35c4e7b7791a · inbound

LLM Reasoning with Process Rewards for Outcome-Guided Steps cites this paper.

LLM Reasoning with Process Rewards for Outcome-Guided Steps Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

Reference 10

Resolution: verified exact; arxiv_id, observed 2026-05-16T06:47:28.413615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7c865a26-9ce9-411d-ab83-358df0c6da9e · inbound

Trust Region On-Policy Distillation cites this paper.

Trust Region On-Policy Distillation Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

Reference 133

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T20:56:13.446782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 697944d0-fab6-4dc2-8468-27ce4ba66e25 · inbound

BALTO: Balanced Token-Level Policy Optimization for Hallucination Mitigation cites this paper.

BALTO: Balanced Token-Level Policy Optimization for Hallucination Mitigation Good Learners Think Their Thinking: Generative PRM Makes Large Reasoning Model More Efficient Math Learner

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-03T17:28:44.644965Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.