Paper Citation Record · LEDGER

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning

As of 6 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 3 inbound Pith citation observations for arXiv:2507.15698.

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

pith.paper-citation-record.v1
2507.15698 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-21T23:24:43.556606Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-06T06:34:29.942622+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T11:06:21.527926Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-06-30T11:54:38.713100Z

Reference resolution

29 of 29 outbound references displayed

verified exact14
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch15

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5b2b89f6-d0dd-4ee0-b31e-116eee59ea4d · outbound

This paper cites Qwen Technical Report.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Qwen Technical Report

Reference 1

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.368154Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 163fec65-6cc6-462f-b789-08baac871e75 · outbound

This paper cites ODIN: Disentangled Reward Mitigates Hacking in RLHF.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning ODIN: Disentangled Reward Mitigates Hacking in RLHF

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.371973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 6de869e4-ab8d-4720-967e-6ff994714573 · outbound

This paper cites The Llama 3 Herd of Models.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning The Llama 3 Herd of Models

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.365176Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9d88245e-cb38-489a-962f-89e09abc6976 · outbound

This paper cites Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Helping or Herding? Reward Model Ensembles Mitigate but do not Eliminate Reward Hacking

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.324401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation f0457bb7-171b-43e5-998b-d3f28515fca2 · outbound

This paper cites LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning LLM Critics Help Catch Bugs in Mathematics: Towards a Better Mathematical Verifier with Natural Language Feedback

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.332497Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 832db875-eaa1-4760-875a-c1ea9ec09a22 · outbound

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

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Measuring Mathematical Problem Solving With the MATH Dataset

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-05-21T23:25:45.316700Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 6dfc41c7-39f8-4962-a5ff-d7e3e45a9360 · outbound

This paper cites Chen et al.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Chen et al

Reference 7

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.352971Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation b1e3dcf4-64f9-4e84-bc91-83c1113b8d8d · outbound

This paper cites GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.340074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 1dff3c38-1b04-47eb-a071-2298d56aea64 · outbound

This paper cites Process Reward Model with Q-Value Rankings.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Process Reward Model with Q-Value Rankings

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.336123Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 024e02c0-bee5-4045-8315-4b0e7c3c85a7 · outbound

This paper cites Let's Verify Step by Step.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Let's Verify Step by Step

Reference 10

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.271500Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation ed1b5cf5-91ac-4b26-9453-d01605e7cf36 · outbound

This paper cites DeepSeek-V3 Technical Report.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning DeepSeek-V3 Technical Report

Reference 11

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.282531Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 0d27e7ee-a36b-4ce5-9891-32da91502027 · outbound

This paper cites Improve Mathematical Reasoning in Language Models by Automated Process Supervision.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Improve Mathematical Reasoning in Language Models by Automated Process Supervision

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-05-21T23:25:45.279073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9adddc11-31b6-4e55-a087-ba9a64a6eb06 · outbound

This paper cites LLM Critics Help Catch LLM Bugs.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning LLM Critics Help Catch LLM Bugs

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.268233Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 65ee2097-0693-4d23-9a6e-91d17f2a279f · outbound

This paper cites GPT-4 Technical Report.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning GPT-4 Technical Report

Reference 14

Resolution: verified exact; local_arxiv, observed 2026-05-21T23:25:45.286097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8d9cd287-48e2-4169-96c8-fb4ab79daf80 · outbound

This paper cites O1 Replication Journey: A Strategic Progress Report -- Part 1.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning O1 Replication Journey: A Strategic Progress Report -- Part 1

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.349208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 62c27199-f8e2-4e43-9735-7098902b0d17 · outbound

This paper cites WARP: On the Benefits of Weight Averaged Rewarded Policies.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning WARP: On the Benefits of Weight Averaged Rewarded Policies

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.301158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation c3d41963-09c7-4cd6-a177-9b69d02f6db5 · outbound

This paper cites DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Reference 17

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.313527Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 46083a4f-feed-45d9-bf47-7d29457ad3d1 · outbound

This paper cites Loose lips sink ships: Mitigating Length Bias in Reinforcement Learning from Human Feedback.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Loose lips sink ships: Mitigating Length Bias in Reinforcement Learning from Human Feedback

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.328850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 24e63f3c-ad87-44a4-b51f-3942077965e3 · outbound

This paper cites A Long Way to Go: Investigating Length Correlations in RLHF.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning A Long Way to Go: Investigating Length Correlations in RLHF

Reference 19

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.297132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation fedc1ac9-4c04-441a-bf70-3ec5c4844a97 · outbound

This paper cites Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

Reference 20

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.360482Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 86982e4b-f595-4084-a8d2-944086c00017 · outbound

This paper cites Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Easy-to-Hard Generalization: Scalable Alignment Beyond Human Supervision

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.309813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation e484e6dd-d2f0-4ee9-a0c9-fcdc4b3c3939 · outbound

This paper cites Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.356641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 099e8384-6906-4034-833d-cc9237fa9108 · outbound

This paper cites Evaluating Mathematical Reasoning Beyond Accuracy.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Evaluating Mathematical Reasoning Beyond Accuracy

Reference 23

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.320305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 8c9865bc-fc99-4cf6-956d-e6d378c1c85c · outbound

This paper cites Qwen3 Technical Report.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Qwen3 Technical Report

Reference 24

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.264818Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 965e8885-c52a-4ce9-961b-875a5e9e0d61 · outbound

This paper cites Generative Verifiers: Reward Modeling as Next-Token Prediction.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Generative Verifiers: Reward Modeling as Next-Token Prediction

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.290017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 0e0c21f7-4a31-4d49-aa00-3063fb45931f · outbound

This paper cites GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoning

Reference 26

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.293816Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation b93e8691-1a74-4db4-ae01-bb89c48410e0 · outbound

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

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning ProcessBench: Identifying Process Errors in Mathematical Reasoning

Reference 27

Resolution: metadata mismatch; arxiv_id, observed 2026-05-21T23:25:45.344436Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 9ebc0511-b75b-49f4-8847-cc68dee08fd6 · outbound

This paper cites Retrieval-Augmented Process Reward Model for Generalizable Mathematical Reasoning.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning Retrieval-Augmented Process Reward Model for Generalizable Mathematical Reasoning

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-21T23:25:45.275361Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 7b0b7362-6f40-4600-af13-74dd7cca7d5c · outbound

This paper cites DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence.

CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning DeepSeek-Coder-V2: Breaking the Barrier of Closed-Source Models in Code Intelligence

Reference 29

Resolution: metadata mismatch; local_arxiv, observed 2026-05-21T23:25:45.304827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Pith citing papers

Observation a3e94bf0-9133-432f-add4-393ededb352e · inbound

ToolPRM: Fine-Grained Inference Scaling of Structured Outputs for Function Calling cites this paper.

ToolPRM: Fine-Grained Inference Scaling of Structured Outputs for Function Calling CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning

Reference 55

Resolution: verified exact; arxiv_id, observed 2026-05-20T02:04:43.676793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 533848bc-7e3c-49a6-9437-236c1e7ff9b4 · inbound

Reward Hacking in the Era of Large Models: Mechanisms, Emergent Misalignment, Challenges cites this paper.

Reward Hacking in the Era of Large Models: Mechanisms, Emergent Misalignment, Challenges CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning

Reference 46

Resolution: verified exact; arxiv_id, observed 2026-05-20T02:04:43.676793Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.

Observation 95d3a8f1-771d-47c0-ae0c-9673fba8a254 · inbound

Beyond the Frontier: Stochastic Backtracking for Efficient Test-Time Scaling cites this paper.

Beyond the Frontier: Stochastic Backtracking for Efficient Test-Time Scaling CoLD: Counterfactually-Guided Length Debiasing for Process Reward Models in Mathematical Reasoning

Reference 61

Resolution: verified exact; local_arxiv, observed 2026-06-30T11:54:38.714362Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-06T06:34:29.942622+00:00.