Paper Citation Record · LEDGER

Enhancing Mathematical Reasoning in LLMs with Background Operators

As of 15 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2412.04110.

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

pith.paper-citation-record.v1
2412.04110 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T21:50:56.090801Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

32 of 32 outbound references displayed

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verified fuzzy0
unresolved31
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External citation measurements

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Outbound references

Observation 558ec046-f4aa-4b89-95b5-790a156d3948 · outbound

This paper cites Graph of Thoughts: Solving Elaborate Problems with Large Language Models.

Enhancing Mathematical Reasoning in LLMs with Background Operators Graph of Thoughts: Solving Elaborate Problems with Large Language Models

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.959745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fd2a3ff4-011d-421a-81a6-8deb570c129d · outbound

This paper cites Piantadosi.

Enhancing Mathematical Reasoning in LLMs with Background Operators Piantadosi

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.964791Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 34c5b34e-9b23-4722-9d8c-3a771d52fb31 · outbound

This paper cites Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks.

Enhancing Mathematical Reasoning in LLMs with Background Operators Program of Thoughts Prompting: Disentangling Computation from Reasoning for Numerical Reasoning Tasks

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.968724Z

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Unavailable: canonical work link unavailable.

Observation 5fd53ee0-d2f0-43ab-a38e-f187f64770f2 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Enhancing Mathematical Reasoning in LLMs with Background Operators Training Verifiers to Solve Math Word Problems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.973353Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83600869-6c59-4a5a-81b3-a4153b6c1831 · outbound

This paper cites The Llama 3 Herd of Models.

Enhancing Mathematical Reasoning in LLMs with Background Operators The Llama 3 Herd of Models

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.977880Z

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Unavailable: canonical work link unavailable.

Observation 511fd88a-6ecb-4c3d-b60a-0f0722c59508 · outbound

This paper cites PAL: Program-aided Language Models.

Enhancing Mathematical Reasoning in LLMs with Background Operators PAL: Program-aided Language Models

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.982022Z

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Unavailable: canonical work link unavailable.

Observation 23cd31c5-caab-4e92-8a2d-116f86f7e1b0 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.636907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 87199d18-5844-44cc-b595-4024afc5049c · outbound

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

Enhancing Mathematical Reasoning in LLMs with Background Operators ToRA: A Tool-Integrated Reasoning Agent for Mathematical Problem Solving

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.991280Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e82fa3ab-8588-4fe2-87a9-051e6a373053 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.995144Z

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Observation a1d39e0f-8439-41d5-a3fc-8567df45dddc · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:55.998767Z

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Unavailable: canonical work link unavailable.

Observation 9a0e9ee3-a41b-4f3b-bf35-a1dec2c4faf5 · outbound

This paper cites Large Language Models Can Self-Improve.

Enhancing Mathematical Reasoning in LLMs with Background Operators Large Language Models Can Self-Improve

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.002994Z

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Observation 1bb92aa8-9bc5-4732-b924-4becb08cc391 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.604116Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 7f405d23-0c6b-42ca-82b7-94b19b98e8d8 · outbound

This paper cites Semi-Supervised Classification with Graph Convolutional Networks.

Enhancing Mathematical Reasoning in LLMs with Background Operators Semi-Supervised Classification with Graph Convolutional Networks

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.012126Z

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Observation ddf01f9a-edb6-4242-b622-71b3665431f5 · outbound

This paper cites Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate.

Enhancing Mathematical Reasoning in LLMs with Background Operators Encouraging Divergent Thinking in Large Language Models through Multi-Agent Debate

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.016365Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fa72afe5-a866-4144-82c7-04497d244e41 · outbound

This paper cites Smith, and Yejin Choi.

Enhancing Mathematical Reasoning in LLMs with Background Operators Smith, and Yejin Choi

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.020430Z

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Observation a721f250-43fb-400d-86ed-e4347b4aa161 · outbound

This paper cites Lila: A Unified Benchmark for Mathematical Reasoning.

Enhancing Mathematical Reasoning in LLMs with Background Operators Lila: A Unified Benchmark for Mathematical Reasoning

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.025234Z

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Observation b99fc4f7-6241-4334-a0ca-2c51cd4d1813 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.586332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d1fab889-bef8-4c96-97b9-292b7e22bf97 · outbound

This paper cites Thought-Like-Pro: Enhancing Reasoning of Large Language Models through Self-Driven Prolog-based Chain-of-Thought.

Enhancing Mathematical Reasoning in LLMs with Background Operators Thought-Like-Pro: Enhancing Reasoning of Large Language Models through Self-Driven Prolog-based Chain-of-Thought

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.034020Z

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Observation 1e7fc33b-4221-4fe8-8706-249c05e9fea9 · outbound

This paper cites Hashimoto.

Enhancing Mathematical Reasoning in LLMs with Background Operators Hashimoto

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.038377Z

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Observation 0f476996-a34a-47fd-90c4-337b40cbd23a · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.042986Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c85827e-3614-4006-9b94-f41229c943e7 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.553159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation d1540126-c874-4240-a1e3-8972229e6d9c · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.535985Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 565e096b-910d-4fb4-a0fe-59b9b08ec3fc · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.054720Z

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Observation cf4d6ff6-eb23-42c0-bd14-ef3efbeba65d · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.058534Z

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Unavailable: canonical work link unavailable.

Observation 64cb4745-1ae6-480f-9b0c-561bff0d381a · outbound

This paper cites Tree of Thoughts: Deliberate Problem Solving with Large Language Models.

Enhancing Mathematical Reasoning in LLMs with Background Operators Tree of Thoughts: Deliberate Problem Solving with Large Language Models

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.062709Z

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Unavailable: canonical work link unavailable.

Observation 48596c00-df96-409d-bec2-44c28d1b6de6 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-11T21:50:56.508855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation ac752482-64dd-49a1-b122-ec7d3f9fde45 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 27

Resolution: verified exact; doi, observed 2026-08-11T21:50:56.131310Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

Observation 92ab54d0-f14a-4f85-9627-7162c21c71df · outbound

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

Enhancing Mathematical Reasoning in LLMs with Background Operators DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.074259Z

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Observation db3a23bb-05f7-40f6-b6f9-9594e9e94ee5 · outbound

This paper cites Least-to-Most Prompting Enables Complex Reasoning in Large Language Models.

Enhancing Mathematical Reasoning in LLMs with Background Operators Least-to-Most Prompting Enables Complex Reasoning in Large Language Models

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.078443Z

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Observation 135cc99e-9616-449f-872c-7c4ef68f9502 · outbound

This paper cites an unresolved cited work.

Enhancing Mathematical Reasoning in LLMs with Background Operators Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.082677Z

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Unavailable: canonical work link unavailable.

Observation 2ffc9afe-6230-45fa-9db3-923e410a843b · outbound

This paper cites online" 'onlinestring :=.

Enhancing Mathematical Reasoning in LLMs with Background Operators online" 'onlinestring :=

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.086653Z

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Observation b61df0c6-5ce2-4276-98ef-8f30e18fe0ad · outbound

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Enhancing Mathematical Reasoning in LLMs with Background Operators write newline

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T21:50:56.090801Z

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Pith citing papers

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