Paper Citation Record · LEDGER

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?

As of 11 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 1 inbound Pith citation observation for arXiv:2507.11408.

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

pith.paper-citation-record.v1
2507.11408 v2

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T17:17:07.109039Z

measured 34 of 34 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T06:37:37.832435Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T07:46:46.602182Z

Reference resolution

33 of 33 outbound references displayed

verified exact1
verified fuzzy0
unresolved32
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a5d830d8-3b33-4306-ba6e-ab3a6f0f7784 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 1

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:08.834678Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 889ec501-e012-416d-bedf-463b6d51c675 · outbound

This paper cites Bogdan, Uzay Macar, Neel Nanda, and Arthur Conmy.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Bogdan, Uzay Macar, Neel Nanda, and Arthur Conmy

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:04.954835Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11d1682d-2bea-4131-9d07-fcc93b6004ae · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Training Verifiers to Solve Math Word Problems

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.007332Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e45c6d40-2a9d-4557-9494-480e9890c62c · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:08.640917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ad34e8fd-920c-42b4-9ea4-56e968b7c37a · outbound

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

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.253333Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d9663fea-2bb2-4c63-bf47-4ca03920ad49 · outbound

This paper cites The Llama 3 Herd of Models.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? The Llama 3 Herd of Models

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.387275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3554ae6e-77a8-41e8-8ed2-896199e7981a · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.495025Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f14230b5-d459-4655-8e4e-fd1afe1841a0 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.592678Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b1b603f-09f4-40a5-9641-6bf998291991 · outbound

This paper cites Measuring Faithfulness in Chain-of-Thought Reasoning.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Measuring Faithfulness in Chain-of-Thought Reasoning

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.673632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e1672ca-eb2b-4662-893f-62aa20d00ed9 · outbound

This paper cites ReasoningFlow: Semantic Structure of Complex Reasoning Traces.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? ReasoningFlow: Semantic Structure of Complex Reasoning Traces

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.769550Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 11949cf2-eac1-4506-805d-9f8473787bbd · outbound

This paper cites LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? LLMs Can Easily Learn to Reason from Demonstrations Structure, not content, is what matters!

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.905312Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e3dc360-929b-426e-8d21-3c379425d7a3 · outbound

This paper cites Let's Verify Step by Step.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Let's Verify Step by Step

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:05.984780Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d319a2b3-3120-4f18-b630-97519837cab4 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:08.485327Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4d0e86f2-69d9-4298-9d3f-23a9aff7df12 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:08.315326Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 93d4aab3-98e9-4271-9aca-01f82aa4554b · outbound

This paper cites OpenAI o1 System Card.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? OpenAI o1 System Card

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.112529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d36bcbd-a5b0-40d3-9ad9-ed6a0a8fc70f · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:08.119153Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation d252b394-8a88-4e1d-ab18-a7d8d51740c2 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.188426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7926c33-c618-48e1-9c30-86cb108a7a69 · outbound

This paper cites Qwen2.5 Technical Report.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Qwen2.5 Technical Report

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.239435Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9ebc9ced-6798-441c-9ce9-e5b486c46400 · outbound

This paper cites Spurious Rewards: Rethinking Training Signals in RLVR.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Spurious Rewards: Rethinking Training Signals in RLVR

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.284535Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ac9def3b-4c90-4447-a0cd-a989c99d49c2 · outbound

This paper cites Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Beyond Semantics: The Unreasonable Effectiveness of Reasonless Intermediate Tokens

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.328065Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9c528f80-d571-4196-9d09-981d99b4fcb0 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:07.903709Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f1bfda2c-2b04-44a2-b8f3-58e8579e74db · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 22

Resolution: verified exact; doi, observed 2026-08-06T17:17:07.297748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f1ad7c41-4c8b-4db2-8d08-bee946a9c411 · outbound

This paper cites Gemma 3 Technical Report.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Gemma 3 Technical Report

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.459419Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3646dda1-cccf-4f8d-8ff8-8fac6981ff50 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.524439Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ea3e9e9-a3e9-41e7-9d59-27846b1a03ca · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.592472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 51092e78-e80e-4545-8f9a-ff0a2bc1cdb3 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.632777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 02853bf4-463f-428f-ba57-2c2d8260d6e1 · outbound

This paper cites Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.695466Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab874204-f249-495b-8819-57d26956f0af · outbound

This paper cites Chi, Quoc V Le, and Denny Zhou.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Chi, Quoc V Le, and Denny Zhou

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.751275Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 04a2ea36-eeb6-4d13-8db7-38f09ccc94ce · outbound

This paper cites Qwen3 Technical Report.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Qwen3 Technical Report

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.809622Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a293c8df-f488-4445-90df-9786c672dfe0 · outbound

This paper cites Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Does Reinforcement Learning Really Incentivize Reasoning Capacity in LLMs Beyond the Base Model?

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:06.887900Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 656446af-f648-4668-8d11-c00d2a3b77c6 · outbound

This paper cites an unresolved cited work.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-06T17:17:07.697841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b5eea71e-131a-4861-8e2d-6acd97c11460 · outbound

This paper cites online" 'onlinestring :=.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? online" 'onlinestring :=

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:07.034919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef09ca13-9a8c-4c9f-8071-7228026493f5 · outbound

This paper cites write newline.

KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning? write newline

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T17:17:07.109039Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 143fc381-3f3f-46bb-8cac-7d6ed9ba31cd · inbound

Arithmetic Pedagogy for Language Models cites this paper.

Arithmetic Pedagogy for Language Models KisMATH: Do LLMs Have Knowledge of Implicit Structures in Mathematical Reasoning?

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-14T01:19:54.087576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.