Paper Citation Record · LEDGER

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs

As of 19 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 2 inbound Pith citation observations for arXiv:2509.06332.

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

pith.paper-citation-record.v1
2509.06332 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:22:41.584970Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T16:01:42.531389Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

35 of 35 outbound references displayed

verified exact0
verified fuzzy5
unresolved30
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 563c97b6-080c-472e-a92b-11d3b7c0df29 · outbound

This paper cites Large Language Models for Mathematical Reasoning: Progresses and Challenges.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Large Language Models for Mathematical Reasoning: Progresses and Challenges

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.482027Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e74c62e3-bb18-4e96-875c-96bd74f1202b · outbound

This paper cites and Simon, H.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs and Simon, H

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:22:41.935528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8eb0b304-0d51-40a0-8d7d-064f8b8ddd11 · outbound

This paper cites Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.489442Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3090bb3e-1248-40cd-9d5b-2f34cc36fac3 · outbound

This paper cites Mechanistic Interpretability for AI Safety -- A Review.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Mechanistic Interpretability for AI Safety -- A Review

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.492537Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b36c995-d71f-495a-9c08-6d7fcad71dd6 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 5

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.926189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 38a49469-74cf-44d0-87d1-8fa4b6788bc8 · outbound

This paper cites On the Measure of Intelligence.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs On the Measure of Intelligence

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.499673Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8863455-ce9e-495e-955e-b7fc2cebcc82 · outbound

This paper cites ARC Prize 2024: Technical Report.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs ARC Prize 2024: Technical Report

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.503330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7285a411-e078-42ae-bb39-0f36d6f4defe · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.915850Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fb2bac42-7974-456f-86e1-7085076075b2 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.905980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ea219bf8-1248-4379-b33e-c24f85b8dcac · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.896341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d3520404-bc2b-4a04-bf99-14f2af93b42a · outbound

This paper cites Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Everything of Thoughts: Defying the Law of Penrose Triangle for Thought Generation

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.515501Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9774737f-4569-4d2d-b1d7-3a08c93e6d60 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.886496Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8d5f03f8-1ac6-45b1-b4e8-30e3cece22ea · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.876991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 87013ca2-c0fb-4a40-bfb3-6745040106d5 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.866508Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1ad0c0d1-a33b-4c7f-8102-48fbc7679245 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.856974Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e44a7fe1-78eb-4081-81a9-afbbdd7345d7 · outbound

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

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Measuring Mathematical Problem Solving With the MATH Dataset

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.530743Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation beb82634-d9c4-47f4-9267-97888ed0eeec · outbound

This paper cites and Dehaene, S.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs and Dehaene, S

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:22:41.847499Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d6261b5a-5750-418a-85c9-7cf1ef50ec5a · outbound

This paper cites and Griffiths, T.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs and Griffiths, T

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:22:41.838084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c8016069-f2a4-47c3-89d5-4a0e97bf78b0 · outbound

This paper cites Progress measures for grokking via mechanistic interpretability.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Progress measures for grokking via mechanistic interpretability

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.539522Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b87bf8c1-68c9-42bd-9022-9d8124608ab2 · outbound

This paper cites C., and Simon, H.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs C., and Simon, H

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:22:41.828769Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9ccdf067-db23-442e-b276-307429e37547 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.545542Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d6406e87-d520-461c-ba11-5be5cf068a58 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.812686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation df8ed7fe-6cba-4832-b9ec-86b3e7662a33 · outbound

This paper cites The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.551144Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 389ed7e6-66a8-471e-9240-ee5633a1846b · outbound

This paper cites and Siegler, R.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs and Siegler, R

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:22:41.803281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b368d931-9ca8-4944-b19a-d6cc64649932 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.793068Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 12e6ba36-bf4f-42ac-a08a-6d0c63ecaa24 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.782891Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4c23943c-de29-4054-84ee-9518190c9c71 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.772305Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 46086144-0bce-41e8-b02b-c7c267f00bf7 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.762151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cb622767-ab98-4efc-a2ad-746e183dbfd2 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 29

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.752574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8d021206-441b-4b2e-8f89-2d311c5fe343 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 30

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.742960Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 250fc1a3-a752-4b9b-8808-0802ccf7be5a · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 31

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.733150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 97d2622e-c844-40a6-a40e-5f840832052a · outbound

This paper cites Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.576055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7364c189-375c-44c1-a039-6cccae936fa6 · outbound

This paper cites V., Zhou, D., et al.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs V., Zhou, D., et al

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.579322Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eba810a2-2146-43e5-9775-5221f2e21d73 · outbound

This paper cites an unresolved cited work.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-15T16:22:41.717510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9783d078-f714-493c-8d1c-dc6e8bfe2551 · outbound

This paper cites MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics.

A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T16:22:41.584970Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 4af255ed-6ef1-4c51-9811-987fcdaf7d25 · inbound

Object Search in Partially-Known Environments via LLM-informed Model-based Planning and Prompt Selection cites this paper.

Object Search in Partially-Known Environments via LLM-informed Model-based Planning and Prompt Selection A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-13T19:22:24.103426Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6353b01d-d2e3-4e3e-8c3e-c2b67654a0d5 · inbound

Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning? cites this paper.

Credit Cards, Confusion, Computation, and Consequences: What Can We Uncover About Language Model Reasoning? A Fragile Number Sense: Probing the Elemental Limits of Numerical Reasoning in LLMs

Reference 176

Resolution: unresolved; no resolver link, observed 2026-07-30T16:01:42.531389Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.