Paper Citation Record · LEDGER

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models

As of 11 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:2606.03645.

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

pith.paper-citation-record.v1
2606.03645 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T23:45:16.789926Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

43 of 43 outbound references displayed

verified exact6
verified fuzzy0
unresolved28
parse uncertain0
malformed identifier0
metadata mismatch9

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9068b11b-b7c4-48d1-8363-f57af34dda33 · outbound

This paper cites Proceedings of the 31st International Conference on Computational Linguistics , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the 31st International Conference on Computational Linguistics , pages=

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

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Observation 6d2901d6-abbe-4e68-b062-52669f9e1fdf · outbound

This paper cites Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the 2025 Conference on Empirical Methods in Natural Language Processing , pages=

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dde560d0-2aaa-4d54-a18c-0c33b5794df2 · outbound

This paper cites Probing the Difficulty Perception Mechanism of Large Language Models.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Probing the Difficulty Perception Mechanism of Large Language Models

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-21T02:20:31.272991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c11a4645-0c93-4e16-ae99-2b3a3c4d2242 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Training Verifiers to Solve Math Word Problems

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T23:52:49.754894Z

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Observation eb95a1d1-713e-4670-bba6-2cacac599de6 · outbound

This paper cites Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2) , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2) , year=

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e8cd926c-a327-4004-8f9b-81512d93cca1 · outbound

This paper cites Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Tokenization counts: the impact of tokenization on arithmetic in frontier LLMs

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:52:49.757156Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1d49900a-a49c-410c-a29f-32c91c56e011 · outbound

This paper cites The Eleventh International Conference on Learning Representations , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models The Eleventh International Conference on Learning Representations , year=

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b077840-f983-44a7-a954-8b50edf9cf89 · outbound

This paper cites The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMs.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models The Lookahead Limitation: Why Multi-Operand Addition is Hard for LLMs

Reference 8

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T23:52:49.750555Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6c97ae13-b793-4e2c-9969-19e606615bd0 · outbound

This paper cites Dissecting Multiplication in Transformers: Insights into LLMs.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Dissecting Multiplication in Transformers: Insights into LLMs

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T23:52:49.748380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a1158daf-d25b-427a-a672-85c45a19a536 · outbound

This paper cites The Twelfth International Conference on Learning Representations , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models The Twelfth International Conference on Learning Representations , year=

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0233c280-4570-4668-8d8c-89b69f9ff8b2 · outbound

This paper cites Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops , pages=

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09761a4f-21cb-45db-a3d0-206b3f7bc6fc · outbound

This paper cites Journal of Machine Learning Research , volume=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Journal of Machine Learning Research , volume=

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

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Observation 51546d0e-3a08-4618-8256-042cb47c8c80 · outbound

This paper cites ICML 2025 Workshop on Reliable and Responsible Foundation Models , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models ICML 2025 Workshop on Reliable and Responsible Foundation Models , year=

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d047cd62-5e04-449f-bb48-39d8bf78ab55 · outbound

This paper cites NeurIPS 2024 Workshop on Symmetry and Geometry in Neural Representations , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models NeurIPS 2024 Workshop on Symmetry and Geometry in Neural Representations , year=

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2e562848-aacd-4504-9d16-771afb5bfb87 · outbound

This paper cites Understanding Addition and Subtraction in Transformers.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Understanding Addition and Subtraction in Transformers

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-07-24T01:22:55.194042Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e9c8fb07-afb1-4f53-a4a0-87713bd90a92 · outbound

This paper cites Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Addition in Four Movements: Mapping Layer-wise Information Trajectories in LLMs

Reference 16

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:52:49.766175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a7d10996-8ed6-412b-ba4a-e2759d56b5a1 · outbound

This paper cites ICLR 2025 Workshop on Building Trust in Language Models and Applications , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models ICLR 2025 Workshop on Building Trust in Language Models and Applications , year=

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd6fbc66-1dcf-4371-acff-1abfaa72402e · outbound

This paper cites Qwen3 Technical Report.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Qwen3 Technical Report

Reference 18

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T23:52:49.744030Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b8ad903b-160d-4186-a68f-ba8cdcad300d · outbound

This paper cites UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction

Reference 19

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T23:52:49.763833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 56b04572-a408-40f4-8bc9-1d5f45936af1 · outbound

This paper cites Towards Unifying Interpretability and Control: Evaluation via Intervention.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Towards Unifying Interpretability and Control: Evaluation via Intervention

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:52:49.741820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation dbf884ad-b672-4c1a-a809-a179c22e8acf · outbound

This paper cites Forty-second International Conference on Machine Learning , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Forty-second International Conference on Machine Learning , year=

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 599ebdfa-0656-43b0-8a0c-3b07afdcd681 · outbound

This paper cites Gemma 3 Technical Report.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Gemma 3 Technical Report

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T23:52:49.739422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 39f43b67-e120-4a37-b982-a95d0b3db30a · outbound

This paper cites The Llama 3 Herd of Models.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models The Llama 3 Herd of Models

Reference 23

Resolution: metadata mismatch; local_arxiv, observed 2026-06-28T23:52:49.737440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 40fa5a83-b64e-4bd1-af05-b323a12b38e1 · outbound

This paper cites Advances in neural information processing systems , volume=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Advances in neural information processing systems , volume=

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4e8e344-7aa5-4f2d-8606-38c685ac2a3e · outbound

This paper cites Proceedings of the 2020 conference on empirical methods in natural language processing: system demonstrations , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the 2020 conference on empirical methods in natural language processing: system demonstrations , pages=

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

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Observation 70e6b636-12cb-4dd1-a244-36a82289b292 · outbound

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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a5bda786-a0e7-4f51-af35-3ac176be20e4 · outbound

This paper cites Proceedings of the Thirteenth International Conference on Learning Representations (ICLR) , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the Thirteenth International Conference on Learning Representations (ICLR) , year=

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f5206372-43d9-4f98-aae9-20ccbd8ac341 · outbound

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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models the Journal of machine Learning research , volume=

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

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Observation 8b3215c1-1d16-4c2c-b893-19c3aa4e2021 · outbound

This paper cites Journal of machine learning research , volume=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Journal of machine learning research , volume=

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f76bc455-cc96-4345-a289-d48de199f386 · outbound

This paper cites Wiley interdisciplinary reviews: computational statistics , volume=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Wiley interdisciplinary reviews: computational statistics , volume=

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ef0d1006-997e-4271-871c-715d1acb9adb · outbound

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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models AI Alignment Forum , year =

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dea85931-6369-4939-a3d2-23f5d75d8000 · outbound

This paper cites Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Unraveling Arithmetic in Large Language Models: The Role of Algebraic Structures

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-06-28T23:52:49.735385Z

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Observation d8c73256-633b-4860-9e03-68d0441ed1e9 · outbound

This paper cites Hypothesis-Driven Feature Manifold Analysis in.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Hypothesis-Driven Feature Manifold Analysis in

Reference 33

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Source-reported events for the cited work

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Observation 25967af6-a8dc-46fc-b6c1-5eb255d3c5b4 · outbound

This paper cites Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the Artificial Intelligence in Measurement and Education Conference (AIME-Con): Full Papers , pages=

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e2fe3597-a5e2-4251-bd05-baa2303e1a23 · outbound

This paper cites A Language Model.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models A Language Model

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

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Observation 0f170d3f-aa72-4a08-85e9-776893606b77 · outbound

This paper cites Planning in a recurrent neural network that plays Sokoban.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Planning in a recurrent neural network that plays Sokoban

Reference 36

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T23:52:49.746258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 7f9165e8-0383-4826-909b-642189bc7e42 · outbound

This paper cites MINT: Foundation Model Interventions , year=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models MINT: Foundation Model Interventions , year=

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40820f97-79ee-401b-b846-c9431ac15593 · outbound

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The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models First Conference on Language Modeling , year=

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 60fdafa4-3310-4cfd-8bad-07aef6bd4f99 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Advances in Neural Information Processing Systems , volume=

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 584a0bc6-9171-4c55-8668-f6e970211fc1 · outbound

This paper cites Proceedings of the 41st International Conference on Machine Learning , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Proceedings of the 41st International Conference on Machine Learning , pages=

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1031672a-1945-4256-8bc2-67981ce73f84 · outbound

This paper cites How well do Large Language Models perform in Arithmetic tasks?.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models How well do Large Language Models perform in Arithmetic tasks?

Reference 41

Resolution: metadata mismatch; arxiv_id, observed 2026-06-28T23:52:49.759382Z

Source-reported events for the cited work

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Observation 516258d5-465b-4128-a76b-7315d6c80601 · outbound

This paper cites Findings of the Association for Computational Linguistics: ACL 2025 , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Findings of the Association for Computational Linguistics: ACL 2025 , pages=

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37e416f0-cd19-4885-9033-6048da82f5cc · outbound

This paper cites Findings of the Association for Computational Linguistics ACL 2024 , pages=.

The Shape of Addition: Geometric Structures of Arithmetic in Large Language Models Findings of the Association for Computational Linguistics ACL 2024 , pages=

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-28T23:45:16.789926Z

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Pith citing papers

No inbound Pith citation observations are available.