Paper Citation Record · LEDGER

Language Models Use Trigonometry to Do Addition

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 16 inbound Pith citation observations for arXiv:2502.00873.

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

pith.paper-citation-record.v1
2502.00873 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 16 of 16 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+00:00

measured 16 of 16 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:58:14.898944Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T17:09:58.946955Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation 96148bfd-984b-4198-a023-be104c764a7c · inbound

Training-Free Tokenizer Transplantation via Orthogonal Matching Pursuit cites this paper.

Training-Free Tokenizer Transplantation via Orthogonal Matching Pursuit Language Models Use Trigonometry to Do Addition

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T05:58:14.898944Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f33cd9a8-f5cd-411c-ba58-cdc7889bfb7e · inbound

Prompting as Scientific Inquiry cites this paper.

Prompting as Scientific Inquiry Language Models Use Trigonometry to Do Addition

Reference 2017

Resolution: unresolved; no resolver link, observed 2026-08-06T21:25:08.514828Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5c765efa-a25b-4f83-9f4d-a273a939d16d · inbound

Modular Arithmetic: Language Models Solve Math Digit by Digit cites this paper.

Modular Arithmetic: Language Models Solve Math Digit by Digit Language Models Use Trigonometry to Do Addition

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T05:02:53.111777Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e0e46d1f-7a1e-440a-a1d7-322fc1782503 · inbound

Singular Vectors of Attention Heads Align with Features cites this paper.

Singular Vectors of Attention Heads Align with Features Language Models Use Trigonometry to Do Addition

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-02T23:38:14.505229Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b174f98e-d704-4f60-99ba-a81369231507 · inbound

Convergent Evolution: How Different Language Models Learn Similar Number Representations cites this paper.

Convergent Evolution: How Different Language Models Learn Similar Number Representations Language Models Use Trigonometry to Do Addition

Reference 12

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T00:49:48.454051Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 287115ce-57f4-4e74-b55f-178692126dce · inbound

H-Probes: Extracting Hierarchical Structures From Latent Representations of Language Models cites this paper.

H-Probes: Extracting Hierarchical Structures From Latent Representations of Language Models Language Models Use Trigonometry to Do Addition

Reference 12

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T14:10:28.805798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2afabde8-57b4-4ec2-957a-9ba22ef5481a · inbound

Tensor Product Representation Probes Reveal Shared Structure Across Linear Directions cites this paper.

Tensor Product Representation Probes Reveal Shared Structure Across Linear Directions Language Models Use Trigonometry to Do Addition

Reference 10

Resolution: malformed identifier; arxiv_id, observed 2026-05-12T07:16:30.325937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 88a6c872-456e-425d-af62-7b6c84f35633 · inbound

Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering cites this paper.

Riemannian-Manifold Steering: Geometry-Aware Generative Autoencoders for Label-Free Steering Language Models Use Trigonometry to Do Addition

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-06-30T12:04:38.989832Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 6d7f1826-bd46-4451-b335-24be6c140d53 · inbound

When and How Long? The Readout-Mediator Angle in Temporal Reasoning cites this paper.

When and How Long? The Readout-Mediator Angle in Temporal Reasoning Language Models Use Trigonometry to Do Addition

Reference 4

Resolution: verified exact; arxiv_id, observed 2026-06-29T13:33:27.890710Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 009a85fa-7163-49b4-a8a4-e2caeb6c0b71 · inbound

FLIPS: Instance-Fingerprinting for LLMs via Pseudo-random Sequences cites this paper.

FLIPS: Instance-Fingerprinting for LLMs via Pseudo-random Sequences Language Models Use Trigonometry to Do Addition

Reference 39

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T01:56:27.961573Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d6c89853-260b-4e1c-9f8e-2ebf8d659259 · inbound

Temporal Preference Concepts and their Functions in a Large Language Model cites this paper.

Temporal Preference Concepts and their Functions in a Large Language Model Language Models Use Trigonometry to Do Addition

Reference 56

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T14:05:47.181093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 2a6f1e7c-6182-438d-bc0f-fc4216c92f25 · inbound

Temporal Preference Concepts and their Functions in a Large Language Model cites this paper.

Temporal Preference Concepts and their Functions in a Large Language Model Language Models Use Trigonometry to Do Addition

Reference 56

Resolution: unresolved; no resolver link, observed 2026-07-12T17:03:44.315006Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2a94d938-24aa-49f4-85fb-b384e7ac3411 · inbound

Closure-Validated Circuit Discovery in Attention Heads: Co-activation Proposes, Ablation Disposes cites this paper.

Closure-Validated Circuit Discovery in Attention Heads: Co-activation Proposes, Ablation Disposes Language Models Use Trigonometry to Do Addition

Reference 6

Resolution: verified exact; arxiv_id, observed 2026-07-03T00:17:29.335948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 1226753f-298a-47bc-a5ec-23d71b465cc1 · inbound

Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds cites this paper.

Structuring Sparsity: Block-Sparse Featurizers Capture Visual Concept Manifolds Language Models Use Trigonometry to Do Addition

Reference 65

Resolution: verified exact; arxiv_id, observed 2026-07-04T17:09:58.948688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 80607a93-ba54-4d1c-8e61-9a53d17a3c5a · inbound

Do Models Read What They Write? Causal Registers in Scratchpad Reasoning cites this paper.

Do Models Read What They Write? Causal Registers in Scratchpad Reasoning Language Models Use Trigonometry to Do Addition

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-06-30T07:34:21.862545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d71de709-ccc5-4234-a5aa-8da26946551c · inbound

Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in LLMs cites this paper.

Are Arithmetic Heuristic Neurons Form-Invariant? A Mechanistic Analysis of Symbols, Text, and Code in LLMs Language Models Use Trigonometry to Do Addition

Reference 74

Resolution: unresolved; no resolver link, observed 2026-08-01T20:19:25.503146Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.