Paper Citation Record · LEDGER

Length Generalization in Arithmetic Transformers

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 11 inbound Pith citation observations for arXiv:2306.15400.

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

pith.paper-citation-record.v1
2306.15400 v1

Coverage vector

measured 0 of 0 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links

measured 11 of 11 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 11 of 11 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:40:56.590936Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

2
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

No outbound reference observations are available for this paper version.

Pith citing papers

Observation d09cb9bb-7f37-4852-a02f-15dfcdb5a0c0 · inbound

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks cites this paper.

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks Length Generalization in Arithmetic Transformers

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:56.590936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 947c460d-62b3-47b1-8a1b-73edab59c729 · inbound

Long-Short Alignment for Effective Long-Context Modeling in LLMs cites this paper.

Long-Short Alignment for Effective Long-Context Modeling in LLMs Length Generalization in Arithmetic Transformers

Reference 2023

Resolution: unresolved; no resolver link, observed 2026-08-07T04:10:20.054268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 945d9ddc-d1c5-4f2e-bc49-d58a8e254d4e · inbound

Learning to Execute Graph Algorithms Exactly with Graph Neural Networks cites this paper.

Learning to Execute Graph Algorithms Exactly with Graph Neural Networks Length Generalization in Arithmetic Transformers

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T06:26:56.403597Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddfc4989-5246-4970-87da-8f8b63fb1e64 · inbound

On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication cites this paper.

On the Mirage of Long-Range Dependency, with an Application to Integer Multiplication Length Generalization in Arithmetic Transformers

Reference 30

Resolution: metadata mismatch; arxiv_id, observed 2026-05-14T21:07:57.629354Z

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 d0b2c7bd-0025-48d3-84dc-de04ab4c6175 · inbound

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior cites this paper.

The Long Delay to Arithmetic Generalization: When Learned Representations Outrun Behavior Length Generalization in Arithmetic Transformers

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-14T21:17:58.880515Z

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 0e51a67e-38c1-483d-bb00-37870565ce9d · inbound

Generalization in LLM Problem Solving: The Case of the Shortest Path cites this paper.

Generalization in LLM Problem Solving: The Case of the Shortest Path Length Generalization in Arithmetic Transformers

Reference 24

Resolution: metadata mismatch; arxiv_id, observed 2026-05-10T10:39:38.193650Z

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 c14b2a64-05ab-4ca7-80cc-c7db45642456 · inbound

Understanding In-Context Learning for Nonlinear Regression with Transformers: Attention as Featurizer cites this paper.

Understanding In-Context Learning for Nonlinear Regression with Transformers: Attention as Featurizer Length Generalization in Arithmetic Transformers

Reference 18

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T18:16:08.541176Z

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 be032f38-555f-46a7-b0e7-2afe15cdf2d2 · inbound

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction cites this paper.

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction Length Generalization in Arithmetic Transformers

Reference 19

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T03:45:57.346516Z

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 6b4a3778-ffa8-40ef-bf67-574ba0eb6392 · inbound

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction cites this paper.

Globally Optimal Training of Spiking Neural Networks via Parameter Reconstruction Length Generalization in Arithmetic Transformers

Reference 19

Resolution: metadata mismatch; arxiv_id, observed 2026-07-01T13:25:44.990787Z

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 b75e99c7-36e9-4379-944b-f2f6d4a8cd61 · inbound

Fine-Tuning Large Language Models for Quantum Reasoning cites this paper.

Fine-Tuning Large Language Models for Quantum Reasoning Length Generalization in Arithmetic Transformers

Reference 52

Resolution: metadata mismatch; arxiv_id, observed 2026-07-04T08:09:41.923308Z

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 4de4381c-a3be-47a4-a41a-096a36215626 · inbound

Frontier Language Models Struggle to Copy: Text Can Be Better Viewed in 2D cites this paper.

Frontier Language Models Struggle to Copy: Text Can Be Better Viewed in 2D Length Generalization in Arithmetic Transformers

Reference 38

Resolution: unresolved; no resolver link, observed 2026-08-01T21:31:00.205807Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.