Paper Citation Record · LEDGER

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement

As of 16 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2608.13129.

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

pith.paper-citation-record.v1
2608.13129 v1

Coverage vector

measured 23 of 23 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:17:47.859203Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+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

23 of 23 outbound references displayed

verified exact0
verified fuzzy1
unresolved22
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7b06d7fb-b5f8-4bdc-8053-5107dd05a0e1 · outbound

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

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Large Language Models for Mathematical Reasoning: Progresses and Challenges

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.556851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10660d69-121f-4372-93e8-4f3bf446ab57 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Training Verifiers to Solve Math Word Problems

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.605797Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 653e56fd-e6b2-464a-97b0-c6e13a14f11a · outbound

This paper cites Language Models Represent Space and Time.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Language Models Represent Space and Time

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.654981Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ca6c5c39-b24d-4ce7-94d6-d431765c593b · outbound

This paper cites Time-LLM: Time Series Forecasting by Reprogramming Large Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Time-LLM: Time Series Forecasting by Reprogramming Large Language Models

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.678936Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be439f0b-5a90-4fb6-b8a0-38df3a2fbd67 · outbound

This paper cites Let's Verify Step by Step.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Let's Verify Step by Step

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.687123Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 32b4bf20-268b-4858-8c61-0e73ce9e1d8d · outbound

This paper cites FinGPT: Democratizing Internet-scale Data for Financial Large Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement FinGPT: Democratizing Internet-scale Data for Financial Large Language Models

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.694066Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9edbd3f0-7f23-44f6-9c88-02bf4a3250be · outbound

This paper cites GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.719372Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c2972dbe-339a-4972-b7a5-f4677ee152aa · outbound

This paper cites Investigating the Limitations of Transformers with Simple Arithmetic Tasks.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Investigating the Limitations of Transformers with Simple Arithmetic Tasks

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.732766Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a4c436f-f42b-4fe5-af57-c670a212bcfc · outbound

This paper cites Show Your Work: Scratchpads for Intermediate Computation with Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Show Your Work: Scratchpads for Intermediate Computation with Language Models

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.748806Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d9833d8-87f4-46cd-b425-2c7ccb9f1b07 · outbound

This paper cites YaRN: Efficient Context Window Extension of Large Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement YaRN: Efficient Context Window Extension of Large Language Models

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.795647Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44add5cc-345b-4452-a27b-5c0a2b5dad3f · outbound

This paper cites DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.808664Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c9f5ede2-2d16-493f-8e4d-5088cc97eab6 · outbound

This paper cites MathScale: Scaling Instruction Tuning for Mathematical Reasoning.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement MathScale: Scaling Instruction Tuning for Mathematical Reasoning

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.815337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1ffe5a15-6abf-401c-b171-0b77ec014f43 · outbound

This paper cites Galactica: A Large Language Model for Science.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Galactica: A Large Language Model for Science

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.826591Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 209ea593-85d5-4ac5-b81c-daf6192d45ef · outbound

This paper cites Solving math word problems with process- and outcome-based feedback.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Solving math word problems with process- and outcome-based feedback

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.839665Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0225a707-0559-4b98-8a24-61ccf1d970c6 · outbound

This paper cites Number Cookbook: Number Understanding of Language Models and How to Improve It.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Number Cookbook: Number Understanding of Language Models and How to Improve It

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.846277Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2f40f32f-55b3-4513-ac66-2457a082f870 · outbound

This paper cites BloombergGPT: A Large Language Model for Finance.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement BloombergGPT: A Large Language Model for Finance

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.859203Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 70939265-7a32-4bc5-bce6-d759deca8545 · outbound

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

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Measuring Mathematical Problem Solving With the MATH Dataset

Reference 1990

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.665861Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad028776-5aac-4b20-8f64-281fd83c127f · outbound

This paper cites The Llama 3 Herd of Models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement The Llama 3 Herd of Models

Reference 2011

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.630256Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83ca18ed-267d-4d0c-ba39-c6da0220b4e5 · outbound

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

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

Reference 2021

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.613609Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fabd9102-37f0-4681-84e0-ca9ee6280816 · outbound

This paper cites Emergent autonomous scientific research capabilities of large language models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Emergent autonomous scientific research capabilities of large language models

Reference 2022

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.571088Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9363f353-05d8-45e4-8d6c-6b8e688ad147 · outbound

This paper cites xVal: A continuous number encoding for large language models.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement xVal: A continuous number encoding for large language models

Reference 2023

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:17:49.654075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.

Observation 1ac7a6e7-5c3e-4039-970a-fd576ab5c714 · outbound

This paper cites Transformers Can Do Arithmetic with the Right Embeddings.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Transformers Can Do Arithmetic with the Right Embeddings

Reference 2024

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.704904Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9287a38c-ce4a-456e-aa35-3325e8ccd5d4 · outbound

This paper cites Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next.

Numeracy in Large Language Models: Fundamental Limitations and Paths to Improvement Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Reference 2025

Resolution: unresolved; no resolver link, observed 2026-08-15T16:17:47.579889Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.