Paper Citation Record · LEDGER

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions

As of 11 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 0 inbound Pith citation observations for arXiv:2604.06799.

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

pith.paper-citation-record.v1
2604.06799 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T17:52:36.115298Z

measured 19 of 19 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+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

19 of 19 outbound references displayed

verified exact10
verified fuzzy8
unresolved0
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3b660930-8769-4b52-99a5-1a9888d23838 · outbound

This paper cites Language Models Need Inductive Biases to Count Inductively.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Language Models Need Inductive Biases to Count Inductively

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.082961Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8974e614-cc8a-43a8-9191-896c620aebc9 · outbound

This paper cites Training Verifiers to Solve Math Word Problems.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Training Verifiers to Solve Math Word Problems

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-11T05:55:59.127342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 8ee06ef5-5ea1-4cd1-8bbb-6d305c95c92b · outbound

This paper cites Self-Attention Limits Working Memory Capacity of Transformer-Based Models.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Self-Attention Limits Working Memory Capacity of Transformer-Based Models

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.076245Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 33a3090b-baa9-4e31-810a-7bfecc3a770c · outbound

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

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Measuring Mathematical Problem Solving With the MATH Dataset

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-05-11T05:55:59.133983Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 7cc24919-6d76-4a51-b211-0e9d5f4796c1 · outbound

This paper cites Frontier LLMs Still Struggle with Simple Reasoning Tasks.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Frontier LLMs Still Struggle with Simple Reasoning Tasks

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.149749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 4144f919-67f1-4c8e-bb90-85359ecc43c1 · outbound

This paper cites The Expressive Power of Transformers with Chain of Thought.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions The Expressive Power of Transformers with Chain of Thought

Reference 6

Resolution: metadata mismatch; arxiv_id, observed 2026-05-11T05:55:59.122059Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation ba0c836a-8f1f-4685-a613-70f026f3163d · outbound

This paper cites Large Language Models Lack Understanding of Character Composition of Words.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Large Language Models Lack Understanding of Character Composition of Words

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.113748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b3264002-5dc6-4572-a12b-776207149d8b · outbound

This paper cites Peiyang Song, Pengrui Han, and Noah Goodman.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Peiyang Song, Pengrui Han, and Noah Goodman

Reference 8

Resolution: verified exact; doi, observed 2026-05-10T20:40:48.461191Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 69a39fdc-d15c-4e4d-8c96-8b06b782605c · outbound

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

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions MathScale: Scaling Instruction Tuning for Mathematical Reasoning

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.090715Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation f5a7bd6f-6c00-4c59-ab5d-4f55df683567 · outbound

This paper cites an unresolved cited work.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Unresolved cited work

Reference 10

Resolution: verified exact; doi, observed 2026-05-10T20:40:48.458547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation eb2e858a-e109-4447-9ace-b35ccb5d74b0 · outbound

This paper cites Counting Ability of Large Language Models and Impact of Tokenization.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Counting Ability of Large Language Models and Impact of Tokenization

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:55:59.098180Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 373c800c-4ca0-4eab-8384-39a7ab62c9f6 · outbound

This paper cites Exploring the compositional deficiency of large language models in mathematical reasoning through trap problems.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Exploring the compositional deficiency of large language models in mathematical reasoning through trap problems

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.807249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 522a8c51-570c-419a-883b-a4a9199058b6 · outbound

This paper cites Each line corresponds to one of the seven models, traced across increasing complexity levels from left to right.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Each line corresponds to one of the seven models, traced across increasing complexity levels from left to right

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.775289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation fde1a1ed-02f9-4c18-b778-f5056ea116d8 · outbound

This paper cites Transformer attention has no explicit register mechanism for this.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Transformer attention has no explicit register mechanism for this

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.798210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation aaa6f490-fbec-4161-a86d-8cd11f98cad3 · outbound

This paper cites The steep cliff structure — not a gradual fade, confirms that models possess discrete working memory limits rather than capacity degradation.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions The steep cliff structure — not a gradual fade, confirms that models possess discrete working memory limits rather than capacity degradation

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.788018Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 863c7966-853c-4dd1-943d-d8979ae7b49c · outbound

This paper cites This is a hard internal limit.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions This is a hard internal limit

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.791600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 1aa744f2-3bbc-4780-a761-a099dd612b6c · outbound

This paper cites The rightmost zone (steps 10–12) is uniformly zero across all models.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions The rightmost zone (steps 10–12) is uniformly zero across all models

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.802626Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation 6e9dd9d6-2e5e-4c39-b499-0ed2728b17e6 · outbound

This paper cites All other models drop dramatically at K=25 or K=60.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions All other models drop dramatically at K=25 or K=60

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.780034Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Observation b7f26133-478c-45e0-b28e-cc37165e6742 · outbound

This paper cites Instead, it amplifies D3 via the O(n) vs O(n2) distinction.

Beyond Accuracy: Diagnosing Algebraic Reasoning Failures in LLMs Across Nine Complexity Dimensions Instead, it amplifies D3 via the O(n) vs O(n2) distinction

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-17T08:31:39.783989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

Pith citing papers

No inbound Pith citation observations are available.