Paper Citation Record · LEDGER

Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 16 inbound Pith citation observations for arXiv:2407.20311.

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

pith.paper-citation-record.v1
2407.20311 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 2026-08-08T06:32:00.761636+00:00

measured 16 of 16 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-08T20:25:16.962705Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T02:55:53.512837Z

Reference resolution

0 of 0 outbound references displayed

verified exact0
verified fuzzy0
unresolved0
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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 2afe56c7-6d14-4adf-aa90-ea0d3ae67e99 · inbound

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

GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 100

Resolution: verified exact; arxiv_id, observed 2026-05-15T00:42:12.064238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0ebf2dd5-3090-49b9-aab4-64a4a05d433a · inbound

MetaMorph: Multimodal Understanding and Generation via Instruction Tuning cites this paper.

MetaMorph: Multimodal Understanding and Generation via Instruction Tuning Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 75

Resolution: verified exact; arxiv_id, observed 2026-05-17T07:51:13.223347Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f8675a3e-e296-438c-86b1-91e4ee6e5ac3 · inbound

GSM-Infinite: How Do Your LLMs Behave over Infinitely Increasing Context Length and Reasoning Complexity? cites this paper.

GSM-Infinite: How Do Your LLMs Behave over Infinitely Increasing Context Length and Reasoning Complexity? Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 41

Resolution: unresolved; no resolver link, observed 2026-08-08T20:25:16.962705Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation de2f23bd-6478-44e5-a598-49830bec22c4 · inbound

When More is Less: Understanding Chain-of-Thought Length in LLMs cites this paper.

When More is Less: Understanding Chain-of-Thought Length in LLMs Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 47

Resolution: unresolved; no resolver link, observed 2026-08-08T13:23:22.156860Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bf5d09d6-6006-4a19-8c48-5ca51cf6d0ae · inbound

Spectral Journey: How Transformers Predict the Shortest Path cites this paper.

Spectral Journey: How Transformers Predict the Shortest Path Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T23:44:10.867138Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1a93c73-b7b8-4ca5-b2fa-62fd4294302c · inbound

Large Language Diffusion Models cites this paper.

Large Language Diffusion Models Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 35

Resolution: verified exact; arxiv_id, observed 2026-05-11T01:42:55.149899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b98c1d62-ff42-4025-a4a4-1836e4359c5f · inbound

Position: We Need An Algorithmic Understanding of Generative AI cites this paper.

Position: We Need An Algorithmic Understanding of Generative AI Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-06T18:41:34.209672Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0430b251-0c01-405d-aa74-f5d5405903f4 · inbound

Depth Gives a False Sense of Privacy: LLM Internal States Inversion cites this paper.

Depth Gives a False Sense of Privacy: LLM Internal States Inversion Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-06T15:18:11.562851Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 584201fc-163b-4893-8b5c-ae40a8d3fc45 · inbound

Scaling Latent Reasoning via Looped Language Models cites this paper.

Scaling Latent Reasoning via Looped Language Models Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-15T07:43:11.789338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 97aa885d-9616-49eb-a14b-67400e1bd408 · inbound

Scaling Latent Reasoning via Looped Language Models cites this paper.

Scaling Latent Reasoning via Looped Language Models Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-04T07:31:30.469195Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12a8783f-c1b0-47a4-a3a0-af15bf677cfb · inbound

The Power of Power Law: Asymmetry Enables Compositional Reasoning cites this paper.

The Power of Power Law: Asymmetry Enables Compositional Reasoning Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 60

Resolution: verified exact; arxiv_id, observed 2026-05-11T19:31:08.411067Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45bd787a-254c-49c8-ac12-2dd1c56bbf05 · inbound

The Power of Power Law: Asymmetry Enables Compositional Reasoning cites this paper.

The Power of Power Law: Asymmetry Enables Compositional Reasoning Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 60

Resolution: unresolved; no resolver link, observed 2026-07-12T18:26:05.728364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0b1125e8-8bf6-420f-a0a4-d757d7d9b988 · inbound

Data Difficulty and the Generalization--Extrapolation Tradeoff in LLM Fine-Tuning cites this paper.

Data Difficulty and the Generalization--Extrapolation Tradeoff in LLM Fine-Tuning Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-05-14T20:07:54.535074Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation e22f475f-a47b-4caa-b7fa-645bad8cc22d · inbound

How Data Shapes RoPE Frequency Usage: From Positional Scale Matching to Length Generalization cites this paper.

How Data Shapes RoPE Frequency Usage: From Positional Scale Matching to Length Generalization Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 45

Resolution: verified exact; local_arxiv, observed 2026-07-09T02:55:53.514975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 626e3a08-4e60-4c35-907e-4d49baadecca · inbound

Understanding Reasoning from Pretraining to Post-Training cites this paper.

Understanding Reasoning from Pretraining to Post-Training Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T21:26:32.620292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f95dbf6d-fb09-494e-91e7-48e4c24f91b3 · inbound

Enough is as good as a feast: A Comprehensive Analysis of How Reinforcement Learning Mitigates Task Conflicts in LLMs cites this paper.

Enough is as good as a feast: A Comprehensive Analysis of How Reinforcement Learning Mitigates Task Conflicts in LLMs Physics of Language Models: Part 2.1, Grade-School Math and the Hidden Reasoning Process

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T06:05:52.779108Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.