Paper Citation Record · LEDGER

Spectral Scaling Laws of Muon

As of 21 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 1 inbound Pith citation observation for arXiv:2606.04058.

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

pith.paper-citation-record.v1
2606.04058 v2

Coverage vector

measured 16 of 16 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-28T11:19:05.939340Z

measured 17 of 17 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T06:45:17.932930Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

16 of 16 outbound references displayed

verified exact8
verified fuzzy0
unresolved2
parse uncertain0
malformed identifier0
metadata mismatch6

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1e39e7cc-0d51-4227-aac6-8f11a2e7ad7c · outbound

This paper cites Disentangling Adaptive Gradient Methods from Learning Rates.

Spectral Scaling Laws of Muon Disentangling Adaptive Gradient Methods from Learning Rates

Reference 1

Resolution: verified exact; arxiv_id, observed 2026-07-02T02:06:26.403597Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 01b91e99-88a7-4eea-9cea-f503bd47e873 · outbound

This paper cites arXiv preprint arXiv:2512.16928 , year=.

Spectral Scaling Laws of Muon arXiv preprint arXiv:2512.16928 , year=

Reference 2

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T02:06:26.394382Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 9477a3b6-ee0e-4b40-b9e5-924ff338c281 · outbound

This paper cites DeepSeek-V3 Technical Report.

Spectral Scaling Laws of Muon DeepSeek-V3 Technical Report

Reference 3

Resolution: metadata mismatch; local_arxiv, observed 2026-07-02T02:06:26.406273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8db40ac3-bd83-40a6-b4c5-20917fe988a7 · outbound

This paper cites GLM-5: from Vibe Coding to Agentic Engineering.

Spectral Scaling Laws of Muon GLM-5: from Vibe Coding to Agentic Engineering

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-07-02T02:06:26.400480Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4b106f6e-62f3-4bbb-bc25-208f601eba25 · outbound

This paper cites Training Compute-Optimal Large Language Models.

Spectral Scaling Laws of Muon Training Compute-Optimal Large Language Models

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-07-02T02:06:26.397138Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 3af9c62b-fb6a-4ef0-a758-83c43904785c · outbound

This paper cites Scaling Laws for Neural Language Models.

Spectral Scaling Laws of Muon Scaling Laws for Neural Language Models

Reference 6

Resolution: metadata mismatch; local_arxiv, observed 2026-07-02T02:06:26.383239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5a1cc1ef-8adb-4f3e-9604-a0a0f72ed15a · outbound

This paper cites Kimi K2.5: Visual Agentic Intelligence.

Spectral Scaling Laws of Muon Kimi K2.5: Visual Agentic Intelligence

Reference 7

Resolution: verified exact; local_arxiv, observed 2026-07-02T02:06:26.391103Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 5ce679bc-5b3c-41b2-bc36-17d220e0bb3a · outbound

This paper cites Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491.

Spectral Scaling Laws of Muon Normuon: Making muon more efficient and scalable.arXiv preprint arXiv:2510.05491

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-07-02T02:06:26.380244Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation edb031b8-dedd-4933-9b91-8b355355e6cd · outbound

This paper cites Muon is Scalable for LLM Training.

Spectral Scaling Laws of Muon Muon is Scalable for LLM Training

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-07-02T02:06:26.387172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 617268c8-7c18-4197-9193-e2c29a2ce2f2 · outbound

This paper cites The Llama 3 Herd of Models.

Spectral Scaling Laws of Muon The Llama 3 Herd of Models

Reference 10

Resolution: verified exact; local_arxiv, observed 2026-07-02T02:06:26.376886Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0b05e4df-5e09-4577-b05a-e3ff329b9e69 · outbound

This paper cites A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale.

Spectral Scaling Laws of Muon A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 11

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T02:06:26.379608Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2c5ec8d1-2c6b-49eb-96dd-3b8758fc033f · outbound

This paper cites 2 OLMo 2 Furious.

Spectral Scaling Laws of Muon 2 OLMo 2 Furious

Reference 12

Resolution: verified exact; local_arxiv, observed 2026-07-02T02:06:26.371907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 94d13898-bea1-4079-be73-c505814531f1 · outbound

This paper cites Fantastic Pretraining Optimizers and Where to Find Them.

Spectral Scaling Laws of Muon Fantastic Pretraining Optimizers and Where to Find Them

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-07-02T02:06:26.373672Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation aee8d983-2224-4d30-94c8-a2bf7f7e5443 · outbound

This paper cites Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer.

Spectral Scaling Laws of Muon Tensor Programs V: Tuning Large Neural Networks via Zero-Shot Hyperparameter Transfer

Reference 14

Resolution: metadata mismatch; arxiv_id, observed 2026-07-02T02:06:26.383110Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 4e14800d-b71f-474e-9c0c-f9f019ea99f2 · outbound

This paper cites an unresolved cited work.

Spectral Scaling Laws of Muon Unresolved cited work

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-28T11:19:05.939340Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1d0f59c1-2758-4896-943c-7d70a2c20134 · outbound

This paper cites While this approximation is very good (see Figure 9), is uses 10 steps and hence is computationally more expensive.

Spectral Scaling Laws of Muon While this approximation is very good (see Figure 9), is uses 10 steps and hence is computationally more expensive

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-28T11:19:05.939340Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 806beb69-1116-4fc1-936b-d60b22816623 · inbound

SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales cites this paper.

SOAP, Muon, and Beyond: Pushing LLM Pretraining Scales Spectral Scaling Laws of Muon

Reference 70

Resolution: unresolved; no resolver link, observed 2026-08-02T06:45:17.932930Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.