Paper Citation Record · LEDGER

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization

As of 5 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 2 inbound Pith citation observations for arXiv:2605.18999.

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

pith.paper-citation-record.v1
2605.18999 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-20T12:24:07.167770Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-29T05:33:27.870787Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-02T23:47:28.501543Z

Reference resolution

13 of 13 outbound references displayed

verified exact8
verified fuzzy4
unresolved1
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b8f7f773-7141-4354-a123-f2877793e1d2 · outbound

This paper cites The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm

Reference 1

Resolution: verified exact; local_arxiv, observed 2026-05-20T12:28:17.204381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 9b697c3b-07b2-45ce-a9c0-1e4fd59fc93f · outbound

This paper cites Old Optimizer, New Norm: An Anthology.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Old Optimizer, New Norm: An Anthology

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-05-20T12:28:17.201526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 908eb45c-ad66-4846-86c3-608f432713d3 · outbound

This paper cites Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-06-01T02:02:25.516693Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 0da511cb-f4d0-4551-8171-f95bd4a1c45d · outbound

This paper cites Muon is Scalable for LLM Training.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Muon is Scalable for LLM Training

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-05-20T12:28:17.207016Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 99863beb-de00-418e-bc6b-75d7540dc9f6 · outbound

This paper cites and Tommasi, T.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization and Tommasi, T

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T12:33:28.789937Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation e329a896-a0a4-4152-85c7-fd230f2d9d5d · outbound

This paper cites an unresolved cited work.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-20T12:33:28.791568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation cffdcd53-cc42-47c5-8700-332b2abe7331 · outbound

This paper cites Training Deep Learning Models with Norm-Constrained LMOs.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Training Deep Learning Models with Norm-Constrained LMOs

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:22:37.653978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 83502c11-e45c-4903-b7db-4141f812ee82 · outbound

This paper cites Fork=s+j, we have kX i=1 ¯ri ≥ kX i=s+1 ¯ri = jX ℓ=1 aℓ,¯r k+1 =a j+1.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Fork=s+j, we have kX i=1 ¯ri ≥ kX i=s+1 ¯ri = jX ℓ=1 aℓ,¯r k+1 =a j+1

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T12:33:28.786157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b2a08abf-7b4d-45bf-b28a-f3ebad2e0c43 · outbound

This paper cites 28 RemarkC.5 (What is distance-free?).The algorithm never receives D=∥x 0 −x ⋆∥ as an input.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization 28 RemarkC.5 (What is distance-free?).The algorithm never receives D=∥x 0 −x ⋆∥ as an input

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-05-20T12:28:17.213526Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 237692fb-6764-479c-8ceb-0d16c04ea4d4 · outbound

This paper cites Table 10 reports the result.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Table 10 reports the result

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T12:33:28.784228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 587a003a-1530-4823-b5c1-b10da6269d90 · outbound

This paper cites We report mean ± standard deviation over seeds {42,1337,2024}.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization We report mean ± standard deviation over seeds {42,1337,2024}

Reference 11

Resolution: verified exact; arxiv_id, observed 2026-05-20T12:28:17.210100Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation aaeaed66-4b9c-482d-970c-bdb1f8448ae6 · outbound

This paper cites Among the Muon variants, the adaptive methods remain close to the tuned fixed-Muon baseline throughout training.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Among the Muon variants, the adaptive methods remain close to the tuned fixed-Muon baseline throughout training

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-20T12:33:28.788293Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 8fee7dae-1f3e-48c8-8113-95ac55774d85 · outbound

This paper cites Table 9: Fixed-Muon learning-rate diagnostic on ViT-Tiny/CIFAR-100 for one representative seed.

Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization Table 9: Fixed-Muon learning-rate diagnostic on ViT-Tiny/CIFAR-100 for one representative seed

Reference 13

Resolution: verified exact; arxiv_id, observed 2026-05-20T12:28:17.220082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Pith citing papers

Observation e6a84eb3-1129-4702-8b51-769517b6b514 · inbound

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality cites this paper.

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization

Reference 6

Resolution: metadata mismatch; local_arxiv, observed 2026-07-02T23:47:28.502982Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 73944a22-f53a-4563-874b-4b8d2c284d79 · inbound

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality cites this paper.

OptMuon: Closed-Loop Orthogonalized Momentum Methods for Stochastic Optimization with Zero-Noise Optimality Distance-Aware Muon: Adaptive Step Scaling for Normalized Optimization

Reference 177

Resolution: verified exact; local_arxiv, observed 2026-06-29T05:43:08.888036Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.