Paper Citation Record · LEDGER

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update

As of 23 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2608.06218.

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

pith.paper-citation-record.v1
2608.06218 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:29:58.637819Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

22 of 22 outbound references displayed

verified exact0
verified fuzzy10
unresolved10
parse uncertain0
malformed identifier0
metadata mismatch2

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c00ac763-8978-4a95-82ba-764e3eb69c24 · outbound

This paper cites https:// kellerjordan.github.io/posts/muon/.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update https:// kellerjordan.github.io/posts/muon/

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:01.821238Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 41f201b9-6c47-45c5-990e-3fa3d6ff7bce · outbound

This paper cites Transactions on Machine Learning Research (2026).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Transactions on Machine Learning Research (2026)

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:01.603442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 65679fbb-7f0e-450e-bc6c-99d0cd67ea6f · outbound

This paper cites https://thinkingmachines.ai/blog/modular- manifolds (2025).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update https://thinkingmachines.ai/blog/modular- manifolds (2025)

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:01.435813Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0f6f0db0-f527-459b-a128-632fcaf2fcbf · outbound

This paper cites https://leloykun.github.io/ponder/steepest-descent-stiefel/.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update https://leloykun.github.io/ponder/steepest-descent-stiefel/

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:01.228447Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 57b0ce46-0362-47a5-822f-bbdad0d01d16 · outbound

This paper cites Muon + Stiefel (2025).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Muon + Stiefel (2025)

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:01.014128Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation de196a39-4bce-4157-bba3-ebe9eb450099 · outbound

This paper cites Preprint at https:// arxiv.org/abs/2601.21487v1 (2026).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Preprint at https:// arxiv.org/abs/2601.21487v1 (2026)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:57.032556Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb5b9a6a-76f4-4b8e-9f2f-a90a973a9074 · outbound

This paper cites Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:57.145506Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 146b4a67-bc95-45cd-b8f7-fab4da6fa28b · outbound

This paper cites Cambridge University Press, Cambridge (2023).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Cambridge University Press, Cambridge (2023)

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:57.249698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fefce23d-2b78-41c0-a095-edaba65b52c3 · outbound

This paper cites Princeton University Press, Princeton, NJ (2008).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Princeton University Press, Princeton, NJ (2008)

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:00.840841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5ba82449-9193-4ea6-9cfb-24afc4b9268f · outbound

This paper cites SIAM journal on Matrix Analysis and Applications20(2), 303–353 (1998).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update SIAM journal on Matrix Analysis and Applications20(2), 303–353 (1998)

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:00.626333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 8d5dd044-d832-4a7f-8528-f396c396ea29 · outbound

This paper cites OrthoFuse: Training-free Riemannian Fusion of Orthogonal Style-Concept Adapters for Diffusion Models.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update OrthoFuse: Training-free Riemannian Fusion of Orthogonal Style-Concept Adapters for Diffusion Models

Reference 11

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T12:29:59.298906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e9428484-b55b-4904-af0c-eac634ed6655 · outbound

This paper cites an unresolved cited work.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:30:00.407054Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4c5384d1-7979-48ef-a05e-20c499f673af · outbound

This paper cites Preprint at https://arxiv.org/abs/2506.03133v2 (2025).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Preprint at https://arxiv.org/abs/2506.03133v2 (2025)

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:57.725472Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e59f5414-bd8f-46da-a57a-b3b448ab6c6b · outbound

This paper cites Tensorion: A Tensor-Aware Generalization of the Muon Optimizer.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Tensorion: A Tensor-Aware Generalization of the Muon Optimizer

Reference 14

Resolution: metadata mismatch; local_arxiv, observed 2026-08-07T12:29:59.056542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation d4796ed9-d712-49ba-b18a-0f70eaf379be · outbound

This paper cites Preprint at https://arxiv.org/abs/2507.12142 (2025).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Preprint at https://arxiv.org/abs/2507.12142 (2025)

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:57.931186Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 773d21b2-9f2e-4589-9b5f-6642a1ff4532 · outbound

This paper cites Preprint at https://arxiv.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Preprint at https://arxiv

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:58.040078Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3f6d9cd8-8e03-4adb-9ce0-b9fb9852e0ad · outbound

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

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:58.118369Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5aa276be-dbfb-4a95-aa5d-071ff6434c83 · outbound

This paper cites SIAM Journal on Numerical Analysis19(3), 445–469 (1982).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update SIAM Journal on Numerical Analysis19(3), 445–469 (1982)

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:30:00.161521Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 21e9fb74-6246-4088-90b9-cc03b2ebed93 · outbound

This paper cites Preprint at https://arxiv.org/abs/2602.11948v1 (2026).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Preprint at https://arxiv.org/abs/2602.11948v1 (2026)

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-07T12:29:58.356291Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c5eb709-f53b-4040-a145-83428d2db201 · outbound

This paper cites SIAM Journal on Matrix Analysis and Applications34(3), 1171–1191 (2013).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update SIAM Journal on Matrix Analysis and Applications34(3), 1171–1191 (2013)

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:29:59.947908Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e7994461-d9b7-4933-840f-729efe15c96e · outbound

This paper cites Journal of Optimization Theory and Applications169(3), 1042–1068 (2016).

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Journal of Optimization Theory and Applications169(3), 1042–1068 (2016)

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T12:29:59.739484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4f379d3f-ef8e-4ea8-a2e6-fd8a301d0d4f · outbound

This paper cites an unresolved cited work.

Muon on the Stiefel Manifold Admits an Exact Closed-Form Update Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-07T12:29:59.568396Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.