Paper Citation Record · LEDGER

Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

As of 4 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 31 inbound Pith citation observations for arXiv:2505.13416.

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

pith.paper-citation-record.v1
2505.13416 v1

Coverage vector

measured 0 of 0 reference resolution

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measured 31 of 31 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-04T06:34:03.388597+00:00

measured 31 of 31 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T13:25:32.825270Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-10T12:15:01.137692Z

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External citation measurements

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Outbound references

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Pith citing papers

Observation e56f3e9c-f65b-43f4-ba78-0851382efaac · inbound

Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training cites this paper.

Low-rank Orthogonalization for Large-scale Matrix Optimization with Applications to Foundation Model Training Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-18T15:51:34.049441Z

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No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 89b0056e-4ca2-4751-b148-1cc2c7646d97 · inbound

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs cites this paper.

DeMuon: A Decentralized Muon for Matrix Optimization over Graphs Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T13:25:32.825270Z

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Observation 95a62f5f-478d-46fb-89b6-07d1f2248832 · inbound

Why Do We Need Warm-up? A Theoretical Perspective cites this paper.

Why Do We Need Warm-up? A Theoretical Perspective Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 52

Resolution: unresolved; no resolver link, observed 2026-08-04T12:38:59.776219Z

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Observation 627a7a76-0783-4fda-b7b0-e2a4541b683d · inbound

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods cites this paper.

Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 15

Resolution: verified exact; arxiv_id, observed 2026-05-21T21:10:38.760232Z

Source-reported events for the cited work

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Observation 38357879-9624-470a-8f55-eb555ee657e4 · inbound

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates cites this paper.

Non-Euclidean SGD for Structured Optimization: Unified Analysis and Improved Rates Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 46

Resolution: unresolved; no resolver link, observed 2026-08-03T22:20:05.602621Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 107d7054-db86-4268-8265-90a09bc9ff55 · inbound

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates cites this paper.

Turbo-Muon: Almost-Orthogonal Pre-Conditioning for Fast Muon Updates Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T18:37:49.615408Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 01af50d3-6af2-442a-80c6-d57f0bc2f4ea · inbound

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning cites this paper.

Hierarchical Semantic Correlation-Aware Masked Autoencoder for Unsupervised Audio-Visual Representation Learning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-13T10:41:51.251736Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29bae2f1-1cda-4efd-be6c-701af07ac116 · inbound

Communication-Efficient Gluon in Federated Learning cites this paper.

Communication-Efficient Gluon in Federated Learning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-05-11T10:56:03.206285Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a8ef95f0-3b7c-4691-a2e9-3fc79a68d2ba · inbound

SUDA-Muon: Structural Design Principles and Boundaries for Fully Decentralized Muon cites this paper.

SUDA-Muon: Structural Design Principles and Boundaries for Fully Decentralized Muon Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-11T22:26:13.675800Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 09849b3b-a548-40b8-964d-9c064b044a18 · inbound

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition cites this paper.

Muon with Nesterov Momentum: Heavy-Tailed Noise and (Randomized) Inexact Polar Decomposition Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-11T05:00:56.688807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 7de08db2-5eec-4436-906c-583c332fcba2 · inbound

Local LMO: Constrained Gradient Optimization via a Local Linear Minimization Oracle cites this paper.

Local LMO: Constrained Gradient Optimization via a Local Linear Minimization Oracle Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-12T08:06:29.281354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 735db6c0-d70e-4e20-84e1-27ad06c33f70 · inbound

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

Intrinsic Muon: Spectral Optimization on Riemannian Matrix Manifolds Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 51

Resolution: verified exact; arxiv_id, observed 2026-05-12T05:36:26.141427Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 31fe0f84-231d-4823-bbf3-461b53326504 · inbound

Phases of Muon: When Muon Eclipses SignSGD cites this paper.

Phases of Muon: When Muon Eclipses SignSGD Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 63

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:41:28.870190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a2a3fb1b-d128-45ec-9d7d-2ece8cb301c5 · inbound

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives cites this paper.

Constrained Stochastic Spectral Preconditioning Converges for Nonconvex Objectives Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 56

Resolution: verified exact; arxiv_id, observed 2026-05-13T05:37:19.241420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation f9874835-7e65-4b90-ad62-dd2862a588f9 · inbound

Rescaled Asynchronous SGD: Optimal Distributed Optimization under Data and System Heterogeneity cites this paper.

Rescaled Asynchronous SGD: Optimal Distributed Optimization under Data and System Heterogeneity Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-05-14T19:32:50.953656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation dc100e25-4d67-42e6-a078-35ace105e5ae · inbound

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers cites this paper.

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 132

Resolution: verified exact; arxiv_id, observed 2026-05-20T09:38:11.220931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation efbc976d-7e8e-47e0-b8e1-62996c62c824 · inbound

Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers cites this paper.

Reference 134

Resolution: verified exact; arxiv_id, observed 2026-06-30T18:45:00.306143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4de886da-5418-4f81-b0af-1259e899adb4 · inbound

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method cites this paper.

Ringmaster LMO: Asynchronous Linear Minimization Oracle Momentum Method Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 299

Resolution: verified exact; arxiv_id, observed 2026-05-20T13:13:18.456147Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 66c05d6b-7ffb-47a8-9121-8ac607731255 · inbound

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models cites this paper.

MiMuon: Mixed Muon Optimizer with Improved Generalization for Large Models Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-05-20T08:13:08.300435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 8bbd071c-aec9-48dc-b830-ca6fbd5bd813 · inbound

LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging cites this paper.

LOSCAR-SGD: Local SGD with Communication-Computation Overlap and Delay-Corrected Sparse Model Averaging Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 300

Resolution: verified exact; arxiv_id, observed 2026-05-21T05:49:40.580934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 193a8c53-2099-4705-85ea-e67c2468cd29 · inbound

Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra cites this paper.

Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 29

Resolution: verified exact; arxiv_id, observed 2026-06-30T13:54:43.950467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4cc498d6-8686-4782-bce3-6e003d64a20c · inbound

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling cites this paper.

Softsign: Smooth Sign in Your Optimizer For Better Parameter Heterogeneity Handling Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 41

Resolution: verified exact; arxiv_id, observed 2026-06-28T22:52:44.824841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 65da08d7-24ba-41a4-9e99-d29d78f95584 · 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 Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 44

Resolution: verified exact; arxiv_id, observed 2026-07-02T23:47:28.520199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation b7f867de-3da4-4d2a-9862-098defe77260 · inbound

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

Reference 191

Resolution: verified exact; arxiv_id, observed 2026-06-29T05:43:08.823150Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 340cbad2-4ed3-42cf-bb9e-75342b618a0c · inbound

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning cites this paper.

Zero-order Parameter-free Optimization for LMO-based Methods: Novel Approach for Efficient Fine-tuning Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 32

Resolution: verified exact; arxiv_id, observed 2026-07-03T17:08:43.708424Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation a709a072-8953-4030-8981-52c91daf5d42 · inbound

Restart and Adaptive Acceleration in Stochastic Gradient Methods cites this paper.

Restart and Adaptive Acceleration in Stochastic Gradient Methods Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-07-04T06:59:37.619277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 5d1fd162-1d0c-46df-b5a3-1a348df4ddb9 · inbound

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case cites this paper.

Convergence Analysis of Muon-type Methods with Inexact LMO in the Degenerate Case Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 64

Resolution: verified exact; arxiv_id, observed 2026-07-04T07:29:38.586902Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-04T06:34:03.388597+00:00.

Observation 4327bb8e-b43a-430d-ae29-0adfc816039a · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-02T05:49:18.355300Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2942369d-0b12-4d62-b9fb-938b1af576fd · inbound

Reassessing Muon for Matrix Factorization cites this paper.

Reassessing Muon for Matrix Factorization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T04:22:55.756619Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dfeb62f0-1d00-4501-bfbd-f5e4fcbd400b · inbound

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback cites this paper.

Sign compression for Muon: SignMuon, MuonSign, and the Limits of Error Feedback Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T02:09:02.175951Z

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Unavailable: canonical work link unavailable.

Observation 05988b0b-7922-4fda-9be0-d7af88850989 · inbound

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization cites this paper.

CMuon: Accelerating and Stabilizing Diffusion Transformer Training via Chunked Momentum Orthogonalization Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T06:04:04.278683Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.