Paper Citation Record · LEDGER

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization

As of 15 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2608.01911.

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pith.paper-citation-record.v1
2608.01911 v1

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-04T18:34:20.705864Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

40 of 40 outbound references displayed

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External citation measurements

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Outbound references

Observation 4e27c118-c959-4b61-ab5b-4d0e7afc1daf · outbound

This paper cites Modular duality in deep learning,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Modular duality in deep learning,

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.606108Z

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Observation 645d8664-7e65-4389-b20c-95b9b44107a7 · outbound

This paper cites Muon is Scalable for LLM Training.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Muon is Scalable for LLM Training

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.611565Z

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Observation 15951063-a247-41d6-96a0-08040ecfa255 · outbound

This paper cites An iterative algorithm for computing the best estimate of an orthogonal matrix,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization An iterative algorithm for computing the best estimate of an orthogonal matrix,

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.614355Z

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Observation b3e4b0e6-c8ae-430f-bc4b-e31d31bf7e93 · outbound

This paper cites Convergence of Muon with Newton–Schulz,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Convergence of Muon with Newton–Schulz,

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.617120Z

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Observation 0ea101fc-16ea-4fbc-a194-01f0579c7431 · outbound

This paper cites A note on the convergence of Muon and further,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A note on the convergence of Muon and further,

Reference 5

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Observation 9cf682c3-8e3a-4ac5-872c-7cca64e82b1b · outbound

This paper cites On the Convergence Analysis of Muon.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization On the Convergence Analysis of Muon

Reference 6

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Observation 16782062-726d-460b-b2a8-ecc3dcfab8dc · outbound

This paper cites Some methods of speeding up the convergence of iter- ation methods,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Some methods of speeding up the convergence of iter- ation methods,

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.629689Z

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Observation 46071b78-eaab-4e50-8ea2-6a0efc8fa527 · outbound

This paper cites A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights,

Reference 8

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Observation cf9748b6-de26-46d7-8beb-b76875a37ac5 · outbound

This paper cites A variational perspective on accelerated methods in optimization,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A variational perspective on accelerated methods in optimization,

Reference 9

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Observation cd44aa40-5f84-4c51-8f4b-c943e980158e · outbound

This paper cites A Lyapunov analysis of accelerated methods in optimization,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A Lyapunov analysis of accelerated methods in optimization,

Reference 10

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Observation 6e870abb-88d7-4ba2-b558-43fbbcd3a373 · outbound

This paper cites Dissipative dynamical systems part I: General theory,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Dissipative dynamical systems part I: General theory,

Reference 11

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Observation 3037d588-eede-4d5e-9c27-e7863c325c95 · outbound

This paper cites Uniting two control Lyapunov functions for affine systems,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Uniting two control Lyapunov functions for affine systems,

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.641804Z

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Observation 378aac47-852f-4636-9912-b950a6045621 · outbound

This paper cites Distributed continuous-time convex opti- mization on weight-balanced digraphs,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Distributed continuous-time convex opti- mization on weight-balanced digraphs,

Reference 13

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Observation 5df263de-f604-4069-aa1a-e90ad271caf5 · outbound

This paper cites Zero-gradient-sum algorithms for distributed convex optimization: The continuous-time case,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Zero-gradient-sum algorithms for distributed convex optimization: The continuous-time case,

Reference 14

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Observation d52acd3f-46d0-4b3f-811c-d90280415a8d · outbound

This paper cites Quantization enabled privacy protection in decentralized stochastic optimization,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Quantization enabled privacy protection in decentralized stochastic optimization,

Reference 15

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Observation 37f6c7ef-11c9-40d4-a01c-776dc9ba54d1 · outbound

This paper cites Stability of extremum seeking feedback for general nonlinear dynamic systems,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Stability of extremum seeking feedback for general nonlinear dynamic systems,

Reference 16

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Observation 2636147d-49f1-43bd-8bca-75af18ac645c · outbound

This paper cites Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.654261Z

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Observation 8e738b1a-1754-4df7-9327-39aa07c22909 · outbound

This paper cites Continuous-time zeroth-order dynam- ics with projection maps: Model-free feedback optimization with safety guarantees,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Continuous-time zeroth-order dynam- ics with projection maps: Model-free feedback optimization with safety guarantees,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.656481Z

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Observation 0160312a-928d-4cf5-875d-2f20d4fd3020 · outbound

This paper cites A Backstepping Framework for Unconstrained Accelerated Optimization Algorithms.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A Backstepping Framework for Unconstrained Accelerated Optimization Algorithms

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.659178Z

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Observation 650fdb09-e37a-4a03-ad1b-11fa43497425 · outbound

This paper cites Complexity of derivative-free policy optimization for structuredH ∞ control,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Complexity of derivative-free policy optimization for structuredH ∞ control,

Reference 20

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Observation a80a3633-0818-4b88-8a9b-9a2560f52479 · outbound

This paper cites Accelerated optimization in deep learning with a proportional-integral-derivative controller,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Accelerated optimization in deep learning with a proportional-integral-derivative controller,

Reference 21

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Observation d4d347ba-4464-4b45-898e-e648f94cd6f9 · outbound

This paper cites Bhatia,Matrix Analysis.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Bhatia,Matrix Analysis

Reference 22

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Observation 5996d370-aac7-4638-8960-29c40fe90a03 · outbound

This paper cites an unresolved cited work.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Unresolved cited work

Reference 23

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Observation a0a5bef9-e950-46e6-8369-c4271b9f002b · outbound

This paper cites Fixed-time stable gradient flows: Applications to continuous-time optimization,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Fixed-time stable gradient flows: Applications to continuous-time optimization,

Reference 24

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Observation 575d78d3-7d17-47ae-a650-0c5c06aaa5ac · outbound

This paper cites Distributed continuous-time optimiza- tion: Nonuniform gradient gains, finite-time convergence, and convex constraint set,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Distributed continuous-time optimiza- tion: Nonuniform gradient gains, finite-time convergence, and convex constraint set,

Reference 25

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Observation f6d578a9-19f5-4509-ae6d-ea4ac7ac541a · outbound

This paper cites Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Reaching an optimal consensus: Dynamical systems that compute intersections of convex sets,

Reference 26

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Observation 693d899f-30ba-4e34-9b6e-4869ca35f4ea · outbound

This paper cites Distributed continuous-time convex optimization with time-varying cost functions,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Distributed continuous-time convex optimization with time-varying cost functions,

Reference 27

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Observation 59bea505-3cfd-4024-b47d-6739b8bbe1cd · outbound

This paper cites Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Distributed continuous-time algorithm for constrained convex optimizations via nonsmooth analysis approach,

Reference 28

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Observation da1dfcc7-f01b-49a2-a30e-355d96134fa3 · outbound

This paper cites Ex- tremum problems with total variation distance and their applications,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Ex- tremum problems with total variation distance and their applications,

Reference 29

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Observation 7645b2ea-5244-4b45-940d-5cb6f9fe7741 · outbound

This paper cites Convex analysis on the Hermitian matrices,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Convex analysis on the Hermitian matrices,

Reference 30

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Observation 25aa71cb-24b8-4ad8-bc79-874fe0f396d7 · outbound

This paper cites Nonsmooth analysis of singular values. part I: Theory,.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Nonsmooth analysis of singular values. part I: Theory,

Reference 31

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Observation cac7645d-81c6-4c70-a7d9-f8b90b295011 · outbound

This paper cites Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Understanding Gradient Orthogonalization for Deep Learning via Non-Euclidean Trust-Region Optimization

Reference 32

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Observation f9b236da-8302-48da-bd60-173139010124 · outbound

This paper cites Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Incentivizing Desirable Effort Profiles in Strategic Classification: The Role of Causality and Uncertainty

Reference 33

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Observation 57398456-c6fc-43a5-afd5-f88868716aa1 · outbound

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A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-04T18:34:20.698203Z

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Observation d88c7f7c-4bd9-4f72-bf2f-79055d5a803d · outbound

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A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Unresolved cited work

Reference 35

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Observation d4bdbf61-dc7d-4297-a408-f999767f5806 · outbound

This paper cites Continuity of∇fgives∇f( ¯W) = 0, and thereforeω(W 0)⊆ S.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Continuity of∇fgives∇f( ¯W) = 0, and thereforeω(W 0)⊆ S

Reference 39

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Observation af5bd74b-0e15-4acf-8415-f0d4f5f489d9 · outbound

This paper cites His research interests cover distributed op- timization, convex optimization, robust control, federated learning theory, and their practical ap- plications in robotic systems.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization His research interests cover distributed op- timization, convex optimization, robust control, federated learning theory, and their practical ap- plications in robotic systems

Reference 40

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Observation 662f1152-960e-400c-a615-32b489446e5a · outbound

This paper cites 3920–3930.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization 3920–3930

Reference 267

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Observation a1d3c900-c92c-43cc-bc91-b7dfc30743e0 · outbound

This paper cites A Note on the Convergence of Muon.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization A Note on the Convergence of Muon

Reference 2025

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Observation 2c1f2d18-9e18-40a9-a373-180cf2917449 · outbound

This paper cites Available: https://arxiv.org/abs/2601.19156.

A Continuous-Time Analysis of Smoothed Matrix-Polar Spectral Gradient Flows for Muon-Type Optimization Available: https://arxiv.org/abs/2601.19156

Reference 2026

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