Paper Citation Record · LEDGER

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature

As of 13 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2608.09763.

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

pith.paper-citation-record.v1
2608.09763 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T11:16:02.781870Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-13T06:32:02.005865+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

35 of 35 outbound references displayed

verified exact0
verified fuzzy16
unresolved18
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 747fe5f5-ad93-4d10-912b-e7c062634538 · outbound

This paper cites 2024 , howpublished =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature 2024 , howpublished =

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.606873Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2d7ef709-5a1f-4956-9e86-56f14546c309 · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods , journal =

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.650053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 25b251f8-d7fc-4e51-81e8-b465152c570b · outbound

This paper cites Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Muon$^2$: Boosting Muon via Adaptive Second-Moment Preconditioning

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.619053Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7ef0bf0b-3ab4-4689-99c4-f3f6ed03c7aa · outbound

This paper cites MALT: Lightweight Curvature-Aware Muon via Diagonal Preconditioning.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature MALT: Lightweight Curvature-Aware Muon via Diagonal Preconditioning

Reference 4

Resolution: metadata mismatch; local_arxiv, observed 2026-08-11T11:16:03.401105Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f245ef62-50ff-46ef-9213-a5db3af821cb · outbound

This paper cites arXiv preprint arXiv:2601.21750 , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature arXiv preprint arXiv:2601.21750 , year =

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.628663Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 858def86-ba5a-4222-a501-18bf7c136057 · outbound

This paper cites arXiv preprint arXiv:2604.01472 , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature arXiv preprint arXiv:2604.01472 , year =

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.634215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 09f5ef9e-3d44-4573-bb89-bd49b9e792c4 · outbound

This paper cites The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature The Potential of Second-Order Optimization for LLMs: A Study with Full Gauss-Newton

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.638494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9388702d-33ce-4a3c-bcd0-af54d294667c · outbound

This paper cites Proceedings of the 35th International Conference on Machine Learning , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the 35th International Conference on Machine Learning , year =

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.636686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 977e569c-b319-46bf-bacf-84ff97f49e6a · outbound

This paper cites Proceedings of the 35th International Conference on Machine Learning , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the 35th International Conference on Machine Learning , year =

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.622336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f6e9eac9-1e96-45de-8664-1fb8a0cc540a · outbound

This paper cites Kingma and Jimmy Ba , title =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Kingma and Jimmy Ba , title =

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.653805Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f188bdd2-0bf6-4109-a6b1-9a11c10f0c5f · outbound

This paper cites Proceedings of the 32nd International Conference on Machine Learning , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the 32nd International Conference on Machine Learning , year =

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.601662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8bd7033f-f4ae-4e46-a6b0-e55c2cb909a1 · outbound

This paper cites Advances in Neural Information Processing Systems , volume =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Advances in Neural Information Processing Systems , volume =

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.588765Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fa97a7a7-5684-4d7e-a6af-565f7cdf20a9 · outbound

This paper cites Journal of Machine Learning Research , volume =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Journal of Machine Learning Research , volume =

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.568869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 31093362-f92c-49b6-a090-72e7fd0be95f · outbound

This paper cites Proceedings of the 35th International Conference on Machine Learning , series =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the 35th International Conference on Machine Learning , series =

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.552653Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 6a825cd6-e0d7-4e1d-9f76-bd2e0ba7306b · outbound

This paper cites Eldar and Alfred O.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Eldar and Alfred O

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.538179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation a3a72c31-c736-4fa1-ad1f-1a2f5810b6d7 · outbound

This paper cites Proceedings of the 39th International Conference on Machine Learning , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the 39th International Conference on Machine Learning , year =

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.524082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation ba8cc0f6-bafa-49c3-86bd-762eacf7af59 · outbound

This paper cites SOAP: Improving and Stabilizing Shampoo using Adam.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature SOAP: Improving and Stabilizing Shampoo using Adam

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.690247Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20d23b47-3de4-4c84-9126-b36b9bab5c49 · outbound

This paper cites arXiv preprint arXiv:2603.09697 , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature arXiv preprint arXiv:2603.09697 , year =

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.695038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10bae23b-a67f-4b20-841c-e0c2f98c55fe · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Old Optimizer, New Norm: An Anthology

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.699941Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 40faad1b-4017-43f4-9768-863865832a6d · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Preconditioned Norms: A Unified Framework for Steepest Descent, Quasi-Newton and Adaptive Methods , journal =

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.507546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 57895356-d817-492d-9a7a-8a8f530a1475 · outbound

This paper cites Advances in Neural Information Processing Systems , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Advances in Neural Information Processing Systems , year =

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.492664Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9468a1af-ffc4-4e7a-97dc-8ad139710870 · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Training Deep Learning Models with Norm-Constrained LMOs

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.714437Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 83ca53af-758f-44ee-92e4-c7ce32a792e1 · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.719180Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 230284a8-62d3-45fb-9a8b-d6de06e205c1 · outbound

This paper cites arXiv preprint arXiv:2510.25000 , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature arXiv preprint arXiv:2510.25000 , year =

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.725272Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 798bb163-808b-4a91-b0ef-28dcdaeead6e · outbound

This paper cites MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature MuonEq: Balancing Before Orthogonalization with Lightweight Equilibration

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.731548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1dfef02-d260-4d90-9cc8-224bdcd9e471 · outbound

This paper cites MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature MUON+: Towards More Effective Muon via One Additional Normalization Step for LLM Pre-training

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.737606Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4fb1d9c2-a4be-460b-b9b4-d6ff2e25d054 · outbound

This paper cites Muon is Scalable for LLM Training.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Muon is Scalable for LLM Training

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.744447Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b7379b12-2715-4549-bd95-30c123260558 · outbound

This paper cites Scalable Second Order Optimization for Deep Learning.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Scalable Second Order Optimization for Deep Learning

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.750228Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0097ea4d-0b47-4d08-92c5-fab831a58252 · outbound

This paper cites Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages =

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.478980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9fa967b1-d8bd-491a-826f-64c36f8925c9 · outbound

This paper cites Gregory Pauloski and Zhao Zhang and Lei Huang and Weijia Xu and Ian T.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Gregory Pauloski and Zhao Zhang and Lei Huang and Weijia Xu and Ian T

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.463970Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 2acd5c92-63ce-4787-a2d8-278ec6c80be5 · outbound

This paper cites Turner and Alireza Makhzani , title =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Turner and Alireza Makhzani , title =

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.451722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 8c105264-f7dc-47a0-83ab-6db0f46e3def · outbound

This paper cites Turner and Hao-Jun Michael Shi , title =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Turner and Hao-Jun Michael Shi , title =

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.438841Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation bf8a8c29-5de5-45b6-9fe8-82c8ec58e0c0 · outbound

This paper cites International Conference on Learning Representations , year =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature International Conference on Learning Representations , year =

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:16:03.426506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation aa4bad77-1d28-4273-81dc-b0f553903da7 · outbound

This paper cites Gregory Pauloski and Qi Huang and Lei Huang and Shivaram Venkataraman and Kyle Chard and Ian Foster and Zhao Zhang , title =.

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature Gregory Pauloski and Qi Huang and Lei Huang and Shivaram Venkataraman and Kyle Chard and Ian Foster and Zhao Zhang , title =

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.777064Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4a0b3809-ca41-41cc-aa65-bcf638e00f14 · outbound

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

Second-Order Muon Done Right: A Principled Marriage of Spectral Geometry and Curvature A Distributed Data-Parallel PyTorch Implementation of the Distributed Shampoo Optimizer for Training Neural Networks At-Scale

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T11:16:02.781870Z

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Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.