Paper Citation Record · LEDGER

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature

As of 23 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 2 inbound Pith citation observations for arXiv:2607.06723.

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

pith.paper-citation-record.v1
2607.06723 v2

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-14T15:58:18.828589Z

measured 36 of 36 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-14T15:54:13.658127Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

34 of 34 outbound references displayed

verified exact12
verified fuzzy0
unresolved21
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5b9508b3-0fb4-4bd2-a212-ba0ba91d8d34 · outbound

This paper cites 12 Miroslav Bačak.Convex Analysis and Optimization in Hadamard Spaces.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature 12 Miroslav Bačak.Convex Analysis and Optimization in Hadamard Spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2eeca81e-92b1-4b23-992b-2b23f53e786b · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 2

Resolution: verified exact; arxiv_id, observed 2026-07-14T16:00:36.284225Z

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 baefb341-0c0c-473a-804f-32e0b6c1951f · outbound

This paper cites Nicolas Boumal.An Introduction to Optimization on Smooth Manifolds.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Nicolas Boumal.An Introduction to Optimization on Smooth Manifolds

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Unavailable: canonical work link unavailable.

Observation d83611af-688e-4b76-9bb4-db341ae88d7d · outbound

This paper cites Nicolas Boutet, Joris Degroote, and Rob Haelterman.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Nicolas Boutet, Joris Degroote, and Rob Haelterman

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 9b9cbb77-1d58-4746-90b3-45ddfe338ccd · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 4230f990-6db9-452e-9b03-7740bf5cdd3e · outbound

This paper cites Michael Crawshaw, Chirag Modi, Mingrui Liu, and Robert M.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Michael Crawshaw, Chirag Modi, Mingrui Liu, and Robert M

Reference 6

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.226022Z

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 7bc7cff6-0332-4748-a6b0-c454481cfe3b · outbound

This paper cites Yu-Hong Dai and Nobuo Yamashita.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Yu-Hong Dai and Nobuo Yamashita

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Unavailable: canonical work link unavailable.

Observation 8817dc0d-744f-470a-9508-c98dd90ab6da · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 8

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.236877Z

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 58fb3f65-dca0-47d1-9f19-1a491826af09 · outbound

This paper cites John Duchi, Elad Hazan, and Yoram Singer.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature John Duchi, Elad Hazan, and Yoram Singer

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e056ac96-d5d7-43fe-bb66-cb01ce86a97a · outbound

This paper cites Practical Efficiency of Muon for Pretraining.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Practical Efficiency of Muon for Pretraining

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 5032039b-100a-4ec3-a6c6-c5101a4e37fd · outbound

This paper cites Wenbo Gao and Donald Goldfarb.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Wenbo Gao and Donald Goldfarb

Reference 11

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.280310Z

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 306f948f-b55b-4b55-a27d-4043878cf892 · outbound

This paper cites Wenzhi Gao, Zhaonan Qu, Madeleine Udell, and Yinyu Ye.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Wenzhi Gao, Zhaonan Qu, Madeleine Udell, and Yinyu Ye

Reference 12

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.245267Z

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 57981d8d-9055-4575-900b-65e4cc57f8a1 · outbound

This paper cites URLhttps://doi.org/10.1007/s10589-026-00770-8.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature URLhttps://doi.org/10.1007/s10589-026-00770-8

Reference 13

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.305368Z

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 350633c4-4849-4866-9791-12824565f189 · outbound

This paper cites Serge Gratton, V.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Serge Gratton, V

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation e96fbc4c-0e88-40a6-8f52-c740c9dcf22b · outbound

This paper cites 13 Robert Grone, Charles R.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature 13 Robert Grone, Charles R

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation 23f4b91a-4848-430d-af20-898e4d4a1e8d · outbound

This paper cites Keller Jordan.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Keller Jordan

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 31ea1a7f-62af-4ab5-85cc-e8155f853f80 · outbound

This paper cites 2011.613073.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature 2011.613073

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 190bf96f-07cb-419e-b12c-ff30df14ecd1 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Adam: A Method for Stochastic Optimization

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1e6fd9ba-55d2-44b2-948c-2df632ad3d46 · outbound

This paper cites Zhaosong Lu and Ting Kei Pong.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Zhaosong Lu and Ting Kei Pong

Reference 19

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.263396Z

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 edd37bd7-ad58-4a0d-8b3d-a0e4881c64b4 · outbound

This paper cites Pierre Maréchal and Jane J.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Pierre Maréchal and Jane J

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Unavailable: canonical work link unavailable.

Observation c52d7a87-80d9-4b3f-b48a-9349320b40c0 · outbound

This paper cites James Martens and Roger Grosse.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature James Martens and Roger Grosse

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 392f0c05-71ba-4566-bc20-9ae9625dbf8c · outbound

This paper cites A New Perspective on Shampoo's Preconditioner.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature A New Perspective on Shampoo's Preconditioner

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation a70313fa-854a-4184-81b8-15c577a38c1c · outbound

This paper cites Xavier Pennec, Pierre Fillard, and Nicholas Ayache.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Xavier Pennec, Pierre Fillard, and Nicholas Ayache

Reference 23

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.234123Z

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 d162bc4b-a39a-40a1-b724-79645aa078ad · outbound

This paper cites Zhaonan Qu, Wenzhi Gao, Oliver Hinder, Yinyu Ye, and Zhengyuan Zhou.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Zhaonan Qu, Wenzhi Gao, Oliver Hinder, Yinyu Ye, and Zhengyuan Zhou

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Unavailable: canonical work link unavailable.

Observation 312b4765-c4ee-4eda-9d4b-a01bebb97daa · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 25

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

Source-reported events for the cited work

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Observation 5e369d32-e2b0-4930-a76b-aaf331b50afc · outbound

This paper cites Robert B.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Robert B

Reference 26

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation d53293c2-087f-41c6-9e20-7d55c074dff3 · outbound

This paper cites 14 Mirai Tanaka and Kazuhide Nakata.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature 14 Mirai Tanaka and Kazuhide Nakata

Reference 27

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.225306Z

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 acaf1ac9-11f9-4331-8ca9-3474e698dd1e · outbound

This paper cites Yongge Tian.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Yongge Tian

Reference 28

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.250301Z

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 6491001f-e8c4-46d5-9610-a524bc1b4131 · outbound

This paper cites Alice Barbara Tumpach and Gabriel Larotonda.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Alice Barbara Tumpach and Gabriel Larotonda

Reference 29

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.231470Z

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 4e25c988-ee31-4a4a-9198-e416885fff4d · outbound

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

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature SOAP: Improving and Stabilizing Shampoo using Adam

Reference 30

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation 0e24d452-e6f0-4b1d-aa41-36fde1bb5842 · outbound

This paper cites Hongyi Zhang and Suvrit Sra.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Hongyi Zhang and Suvrit Sra

Reference 31

Resolution: verified exact; doi, observed 2026-07-14T16:00:36.299279Z

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 8c6f5f3e-325b-4945-bfa4-f729433f3e8e · outbound

This paper cites It is closed, and block distance splitting gives dAI(diag(M,ρΣ0),diag(M,ρΣ1)) =d AI(Σ 0,Σ 1).

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature It is closed, and block distance splitting gives dAI(diag(M,ρΣ0),diag(M,ρΣ1)) =d AI(Σ 0,Σ 1)

Reference 32

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation 32be0acf-853b-4cfd-91c2-c4141fc4e507 · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Observation 7b690fb2-a318-4de2-a7b6-1f1ce8c8228f · outbound

This paper cites an unresolved cited work.

Optimization Geometrodynamics: Variational Reduction and Interaction Curvature Unresolved cited work

Reference 34

Resolution: unresolved; no resolver link, observed 2026-07-14T15:58:18.828589Z

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Pith citing papers

Observation 6076c7df-8973-4adb-8ea0-53c6152c8d23 · inbound

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response cites this paper.

Restricted Dynamic Geometric Complexity: Path-Space Reduction and M\"obius--Jacobi Response Optimization Geometrodynamics: Variational Reduction and Interaction Curvature

Reference 29

Resolution: unresolved; no resolver link, observed 2026-07-14T15:54:13.658127Z

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Observation 00f89c9f-558e-4227-9a48-3de0d537a090 · inbound

Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions cites this paper.

Causal Optimizer Interaction Calculus: Hidden Geometric Relaxation and Identifiable Interventions Optimization Geometrodynamics: Variational Reduction and Interaction Curvature

Reference 161

Resolution: unresolved; no resolver link, observed 2026-07-14T15:50:41.329016Z

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