Paper Citation Record · LEDGER

On gradient descent-ascent flows in metric spaces

As of 18 August 2026, this Paper Citation Record lists 45 of 45 outbound references and 1 inbound Pith citation observation for arXiv:2506.20258.

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

pith.paper-citation-record.v1
2506.20258 v1

Coverage vector

measured 45 of 45 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T23:05:03.314767Z

measured 46 of 46 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:41:54.595246Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

45 of 45 outbound references displayed

verified exact8
verified fuzzy29
unresolved5
parse uncertain0
malformed identifier3
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 16819bee-b85a-405c-97f2-c4e0e4e80a8b · outbound

This paper cites Gradient Flows in Metric Spaces and in the Space of Probability Measures.

On gradient descent-ascent flows in metric spaces Gradient Flows in Metric Spaces and in the Space of Probability Measures

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:12.201997Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e03e03f4-e820-49b1-bcb0-4c2d5e60697c · outbound

This paper cites A Gradient Method for Approximating Saddle Points and Constrained Maxima.

On gradient descent-ascent flows in metric spaces A Gradient Method for Approximating Saddle Points and Constrained Maxima

Reference 2

Resolution: verified exact; doi, observed 2026-08-06T23:05:05.126542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1b2a5489-2cac-4577-8493-3013bdbc835b · outbound

This paper cites Studies in Linear and Non-Linear Programming.

On gradient descent-ascent flows in metric spaces Studies in Linear and Non-Linear Programming

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.984363Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ee8cb63d-5ae7-4e21-812a-b9a5f36afbac · outbound

This paper cites Maximal Monotone Operators Associated with Saddle Functions.

On gradient descent-ascent flows in metric spaces Maximal Monotone Operators Associated with Saddle Functions

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.776714Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a0c6dd36-a4b0-47f4-b480-6440a7a9e541 · outbound

This paper cites Continuous Time Approximation of Nash Equilib- ria in Monotone Games.

On gradient descent-ascent flows in metric spaces Continuous Time Approximation of Nash Equilib- ria in Monotone Games

Reference 5

Resolution: verified exact; doi, observed 2026-08-06T23:05:04.764226Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ca21e5d6-76d0-4af6-80f1-f25cf7783900 · outbound

This paper cites Convex Analysis and Optimization in Hadamard Spaces.

On gradient descent-ascent flows in metric spaces Convex Analysis and Optimization in Hadamard Spaces

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.619048Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9df37f6c-c490-4953-95ff-920099e8c5bd · outbound

This paper cites Uncertainty Quantification of the 4th Kind; Optimal Posterior Accuracy- UncertaintyTradeoffwiththeMinimumEnclosingBall.

On gradient descent-ascent flows in metric spaces Uncertainty Quantification of the 4th Kind; Optimal Posterior Accuracy- UncertaintyTradeoffwiththeMinimumEnclosingBall

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.557988Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 8bb324f4-b121-417a-9afa-f38c5a7a0ed4 · outbound

This paper cites Hypercontractivité De Semi-Groupes De Diffusion.

On gradient descent-ascent flows in metric spaces Hypercontractivité De Semi-Groupes De Diffusion

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.525452Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c9e49aab-c306-4811-913c-749624433dbe · outbound

This paper cites Numerical Solution of Saddle Point Problems.

On gradient descent-ascent flows in metric spaces Numerical Solution of Saddle Point Problems

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.458833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 7eb7e424-26ff-4ddd-a397-1b75bf94a8a0 · outbound

This paper cites A Hybrid Variational Principle for the Keller–segel System in R2.

On gradient descent-ascent flows in metric spaces A Hybrid Variational Principle for the Keller–segel System in R2

Reference 10

Resolution: verified exact; raw_fallback, observed 2026-08-06T23:05:06.778670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 0950197a-cfd1-48d3-97bb-1e25a83cb777 · outbound

This paper cites Opérateurs Maximaux Monotones Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert.

On gradient descent-ascent flows in metric spaces Opérateurs Maximaux Monotones Et Semi-Groupes De Contractions Dans Les Espaces De Hilbert

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.442786Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b40f76c2-d64c-4920-ac6f-5071982125ca · outbound

This paper cites Functional Analysis, Sobolev Spaces and Partial Differential Equations.

On gradient descent-ascent flows in metric spaces Functional Analysis, Sobolev Spaces and Partial Differential Equations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.424768Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 08f3e8d2-8708-4689-a0d6-67f5baf93057 · outbound

This paper cites On the Convergence of Min-Max Langevin Dynamics and Algorithm.

On gradient descent-ascent flows in metric spaces On the Convergence of Min-Max Langevin Dynamics and Algorithm

Reference 13

Resolution: verified exact; local_arxiv, observed 2026-08-06T23:05:06.249481Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fa4f24d4-ddf5-4f62-b63a-13e6dcf2713e · outbound

This paper cites Asymptotic Convergence of Constrained Primal- Dual Dynamics.

On gradient descent-ascent flows in metric spaces Asymptotic Convergence of Constrained Primal- Dual Dynamics

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.412336Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 94ac41da-caab-446f-b2d9-6605d19bb6a9 · outbound

This paper cites Introduction to Gradient Flows in Metric Spaces.

On gradient descent-ascent flows in metric spaces Introduction to Gradient Flows in Metric Spaces

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.384853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation f32cab28-6399-434b-8b7a-52eb0b23bc28 · outbound

This paper cites Introduction to Gradient Flows in Metric Spaces (II).

On gradient descent-ascent flows in metric spaces Introduction to Gradient Flows in Metric Spaces (II)

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.298196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1e6ef21e-3fec-4f20-8a64-5af3a7826229 · outbound

This paper cites Game on Random Environment, Mean-Field Langevin System, and Neural Networks.

On gradient descent-ascent flows in metric spaces Game on Random Environment, Mean-Field Langevin System, and Neural Networks

Reference 17

Resolution: verified exact; raw_fallback, observed 2026-08-06T23:05:06.019058Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a2111902-dacf-41b6-bae9-acefa45988ab · outbound

This paper cites Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flows.

On gradient descent-ascent flows in metric spaces Strategic Distribution Shift of Interacting Agents via Coupled Gradient Flows

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.277933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 23413a9a-7501-4108-aee0-d9e8d8a0aa86 · outbound

This paper cites Coupled Wasserstein Gradient Flows for Min-Max and Cooperative Games.

On gradient descent-ascent flows in metric spaces Coupled Wasserstein Gradient Flows for Min-Max and Cooperative Games

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-06T23:05:05.499189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 435fd7c2-083a-46e2-a4a1-588277b5b22e · outbound

This paper cites Generation of Semi-Groups of Nonlinear Transforma- tions on General Banach Spaces.

On gradient descent-ascent flows in metric spaces Generation of Semi-Groups of Nonlinear Transforma- tions on General Banach Spaces

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T23:05:00.001214Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b691a19-78de-4658-b5c2-9cedace24906 · outbound

This paper cites Problemi Di Evoluzione in Spazi Metrici E Curve Di Massima Pendenza.

On gradient descent-ascent flows in metric spaces Problemi Di Evoluzione in Spazi Metrici E Curve Di Massima Pendenza

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.251455Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e565e2b7-eb8d-4940-b3d3-4d7620f7f255 · outbound

This paper cites A Mean-Field Analysis of Two-Player Zero-Sum Games.

On gradient descent-ascent flows in metric spaces A Mean-Field Analysis of Two-Player Zero-Sum Games

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.218814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation be760eaf-2d24-419a-b440-70f8cfa3d9d2 · outbound

This paper cites Analysis of Kernel Mirror Prox for Measure Optimiza- tion.

On gradient descent-ascent flows in metric spaces Analysis of Kernel Mirror Prox for Measure Optimiza- tion

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.150568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 16e81ac3-297f-4ea3-ab01-a0d0a0bb5a38 · outbound

This paper cites Convex Analysis and Variational Problems.

On gradient descent-ascent flows in metric spaces Convex Analysis and Variational Problems

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.084746Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation df4ec856-d21c-41d6-a17c-219f5871e9da · outbound

This paper cites Gradient Flows of Time-Dependent Func- tionals in Metric Spaces and Applications to PDEs.

On gradient descent-ascent flows in metric spaces Gradient Flows of Time-Dependent Func- tionals in Metric Spaces and Applications to PDEs

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-06T23:05:00.724751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ddc327fb-f11d-405e-96ac-c64045ed6e4a · outbound

This paper cites On the Subdifferential of a Saddle Function.

On gradient descent-ascent flows in metric spaces On the Subdifferential of a Saddle Function

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:11.024901Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b5ecc955-5f96-4feb-aa52-1ea98824eeaf · outbound

This paper cites Finding Mixed Nash Equilibria of Generative Adver- sarial Networks.

On gradient descent-ascent flows in metric spaces Finding Mixed Nash Equilibria of Generative Adver- sarial Networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:10.815568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b2dba673-db91-44cd-8ad3-9448e580f1f5 · outbound

This paper cites Evolution of Mixed Strategies in Monotone Games.

On gradient descent-ascent flows in metric spaces Evolution of Mixed Strategies in Monotone Games

Reference 28

Resolution: verified exact; doi, observed 2026-08-06T23:05:04.034778Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 08b8effd-ee22-41aa-9437-0e72a25c592c · outbound

This paper cites The Variational Formulation of the Fokker– Planck Equation.

On gradient descent-ascent flows in metric spaces The Variational Formulation of the Fokker– Planck Equation

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-06T23:05:01.334751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6bad28e3-d971-4970-91b5-e97349af1774 · outbound

This paper cites Symmetric Mean-Field Langevin DynamicsforDistributionalMinimaxProblems.

On gradient descent-ascent flows in metric spaces Symmetric Mean-Field Langevin DynamicsforDistributionalMinimaxProblems

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:10.196645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 6af0a3b5-e144-4b96-b091-109c8ee5a0b7 · outbound

This paper cites Gradient Flow for the Boltzmann Entropy and Cheeger’s Energy on Time- Dependent Metric Measure Spaces.

On gradient descent-ascent flows in metric spaces Gradient Flow for the Boltzmann Entropy and Cheeger’s Energy on Time- Dependent Metric Measure Spaces

Reference 31

Resolution: malformed identifier; no resolver link, observed 2026-08-06T23:05:01.574751Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f32adbc2-d613-4805-a95a-d180a210132f · outbound

This paper cites An O(sr)-Resolution ODE Framework for Understanding Discrete-Time Algo- rithms and Applications to the Linear Convergence of Minimax Problems.

On gradient descent-ascent flows in metric spaces An O(sr)-Resolution ODE Framework for Understanding Discrete-Time Algo- rithms and Applications to the Linear Convergence of Minimax Problems

Reference 32

Resolution: malformed identifier; no resolver link, observed 2026-08-06T23:05:01.714748Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a5c7c6f-7c66-4b09-b239-a0da42e7de85 · outbound

This paper cites The Variational Formulation of the Fully Parabolic Keller–Segel System with Degenerate Diffusion.

On gradient descent-ascent flows in metric spaces The Variational Formulation of the Fully Parabolic Keller–Segel System with Degenerate Diffusion

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:09.940026Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e7308e13-030a-4da9-a47f-7444817e6ac5 · outbound

This paper cites GradientFlowsandEvolutionVariationalInequalitiesinMet- ric Spaces. I: Structural Properties.

On gradient descent-ascent flows in metric spaces GradientFlowsandEvolutionVariationalInequalitiesinMet- ric Spaces. I: Structural Properties

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:09.556628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 742763bb-fdca-4e29-af39-454297205a88 · outbound

This paper cites On the Arrow–Hurwicz Differential System for Linearly Constrained Convex Minimization.

On gradient descent-ascent flows in metric spaces On the Arrow–Hurwicz Differential System for Linearly Constrained Convex Minimization

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-06T23:05:02.284832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f5ffbdb-0988-4799-95a4-528cd4b8923f · outbound

This paper cites Note on Non-Cooperative Convex Games.

On gradient descent-ascent flows in metric spaces Note on Non-Cooperative Convex Games

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:09.269577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1b6f1084-9357-4acc-8b8a-ca982d965462 · outbound

This paper cites Generalized Barycenters and Variance Maximization on Metric Spaces.

On gradient descent-ascent flows in metric spaces Generalized Barycenters and Variance Maximization on Metric Spaces

Reference 37

Resolution: malformed identifier; raw_fallback, observed 2026-08-06T23:05:08.947093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation a8fe5198-a4c7-4d1b-9a7c-00ddf1408047 · outbound

This paper cites Monotone Operators Associated with Saddle-Functions and Minimax Problems.

On gradient descent-ascent flows in metric spaces Monotone Operators Associated with Saddle-Functions and Minimax Problems

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:08.548525Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4173c338-742d-4a83-aebb-595000e89a20 · outbound

This paper cites Monotone Operators and the Proximal Point Algorithm.

On gradient descent-ascent flows in metric spaces Monotone Operators and the Proximal Point Algorithm

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-06T23:05:02.779731Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation db47fd21-81b4-4a81-9073-2be631d730be · outbound

This paper cites Saddle-Points and Convex Analysis.

On gradient descent-ascent flows in metric spaces Saddle-Points and Convex Analysis

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:08.224754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation b9eeb5d5-ac23-427f-8754-990afb9ec994 · outbound

This paper cites Convex Functionals of Probability Measures and Nonlinear Diffusions on Manifolds.

On gradient descent-ascent flows in metric spaces Convex Functionals of Probability Measures and Nonlinear Diffusions on Manifolds

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:07.767015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 4725284b-26ec-4122-a00d-93250d1fad01 · outbound

This paper cites Open Problem: Convergence of Single-Timescale Mean-Field Langevin Descent-Ascent for Two-Player Zero-Sum Games.

On gradient descent-ascent flows in metric spaces Open Problem: Convergence of Single-Timescale Mean-Field Langevin Descent-Ascent for Two-Player Zero-Sum Games

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:07.404833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation faa5bfa6-1214-40b3-82a7-de89e2216975 · outbound

This paper cites Saddle Flow Dynamics: Observable Certificates and Separable Regularization.

On gradient descent-ascent flows in metric spaces Saddle Flow Dynamics: Observable Certificates and Separable Regularization

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:07.054859Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation ba263345-48b9-4028-ac45-477259fdf937 · outbound

This paper cites Sion’s Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm.

On gradient descent-ascent flows in metric spaces Sion’s Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm

Reference 44

Resolution: verified exact; doi, observed 2026-08-06T23:05:03.624759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 940da1b4-911b-44f0-9bcf-80b291f2dac6 · outbound

This paper cites 2810–2819.url: https://proceedings.mlr.press/v97/hsieh19b.html (cit.

On gradient descent-ascent flows in metric spaces 2810–2819.url: https://proceedings.mlr.press/v97/hsieh19b.html (cit

Reference 97

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T23:05:10.510978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 39328ca8-b4ae-4aaa-9466-8d5f9864815b · inbound

Local exponential stability of mean-field Langevin descent-ascent and associated particle system cites this paper.

Local exponential stability of mean-field Langevin descent-ascent and associated particle system On gradient descent-ascent flows in metric spaces

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T05:41:54.595246Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.