Paper Citation Record · LEDGER

A Unified Variational Framework for Optimal Transport with Lagrangian Costs

As of 14 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2607.15471.

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

pith.paper-citation-record.v1
2607.15471 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-01T23:25:32.413571Z

measured 37 of 37 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

37 of 37 outbound references displayed

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External citation measurements

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Outbound references

Observation 6cb0a69d-5380-4ba8-87ba-cfa3d8294877 · outbound

This paper cites Ambrosio and W.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Ambrosio and W

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.226322Z

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Observation 88f022ab-5798-440e-b76c-0d979e620b04 · outbound

This paper cites Ambrosio, N.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Ambrosio, N

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.232133Z

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Observation c40822ac-a618-41d3-be5e-917bf4b06329 · outbound

This paper cites Wasserstein Generative Adversarial Networks.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Wasserstein Generative Adversarial Networks

Reference 3

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Observation fe2a65c0-696e-4283-9689-a5c1f141b7d9 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 4

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Observation 765612fb-950b-4304-a38c-02ed131b1289 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 5

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Observation b5979861-2e8d-45e4-a56a-680bbb7c63c5 · outbound

This paper cites Optimal mass transportation and Mather theory.J.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Optimal mass transportation and Mather theory.J

Reference 6

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Observation 41bdc04c-c12b-483f-b26c-73180fcc26de · outbound

This paper cites and Capuzzo-Dolcetta, I.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs and Capuzzo-Dolcetta, I

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.258300Z

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Observation d8253ee7-b4a8-4226-8413-0c08b635dcfd · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.263816Z

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Observation 331048d3-04bb-4d28-8a1d-5e9ebfe730a3 · outbound

This paper cites On the Global Convergence of Gradient Descent for Over- parameterized Models Using Optimal Transport.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs On the Global Convergence of Gradient Descent for Over- parameterized Models Using Optimal Transport

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.268976Z

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Observation 246b6cf6-6599-49f0-8f95-43254d0af688 · outbound

This paper cites Optimal Transport for Domain Adaptation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(9), 1853–1867, 2017.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Optimal Transport for Domain Adaptation, IEEE Transactions on Pattern Analysis and Machine Intelligence, 39(9), 1853–1867, 2017

Reference 10

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Observation 6d673bcf-6fc0-4386-a6bc-68471e7112fd · outbound

This paper cites Sinkhorn Distances: Lightspeed Computation of Optimal Transport.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Sinkhorn Distances: Lightspeed Computation of Optimal Transport

Reference 11

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Observation 78105eb6-5729-4a10-bcd7-9353437af56a · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.284089Z

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Observation 706bf418-f8db-4b2b-88e2-633266326d35 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.289403Z

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Observation f783c672-2243-45ae-85ab-ed23dda94b38 · outbound

This paper cites Direct Methods in the Calculus of Variations.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Direct Methods in the Calculus of Variations

Reference 14

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Observation 8bb54b2d-d71c-4c92-85c7-efd02b47ac18 · outbound

This paper cites Weinan, Jiequn Han, and Qianxiao Li.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Weinan, Jiequn Han, and Qianxiao Li

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.299331Z

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Observation 6af3b209-f4cb-46b0-967b-56fb9c680ae5 · outbound

This paper cites Partial differential equations and Monge–Kantorovich mass transfer.Lecture Notes, 1989.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Partial differential equations and Monge–Kantorovich mass transfer.Lecture Notes, 1989

Reference 16

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Observation 2820e2eb-5eb8-4494-abb2-a6edcc4577e5 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.310660Z

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Observation 3e0c1945-dbd4-4b6b-8be6-a77fc1cab388 · outbound

This paper cites POT: Python Optimal Transport.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs POT: Python Optimal Transport

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.316286Z

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Observation 954bfcde-9008-4de0-a972-cd76cc82ec5f · outbound

This paper cites Fathi and A.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Fathi and A

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.321091Z

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Observation 020290d7-c8e4-4575-8238-d853d4540771 · outbound

This paper cites Figalli, W.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Figalli, W

Reference 20

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Observation f5bd3636-7230-42b7-8501-8f7b3ee4267d · outbound

This paper cites Weak KAM Theorem in Lagrangian Dynamics.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Weak KAM Theorem in Lagrangian Dynamics

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.330527Z

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Observation c6f38312-8c24-41be-9fd5-b85bc4c23719 · outbound

This paper cites Gangbo and R.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Gangbo and R

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.336235Z

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Observation a219ec2b-5cf5-47ca-bb6a-de9e7b8379e9 · outbound

This paper cites Jordan, D.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Jordan, D

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.341258Z

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Observation 839a7b21-c190-4ae9-b7da-fce8e3face9a · outbound

This paper cites Kantorovich.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Kantorovich

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.345936Z

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Observation d3b91370-2b70-4df4-a367-70b86ee4f517 · outbound

This paper cites Knott and C.S.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Knott and C.S

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.351150Z

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Observation 429cc44e-95fd-44e8-bf12-ff61571ca13c · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.355984Z

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Observation 6eb80995-d60b-47b9-a897-5bc197154e02 · outbound

This paper cites Mean field games.Japanese Journal of Mathematics, 2 (1): 229–260, 2007.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Mean field games.Japanese Journal of Mathematics, 2 (1): 229–260, 2007

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.361177Z

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Observation 9210283a-ec57-465d-b83b-025d06c07c51 · outbound

This paper cites Variational structure of Fokker-Planck equations with variable mobility.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Variational structure of Fokker-Planck equations with variable mobility

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.365848Z

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Observation 493edaa7-861d-4d70-82f8-480c5b796415 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.371172Z

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Observation 26530e60-912f-47c7-8dda-2586d8e8f99c · outbound

This paper cites A Mean Field View of the Landscape of Two-Layer Neural Networks.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs A Mean Field View of the Landscape of Two-Layer Neural Networks

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.376325Z

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Observation c1db9b41-98ce-4615-8b55-abc033fa7f46 · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.381575Z

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Observation ae11532d-b318-454a-868b-8029bbaec035 · outbound

This paper cites Computational Optimal Transport.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Computational Optimal Transport

Reference 32

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Observation 53c8388a-ed8c-413d-b775-8366ee7dbcb4 · outbound

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A Unified Variational Framework for Optimal Transport with Lagrangian Costs Rachev and L

Reference 33

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Observation 926d0e6c-0144-4a8a-a8b4-76ad46adaa37 · outbound

This paper cites The Earth Mover’s Distance as a Metric for Image Retrieval.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs The Earth Mover’s Distance as a Metric for Image Retrieval

Reference 34

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Observation e6d770b4-126b-4dad-99d0-640ee3443fa1 · outbound

This paper cites Rotskoff and Eric Vanden-Eijnden, Neural Networks as Interacting Particle Systems: Asymptotic Convexity of the Loss Landscape and Universal Scaling of the Approximation Error.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Rotskoff and Eric Vanden-Eijnden, Neural Networks as Interacting Particle Systems: Asymptotic Convexity of the Loss Landscape and Universal Scaling of the Approximation Error

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.403350Z

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Observation 4c96351c-c0bf-4825-a9fa-1f72d3b09a9b · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.408225Z

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Observation eba06fc2-2e78-4f65-a159-e1ac47b4940d · outbound

This paper cites an unresolved cited work.

A Unified Variational Framework for Optimal Transport with Lagrangian Costs Unresolved cited work

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-01T23:25:32.413571Z

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