Paper Citation Record · LEDGER

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics

As of 9 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 0 inbound Pith citation observations for arXiv:2607.04738.

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

pith.paper-citation-record.v1
2607.04738 v1

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-11T14:18:40.632382Z

measured 24 of 24 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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

24 of 24 outbound references displayed

verified exact0
verified fuzzy0
unresolved24
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0feaca8f-222a-435c-9ac1-5a72d8b1ca1d · outbound

This paper cites Identifying drift, diffusion, and causal structure from temporal snapshots.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Identifying drift, diffusion, and causal structure from temporal snapshots

Reference 1

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfdd6c03-f621-4327-afb6-852cbb658de3 · outbound

This paper cites Generative Path-Finding Method for Wasserstein Gradient Flow.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Generative Path-Finding Method for Wasserstein Gradient Flow

Reference 2

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0b5cc29-23c0-481c-b32b-93c516309a15 · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7d1c7b5b-0085-4a97-a748-63dcee2a3adf · outbound

This paper cites Learning interacting particle systems from unlabeled data.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Learning interacting particle systems from unlabeled data

Reference 4

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 005fde95-3d20-4f9f-a51b-901e6f070280 · outbound

This paper cites We refer the reader to Ambrosio et al.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics We refer the reader to Ambrosio et al

Reference 5

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f3377e3-0c8d-4180-ae3b-1668f60b5779 · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 6

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 99c19410-19cd-4b8e-9037-84161a110a17 · outbound

This paper cites The first inequality is an equality if and only if ˙xr =−c r ∇f(x r) for some cr ≥0 , while the second inequality is an equality if and only if ∥˙xr∥=∥∇f(x r)∥.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics The first inequality is an equality if and only if ˙xr =−c r ∇f(x r) for some cr ≥0 , while the second inequality is an equality if and only if ∥˙xr∥=∥∇f(x r)∥

Reference 7

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 514352f6-22a6-48dc-bdfa-afdfc9fd5758 · outbound

This paper cites (26) Proof.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics (26) Proof

Reference 8

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 579fe81d-406a-4d80-906b-355805104cc1 · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 9

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a43167c-9a0c-48ce-9a5c-e5bebf4024d0 · outbound

This paper cites JKONet uses Brenier’s theorem to characterize the solution to (JKO) as an optimization problem over a convex function ψ.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics JKONet uses Brenier’s theorem to characterize the solution to (JKO) as an optimization problem over a convex function ψ

Reference 10

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1c5d0a4-01ab-4e09-bb37-c1915e2739c1 · outbound

This paper cites In this style of algorithms the optimal transport problem is first solved between any two consecutive marginals in {qt}t∈Tobs.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics In this style of algorithms the optimal transport problem is first solved between any two consecutive marginals in {qt}t∈Tobs

Reference 11

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f2a99a17-c40d-46e6-90dd-095ca236e833 · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 12

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c0ad3b72-b9a6-4deb-a0ce-383f84d729f6 · outbound

This paper cites They are thus solving a strictly weaker problem: they recover dynamics, but not an underlying energy.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics They are thus solving a strictly weaker problem: they recover dynamics, but not an underlying energy

Reference 13

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26dafc25-95d6-42d4-88e6-0aeddfbbd77f · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 14

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 189b3511-f71c-494d-a088-e089e82f2dd7 · outbound

This paper cites Carrillo et al.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Carrillo et al

Reference 15

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fb5a6f4f-b3ef-436e-885e-8f360599d18a · outbound

This paper cites Other hyperparameters: (64,64) hidden, lr= 10 −3, 10K iterations, OT-Hungarian coupling between consecutive snapshot pairs.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Other hyperparameters: (64,64) hidden, lr= 10 −3, 10K iterations, OT-Hungarian coupling between consecutive snapshot pairs

Reference 16

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 488c5271-7f0d-471c-a8eb-5608101346e4 · outbound

This paper cites R2 raw is sensitive to additive and multiplicative shifts of V θ.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics R2 raw is sensitive to additive and multiplicative shifts of V θ

Reference 17

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4798d7ca-bd32-4a47-9a72-569da45a93cd · outbound

This paper cites (2026, Tab.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics (2026, Tab

Reference 18

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10da5c2b-4168-4cf6-9d65-63d025b8b7cb · outbound

This paper cites (2024), in both regimes.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics (2024), in both regimes

Reference 19

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 925eaeeb-7dbf-4159-a578-29987f00f1b1 · outbound

This paper cites (2019) comprises ∼17,000 cells observed across five 3-day windows of human embryonic stem cell differentiation.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics (2019) comprises ∼17,000 cells observed across five 3-day windows of human embryonic stem cell differentiation

Reference 20

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 23a713ba-3751-4ade-a660-961b2c87a05e · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 21

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 69d133b0-26d2-4baf-add3-c1f477e41750 · outbound

This paper cites Evaluation protocols.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Evaluation protocols

Reference 22

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb9d11aa-c9cd-46fa-a39b-946bec3184bd · outbound

This paper cites Pattern R2 for V and W .WGF inference from snapshots is identifiable only up to a joint (V, W, σ)- scale ambiguity (Persiianov et al., 2026, App.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Pattern R2 for V and W .WGF inference from snapshots is identifiable only up to a joint (V, W, σ)- scale ambiguity (Persiianov et al., 2026, App

Reference 23

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bee06a53-393e-4d13-819b-4e4819cbbe7d · outbound

This paper cites an unresolved cited work.

Wasserstein Residuals: Learning Gradient Flows from Population Dynamics Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-07-11T14:18:40.632382Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.