Paper Citation Record · LEDGER

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems

As of 21 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 1 inbound Pith citation observation for arXiv:2509.03340.

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

pith.paper-citation-record.v1
2509.03340 v4

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:35:02.496440Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-09T16:03:52.568375Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-09T16:06:20.108640Z

Reference resolution

34 of 34 outbound references displayed

verified exact1
verified fuzzy20
unresolved13
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b4698682-009d-4c2e-bfd8-c24392ec963e · outbound

This paper cites Improved protein structure prediction using potentials from deep learning.Nature, 577(7792):706–710, 2020.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Improved protein structure prediction using potentials from deep learning.Nature, 577(7792):706–710, 2020

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.363749Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a831ad6-1fdb-4f64-9913-e4fcf2184622 · outbound

This paper cites Machine learning for fluid mechanics.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Machine learning for fluid mechanics

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.368752Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1567984-2b21-45bb-a47e-c606f4322b80 · outbound

This paper cites Learning mesh-based simulation with graph networks.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Learning mesh-based simulation with graph networks

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.372839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e444f34-1cc8-4aab-885a-357e1e4da64a · outbound

This paper cites Similarity equivariant graph neural networks for homogenization of metamaterials.Computer Methods in Applied Mechanics and Engineering, 439:117867, 2025.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Similarity equivariant graph neural networks for homogenization of metamaterials.Computer Methods in Applied Mechanics and Engineering, 439:117867, 2025

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.957214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7e3f7e13-7cf9-4ca5-9ca3-39251c9f41b4 · outbound

This paper cites Discovering interaction mechanisms in crowds via deep generative surrogate experiments.Scientific Reports, 15(1):10385, 2025.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Discovering interaction mechanisms in crowds via deep generative surrogate experiments.Scientific Reports, 15(1):10385, 2025

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.944973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b2cf4930-fd14-4fc7-9e3f-1c58b9aa37e4 · outbound

This paper cites STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems STFlow: Data-Coupled Flow Matching for Geometric Trajectory Simulation

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:35:02.689600Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6d00d1dc-3a4d-41d3-94a6-f9a1cf66d54c · outbound

This paper cites On the nature of turbulence.Les rencontres physiciens-mathématiciens de Strasbourg-RCP25, 12:1–44, 1971.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems On the nature of turbulence.Les rencontres physiciens-mathématiciens de Strasbourg-RCP25, 12:1–44, 1971

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.932635Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 7262b017-2a91-47ed-8fe6-71674fdcdac8 · outbound

This paper cites Exceeding 1.5 c global warming could trigger multiple climate tipping points.Science, 377(6611):eabn7950, 2022.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Exceeding 1.5 c global warming could trigger multiple climate tipping points.Science, 377(6611):eabn7950, 2022

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.919620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 526b0de8-a059-4ec1-a11a-b007e5b4b230 · outbound

This paper cites Earlier collapse of anthropocene ecosystems driven by multiple faster and noisier drivers.Nature Sustainability, 6(11):1331–1342, 2023.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Earlier collapse of anthropocene ecosystems driven by multiple faster and noisier drivers.Nature Sustainability, 6(11):1331–1342, 2023

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.907179Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 018b8fe9-5c23-49ff-936d-92f310b4244b · outbound

This paper cites Evasion of tipping in complex systems through spatial pattern formation.Science, 374(6564): eabj0359, 2021.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Evasion of tipping in complex systems through spatial pattern formation.Science, 374(6564): eabj0359, 2021

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.894611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation cf9e8856-e9c1-41bc-bb94-ad2438afdb23 · outbound

This paper cites Trajectories of the earth system in the anthropocene.Proceedings of the national academy of sciences, 115(33):8252–8259, 2018.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Trajectories of the earth system in the anthropocene.Proceedings of the national academy of sciences, 115(33):8252–8259, 2018

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.882652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 6909036e-9820-4c65-8048-321a45382a46 · outbound

This paper cites Fatenet: an integration of dynamical systems and deep learning for cell fate prediction.Bioinformatics, 40(9):btae525, 2024.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Fatenet: an integration of dynamical systems and deep learning for cell fate prediction.Bioinformatics, 40(9):btae525, 2024

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.870078Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a1fb5329-1236-41d2-970f-1682cde0ecde · outbound

This paper cites Jamming transition in pedestrian counter flow.Physica A: Statistical Mechanics and its Applications, 267(3-4):487–498, 1999.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Jamming transition in pedestrian counter flow.Physica A: Statistical Mechanics and its Applications, 267(3-4):487–498, 1999

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.856860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 31f4a587-062e-4930-97bc-3d747b9c4b44 · outbound

This paper cites Emergence of collective oscillations in massive human crowds.Nature, 638(8049):112–119, 2025.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Emergence of collective oscillations in massive human crowds.Nature, 638(8049):112–119, 2025

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.844343Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 8f5c99af-6360-4758-a292-e952082b3c26 · outbound

This paper cites A bifurcation in visually-guided behavior when following a crowd.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems A bifurcation in visually-guided behavior when following a crowd

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.831875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 80838077-ab35-4fc6-9100-acbbd6909057 · outbound

This paper cites Artificial intelligence for science in quantum, atomistic, and continuum systems.Foundations and Trends® in Machine Learning, 18(4):385–912, 2025.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Artificial intelligence for science in quantum, atomistic, and continuum systems.Foundations and Trends® in Machine Learning, 18(4):385–912, 2025

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.819637Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation ea495d88-f11b-4f15-bc41-749d09bf1ff0 · outbound

This paper cites Improving Equivariant Networks with Probabilistic Symmetry Breaking.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Improving Equivariant Networks with Probabilistic Symmetry Breaking

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.429514Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2fbba761-cc2a-4c74-8066-602c8588ed5a · outbound

This paper cites Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.433761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c83b4653-932a-4b3d-a4cc-420358ffcea7 · outbound

This paper cites Enabling local neural operators to perform equation-free system-level analysis.arXiv preprint arXiv:2505.02308, 2025.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Enabling local neural operators to perform equation-free system-level analysis.arXiv preprint arXiv:2505.02308, 2025

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.437940Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9eaed13c-1a8b-4151-bf26-d7178befb24c · outbound

This paper cites Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Surrogate normal-forms for the numerical bifurcation and stability analysis of navier-stokes flows via machine learning

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.441732Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cfd97c9c-7c55-4efa-8780-a030da7e10f7 · outbound

This paper cites Massachusetts Institute of Technology, 2024.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Massachusetts Institute of Technology, 2024

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.807671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 19e81dac-114d-4785-a1e1-f82bc03b4830 · outbound

This paper cites On the spectral bias of neural networks.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems On the spectral bias of neural networks

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.450038Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3c8ad748-73a6-4a54-ae39-6185e7b8f8d6 · outbound

This paper cites Autoencoding beyond pixels using a learned similarity metric.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Autoencoding beyond pixels using a learned similarity metric

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.787574Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 858f074d-854f-4291-b33d-4f5447ec4a58 · outbound

This paper cites From optimal transport to generative modeling: the VEGAN cookbook.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems From optimal transport to generative modeling: the VEGAN cookbook

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.457885Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e9118108-faf5-4ea0-83d5-ec703f2310cb · outbound

This paper cites Generating images with perceptual similarity metrics based on deep networks.Advances in neural information processing systems, 29, 2016.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Generating images with perceptual similarity metrics based on deep networks.Advances in neural information processing systems, 29, 2016

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.775556Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation b3951dff-adff-4fe8-8621-c4b5908f632d · outbound

This paper cites Can push-forward generative models fit multimodal distributions?Advances in Neural Information Processing Systems, 35:10766–10779, 2022.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Can push-forward generative models fit multimodal distributions?Advances in Neural Information Processing Systems, 35:10766–10779, 2022

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.465744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 29cb1d4c-ba6d-48e1-b04f-5f56a3f599a2 · outbound

This paper cites Flow Matching for Generative Modeling.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Flow Matching for Generative Modeling

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.469657Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d52d6281-6fb3-48a5-a476-4a34ae9eefe6 · outbound

This paper cites Improving and generalizing flow-based generative models with minibatch optimal transport.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Improving and generalizing flow-based generative models with minibatch optimal transport

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.473862Z

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Unavailable: canonical work link unavailable.

Observation 7c003813-863c-4080-b9cc-c937b8b191a5 · outbound

This paper cites Equivariant flow matching.Advances in Neural Information Processing Systems, 36:59886–59910, 2023.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Equivariant flow matching.Advances in Neural Information Processing Systems, 36:59886–59910, 2023

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.754143Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 950f4312-8880-43b5-934f-99f12346ca0f · outbound

This paper cites Equivariant flow matching with hybrid probability transport for 3d molecule generation.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Equivariant flow matching with hybrid probability transport for 3d molecule generation

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.741339Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation 154c17e7-5f84-4508-bf3b-63461695f373 · outbound

This paper cites Equivariance with learned canonicalization functions.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Equivariance with learned canonicalization functions

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.728607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation bf04fd26-924a-4276-a42d-24345a6bf6b0 · outbound

This paper cites Symmetry Breaking and Equivariant Neural Networks.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Symmetry Breaking and Equivariant Neural Networks

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T16:35:02.488753Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 37045caf-a640-42a6-9884-8f55e078fde0 · outbound

This paper cites Equivariant neural simulators for stochastic spatiotemporal dynamics.Advances in Neural Information Processing Systems, 36:38930–38957, 2023.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems Equivariant neural simulators for stochastic spatiotemporal dynamics.Advances in Neural Information Processing Systems, 36:38930–38957, 2023

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.715794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Observation a78ea7d8-e60f-4302-934b-df07cca2b0dd · outbound

This paper cites E (n) equivariant graph neural networks.

Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems E (n) equivariant graph neural networks

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:35:02.703294Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

Pith citing papers

Observation 754ee3fd-9338-48ec-9474-a4ac2ee651d8 · inbound

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces cites this paper.

BubbleSH: A Dataset of Rising Bubbles with Deformable Interfaces Equivariant Flow Matching for Symmetry-Breaking Bifurcation Problems

Reference 15

Resolution: verified exact; local_arxiv, observed 2026-07-09T16:06:20.109957Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.