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Paper Citation Record · LEDGER

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems

As of 11 August 2026, this Paper Citation Record lists 64 of 64 outbound references and 0 inbound Pith citation observations for arXiv:2505.14828.

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

pith.paper-citation-record.v1
2505.14828 v1

Coverage vector

measured 64 of 64 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:34:20.891900Z

measured 64 of 64 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+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

64 of 64 outbound references displayed

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  • verified fuzzy23
  • unresolved31
  • parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 62d57252-94d4-4044-a5c3-9a03034baa9a · outbound

This paper cites write newline.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems write newline

Reference 1

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Observation 9e30a425-a1ce-46b6-b469-34466032dbf5 · outbound

This paper cites D., Carroll, T., Pecora, L., Sidorowich, J., and Tsimring, L.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems D., Carroll, T., Pecora, L., Sidorowich, J., and Tsimring, L

Reference 2

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Observation aa5c412b-87a1-48ae-9587-1f1b41bb98c3 · outbound

This paper cites M., Santoso, A., McGregor, S., and England, M.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems M., Santoso, A., McGregor, S., and England, M

Reference 3

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This paper cites an unresolved cited work.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 4

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Observation 192d17fa-12b4-4685-9fb3-0e4fd60e03c7 · outbound

This paper cites Theory of reproducing kernels.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Theory of reproducing kernels

Reference 5

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Observation 563249c2-4927-4613-9722-521b4c269d53 · outbound

This paper cites B., Lin, V., and Mahoney, M.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems B., Lin, V., and Mahoney, M

Reference 6

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Observation 9d3290e7-6871-47f3-8bb3-5bac1212f32a · outbound

This paper cites D., Ibeling, D., and Icard, T.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems D., Ibeling, D., and Icard, T

Reference 7

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Observation 66d8ad6d-3c71-420c-8cd5-13e3e28d5c3a · outbound

This paper cites F., and Fiedler, S.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems F., and Fiedler, S

Reference 8

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Source-reported events for the cited work

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Observation 74f064b7-1ef9-4141-aee4-2d0c2dcb34ff · outbound

This paper cites Dynamic Structural Causal Models.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Dynamic Structural Causal Models

Reference 9

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Observation d09c4c88-aaaa-4f4e-b953-61ff45fd7403 · outbound

This paper cites L., Brunton, B.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems L., Brunton, B

Reference 10

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Observation 0f5c1c76-61d0-44bd-94e2-c738786419b7 · outbound

This paper cites L., Budišić, M., Kaiser, E., and Kutz, J.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems L., Budišić, M., Kaiser, E., and Kutz, J

Reference 11

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Observation 3f61322d-2982-402a-bf7a-4b88f2c39f04 · outbound

This paper cites L., Zolman, N., Kutz, J.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems L., Zolman, N., Kutz, J

Reference 12

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Observation ee50ec28-44f3-4163-8b4e-87aaf168b748 · outbound

This paper cites Tangent space causal inference: Leveraging vector fields for causal discovery in dynamical systems.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Tangent space causal inference: Leveraging vector fields for causal discovery in dynamical systems

Reference 13

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 14

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Observation f13ec00c-3f8c-4e89-8ea5-bd29b12c5bfb · outbound

This paper cites Discovering causal relations and equations from data.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Discovering causal relations and equations from data

Reference 15

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This paper cites and De Vito, E.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and De Vito, E

Reference 16

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Observation 474b33b4-1611-4434-9cb1-ce0a04928333 · outbound

This paper cites EcoPro-LSTMv0: A Memory-based Machine Learning Approach to Predicting Ecosystem Dynamics across Time Scales in Mediterranean Environments.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems EcoPro-LSTMv0: A Memory-based Machine Learning Approach to Predicting Ecosystem Dynamics across Time Scales in Mediterranean Environments

Reference 17

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Observation da03d4a0-942d-4f9d-9249-ee5747b78381 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems D., and Peters, J

Reference 18

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Observation 4610b60e-172b-4590-a185-dc63e8aba933 · outbound

This paper cites R., Pike, M., and Slawinska, J.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems R., Pike, M., and Slawinska, J

Reference 19

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Observation e83b327f-258b-4c06-9125-374b30517f66 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Generative learning for nonlinear dynamics

Reference 20

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 21

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This paper cites H., Katz, R., and Krentz, Maria and, N.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems H., Katz, R., and Krentz, Maria and, N

Reference 22

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Observation 08db89ac-73c3-466d-8ba2-2f03fc06268e · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 23

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Observation 4385c622-cdd7-4dd4-a44b-601a7d8a3ff3 · outbound

This paper cites and Fedorov, A.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Fedorov, A

Reference 24

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Observation 3ac28310-6da7-47fa-861c-fcc27c4a9dd4 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 25

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This paper cites Causally-informed deep learning to improve climate models and projections.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Causally-informed deep learning to improve climate models and projections

Reference 26

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Observation b45cdc88-52ae-45b5-954b-12afeacf0fa9 · outbound

This paper cites G., Barnett, N., and Crutchfield, J.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems G., Barnett, N., and Crutchfield, J

Reference 27

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Observation 1222d265-bef8-4dd0-a702-ac5d21fc89d0 · outbound

This paper cites An Equatorial Ocean Recharge Paradigm for ENSO.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems An Equatorial Ocean Recharge Paradigm for ENSO

Reference 28

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Observation 0f29be6b-2894-459a-8911-45e5b0c3d5de · outbound

This paper cites Spatiotemporal upscaling of sparse air-sea pco2 data via physics-informed transfer learning.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Spatiotemporal upscaling of sparse air-sea pco2 data via physics-informed transfer learning

Reference 29

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Observation 30620747-8d86-4555-876c-3b684774a2bb · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 30

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Observation 891c558d-1e06-4ddf-be8d-344193d0baee · outbound

This paper cites and Mezić, I.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Mezić, I

Reference 31

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Observation ad3b1d37-c152-4999-8142-868c719ee95f · outbound

This paper cites Learning dynamical systems via koopman operator regression in reproducing kernel hilbert spaces.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Learning dynamical systems via koopman operator regression in reproducing kernel hilbert spaces

Reference 32

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Observation 126a13f7-959e-4536-8941-297d77183566 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems N., Proctor, J

Reference 33

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Observation 348ea00c-7e16-46e7-a2f3-c4bda6ce4618 · outbound

This paper cites D., van Lier-Walqui, M., Santos, S., and Morrison, H.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems D., van Lier-Walqui, M., Santos, S., and Morrison, H

Reference 34

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Observation 9a005a40-6496-4d61-ab1e-2dc76b17f2ec · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 35

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Observation 08a59a40-aade-4b53-b9c6-25e769b40b91 · outbound

This paper cites R., Giannakis, D., Pike, M., and Slawinska, J.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems R., Giannakis, D., Pike, M., and Slawinska, J

Reference 36

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Observation a59d9026-22a0-4e39-bcf0-16c74510a2db · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 37

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems N., and Brunton, S

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 42

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This paper cites Analysis of Fluid Flows via Spectral Properties of the Koopman Operator.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Analysis of Fluid Flows via Spectral Properties of the Koopman Operator

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Observation ce6943e4-14c0-4f3b-ba56-2c95e83bada1 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Gentine, P

Reference 44

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This paper cites Metaflux: Meta-learning global carbon fluxes from sparse spatiotemporal observations.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Metaflux: Meta-learning global carbon fluxes from sparse spatiotemporal observations

Reference 45

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This paper cites ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems ChaosBench: A Multi-Channel, Physics-Based Benchmark for Subseasonal-to-Seasonal Climate Prediction

Reference 46

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Observation 080d7a45-4d3c-4106-a531-c0f3fdfbaec6 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Causal models for dynamical systems

Reference 47

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Observation d7d464b6-ec22-43a7-8c82-042d61d54482 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems The theory of signal detectability

Reference 48

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Recht, B

Reference 49

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This paper cites Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Analyzing Koopman approaches to physics-informed machine learning for long-term sea-surface temperature forecasting

Reference 50

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Observation d606897b-58bf-4e68-9c6b-70186f3a887e · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems M., Fons, E., Ballinger, A

Reference 51

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This paper cites From Deterministic ODEs to Dynamic Structural Causal Models.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems From Deterministic ODEs to Dynamic Structural Causal Models

Reference 52

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This paper cites Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets

Reference 53

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This paper cites D., Mu \ n oz-Mar \' , J., et al.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems D., Mu \ n oz-Mar \' , J., et al

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Crutchfield, J

Reference 55

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Causal Discovery in Nonlinear Dynamical Systems using Koopman Operators , October 2024

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems O., Hyv \"a rinen, A., Kerminen, A., and Jordan, M

Reference 57

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Observation 5f577311-a90d-4734-997f-54b2f5b9a458 · outbound

This paper cites Detecting Causality in Complex Ecosystems.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Detecting Causality in Complex Ecosystems

Reference 58

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 59

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Observation f210c267-6886-4eee-af56-493e1e404fa3 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems and Picaut, J

Reference 60

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation aadd6e6b-3866-46b0-8a21-675b5c54d489 · outbound

This paper cites Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts

Reference 61

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Observation 39b57622-4a93-44fe-8bfa-2f9fd35eba91 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems T., Smallman, T

Reference 62

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Observation d8026d95-85c0-4cee-b20c-efe51cd0a439 · outbound

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Deep Koopman operator framework for causal discovery in nonlinear dynamical systems Unresolved cited work

Reference 63

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No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

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Observation 1cd8a4b7-a3c5-4844-840e-1f25ca7abccc · outbound

This paper cites A., Tietsche, S., Mogensen, K., and Mayer, M.

Deep Koopman operator framework for causal discovery in nonlinear dynamical systems A., Tietsche, S., Mogensen, K., and Mayer, M

Reference 64

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