Paper Citation Record · LEDGER

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections

As of 5 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2512.24953.

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pith.paper-citation-record.v1
2512.24953 v3

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measured 37 of 37 reference resolution

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Source: paper_references, paper_reference_links, observed 2026-08-04T06:40:31.172318Z

measured 37 of 37 standing notices

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37 of 37 outbound references displayed

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Outbound references

Observation 62516ef9-be1e-4b89-bdf0-e1e9364dba4d · outbound

This paper cites Geodesic flows on closed riemannian manifolds with negative curvature.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Geodesic flows on closed riemannian manifolds with negative curvature

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:27.026372Z

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Observation 2cd0ef68-cb78-479c-8a97-81601942cfb5 · outbound

This paper cites American Mathematical Soc., 1927.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections American Mathematical Soc., 1927

Reference 2

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Observation 3c24fe22-2a82-41ba-a4e6-c3ecfdb8bbdf · outbound

This paper cites Applied koopmanism.Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4), 2012.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Applied koopmanism.Chaos: An Interdisciplinary Journal of Nonlinear Science, 22(4), 2012

Reference 3

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Observation 82187f80-9e75-4a12-8960-641daf570e97 · outbound

This paper cites Chaitin-Chatelin.Spectral Approximation of Linear Operators.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Chaitin-Chatelin.Spectral Approximation of Linear Operators

Reference 4

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Observation be3b5ed2-b19f-49f0-91f9-027601b44804 · outbound

This paper cites Rigorous data-driven computation of spectral properties of koopman operators for dynamical systems.Communications on Pure and Applied Mathematics, 77(1):221–283, 2024.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Rigorous data-driven computation of spectral properties of koopman operators for dynamical systems.Communications on Pure and Applied Mathematics, 77(1):221–283, 2024

Reference 5

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Observation 4470e687-dee8-46df-89d6-c4117dece2a1 · outbound

This paper cites Springer, 2019.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Springer, 2019

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:27.939774Z

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Observation de9b5bb5-4230-47b5-9e1c-7099e46b44c6 · outbound

This paper cites Higher order extended dynamic mode decomposition based on the structured total least squares.SIAM Journal on Scientific Computing, 45(2):A985–A1011, 2023.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Higher order extended dynamic mode decomposition based on the structured total least squares.SIAM Journal on Scientific Computing, 45(2):A985–A1011, 2023

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:28.150958Z

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Observation 1cc2429a-e87c-43c9-a578-1bc15d6aa3f7 · outbound

This paper cites Engel, S.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Engel, S

Reference 8

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Observation e062eb1a-1ebe-4b1c-831f-ed11a8a69c41 · outbound

This paper cites Consistent spectral approximation of koopman operators using resolvent compactification.Nonlinearity, 37(7):075021, 2024.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Consistent spectral approximation of koopman operators using resolvent compactification.Nonlinearity, 37(7):075021, 2024

Reference 9

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Observation 32b94fff-7e21-4d65-8c99-378d5edf4ea1 · outbound

This paper cites A lemma in the theory of structural stability of differential equations.Proceedings of the American Mathematical Society, 11(4):610–620, 1960.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections A lemma in the theory of structural stability of differential equations.Proceedings of the American Mathematical Society, 11(4):610–620, 1960

Reference 10

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Observation 47237f0a-9e4f-4141-b68e-15191b3e5007 · outbound

This paper cites SIAM, 2002.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections SIAM, 2002

Reference 11

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Observation abfc4dd9-794a-4b9e-84d6-28fa94706b29 · outbound

This paper cites Data-driven resolvent analysis.Journal of Fluid Mechanics, 918:A10, 2021.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Data-driven resolvent analysis.Journal of Fluid Mechanics, 918:A10, 2021

Reference 12

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Observation 79b9df9b-0b3f-4b41-af2e-1fbbe54b6a29 · outbound

This paper cites Koopman operators with intrinsic observables in rigged reproducing kernel hilbert spaces.Nonlinearity, 38(11):115022, 2025.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Koopman operators with intrinsic observables in rigged reproducing kernel hilbert spaces.Nonlinearity, 38(11):115022, 2025

Reference 13

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Observation ffb20fdf-d398-4386-810b-23e5ea5ee25a · outbound

This paper cites Kato.Perturbation Theory for Linear Operators.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Kato.Perturbation Theory for Linear Operators

Reference 14

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Observation 9e3239ec-4ac9-42f5-acd9-1484d92e6fa2 · outbound

This paper cites Number 54.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Number 54

Reference 15

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Observation 0bc2a675-047e-4723-90c5-df4f31786a14 · outbound

This paper cites On the numerical approximation of the Perron-Frobenius and Koopman operator.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections On the numerical approximation of the Perron-Frobenius and Koopman operator

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.034927Z

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Observation b711aff2-5fae-43bb-9e13-75dda3a6712c · outbound

This paper cites Data- driven approximation of the koopman generator: Model reduction, system identification, and control.Physica D: Nonlinear Phenomena, 406:132416, 2020.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Data- driven approximation of the koopman generator: Model reduction, system identification, and control.Physica D: Nonlinear Phenomena, 406:132416, 2020

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.107214Z

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Observation e2698203-6832-4296-9930-946affef0d65 · outbound

This paper cites Hamiltonian systems and transformation in Hilbert space.Proceedings of the National Academy of Sciences, 17(5):315, 1931.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Hamiltonian systems and transformation in Hilbert space.Proceedings of the National Academy of Sciences, 17(5):315, 1931

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.166562Z

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Observation 0625a405-0fa0-4c2f-a50e-44790322f1ea · outbound

This paper cites Koopman and John von Neumann.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Koopman and John von Neumann

Reference 19

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Observation 1512deb8-037f-4621-9693-73bcff16c834 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the koopman operator.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections On convergence of extended dynamic mode decomposition to the koopman operator

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.282622Z

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Observation 77eff93e-b1e1-46ab-85ec-ec5a0303f03b · outbound

This paper cites Kernel methods for the approximation of the eigenfunctions of the koopman operator.Physica D: Nonlinear Phenomena, 476:134662, June 2025.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Kernel methods for the approximation of the eigenfunctions of the koopman operator.Physica D: Nonlinear Phenomena, 476:134662, June 2025

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.337732Z

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Observation 54fc870f-d4c4-4967-9d68-2ec08959ff80 · outbound

This paper cites Deep learning for universal linear embeddings of nonlinear dynamics.Nature communications, 9(1):4950, 2018.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Deep learning for universal linear embeddings of nonlinear dynamics.Nature communications, 9(1):4950, 2018

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.412995Z

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Observation 603ceab6-ccde-455c-a12e-531a38b2e74f · outbound

This paper cites Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41:309–325, 2005.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Spectral properties of dynamical systems, model reduction and decompositions.Nonlinear Dynamics, 41:309–325, 2005

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.423810Z

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Observation 642b847a-3845-40dc-b33e-cd20e2c02cec · outbound

This paper cites Koopman operator, geometry, and learning.arXiv: Dynamical Systems, 2020.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Koopman operator, geometry, and learning.arXiv: Dynamical Systems, 2020

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.496775Z

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Observation a82d027b-cea3-43c3-9f95-c57c448b4fc4 · outbound

This paper cites Mills, Jr.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Mills, Jr

Reference 25

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Observation ab3b6e34-4e7b-44db-a944-768041c4fd9d · outbound

This paper cites Pazy.Semigroups of Linear Operators and Applications to Partial Differential Equations.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Pazy.Semigroups of Linear Operators and Applications to Partial Differential Equations

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.814763Z

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Observation 2b6357af-5ea4-4156-8fa1-2d800be87bed · outbound

This paper cites Sur le problème des trois corps et les équations de la dynamique.Acta mathematica, 13(1):A3– A270, 1890.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Sur le problème des trois corps et les équations de la dynamique.Acta mathematica, 13(1):A3– A270, 1890

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:29.972801Z

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Observation 863e6d33-6263-4ae5-998f-2be8162b2155 · outbound

This paper cites Random features for large-scale kernel machines.Advances in neural information processing systems, 20, 2007.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Random features for large-scale kernel machines.Advances in neural information processing systems, 20, 2007

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:30.039675Z

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Observation 6a649ac3-ec5c-4fdb-b19b-64a2f2e1dbe9 · outbound

This paper cites Enhancing spectral analysis in nonlinear dynamics with pseudoeigen- functions from continuous spectra.Scientific Reports, 14(1):19276, 2024.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Enhancing spectral analysis in nonlinear dynamics with pseudoeigen- functions from continuous spectra.Scientific Reports, 14(1):19276, 2024

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:30.106964Z

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Observation 0bac0a88-5403-494b-aa6a-8648b1f92280 · outbound

This paper cites Differentiable dynamical systems.Bulletin of the American mathematical Society, 73(6):747–817, 1967.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Differentiable dynamical systems.Bulletin of the American mathematical Society, 73(6):747–817, 1967

Reference 30

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Observation 2d79bbb6-d96e-4f3c-b523-c3a0f087ab8e · outbound

This paper cites Chapman and Hall/CRC, 2024.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Chapman and Hall/CRC, 2024

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:30.271670Z

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Observation 00e6156b-88ff-4d60-b783-f6717c75e40e · outbound

This paper cites Koopman resolvent: A laplace-domain analysis of nonlinear autonomous dynamical systems.SIAM Journal on Applied Dynamical Systems, 20(4):2013–2036, 2021.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Koopman resolvent: A laplace-domain analysis of nonlinear autonomous dynamical systems.SIAM Journal on Applied Dynamical Systems, 20(4):2013–2036, 2021

Reference 32

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Observation ceb2acd9-c136-4e69-819a-601a320917c4 · outbound

This paper cites PhD thesis, Princeton University, 2013.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections PhD thesis, Princeton University, 2013

Reference 33

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Observation ed635777-6df3-414b-ae34-fac9385029fc · outbound

This paper cites Williams, Ioannis G.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Williams, Ioannis G

Reference 34

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Observation 32b1cbd4-4db0-462e-a4cb-4b9448c99ae2 · outbound

This paper cites Woodbury and Princeton University.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Woodbury and Princeton University

Reference 35

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Observation 9258fd56-78f6-4f89-8827-e64ae3dbd5f7 · outbound

This paper cites A data-driven framework for koopman semigroup estimation in stochastic dynamical systems, 2025.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections A data-driven framework for koopman semigroup estimation in stochastic dynamical systems, 2025

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:30.951925Z

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Observation 5c7d41b8-75f1-418b-bf84-511da5a91a65 · outbound

This paper cites Generative modeling through koopman spectral analysis: An operator-theoretic perspective, 2026.

Resolvent-Based Singular-Value Diagnostics for Data-Driven Koopman Finite Sections Generative modeling through koopman spectral analysis: An operator-theoretic perspective, 2026

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-04T06:40:31.172318Z

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