Paper Citation Record · LEDGER

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism

As of 13 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 1 inbound Pith citation observation for arXiv:2606.27982.

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

pith.paper-citation-record.v1
2606.27982 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T02:13:07.016394Z

measured 30 of 30 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-01T01:05:37.042919Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

verified exact0
verified fuzzy0
unresolved29
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bca5c3b1-ab50-470e-877a-b42273e38a99 · outbound

This paper cites Optimization with sparsity-inducing penalties, 2011.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Optimization with sparsity-inducing penalties, 2011

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e27afce-7e49-4bcb-9d27-ef707ceec129 · outbound

This paper cites Colbrook, and Gustav Conradie.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook, and Gustav Conradie

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 941bb9d2-d0f5-4222-afd0-7ef742a76473 · outbound

This paper cites an unresolved cited work.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8a619760-6c2a-4da2-834e-3c8805852667 · outbound

This paper cites Brunton, Marko Budiˇ si´ c, Eurika Kaiser, and J.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Brunton, Marko Budiˇ si´ c, Eurika Kaiser, and J

Reference 4

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b5d04a1c-6bf8-4323-b6d4-467418b7641f · outbound

This paper cites Brunton, Joshua L.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Brunton, Joshua L

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1715dda6-7f09-4efe-b574-83fd7ff540fe · outbound

This paper cites Brunton, Joshua L.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Brunton, Joshua L

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7cdb1376-c45c-483d-8f28-7dc04966f723 · outbound

This paper cites Colbrook.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 12eab912-6626-4923-926e-1b45d85b66ea · outbound

This paper cites Colbrook.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e652ee0e-9d9d-47fa-ae20-3fe2c8fc18be · outbound

This paper cites Colbrook, Lorna J.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook, Lorna J

Reference 9

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f1540e89-e14d-45e4-82b1-8dad4d8d876a · outbound

This paper cites Colbrook, Catherine Drysdale, and Andrew Horning.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook, Catherine Drysdale, and Andrew Horning

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d31c9e66-e3ab-43c4-8295-2b61947f8876 · outbound

This paper cites Colbrook, Igor Mezi´ c, and Alexei Stepanenko.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook, Igor Mezi´ c, and Alexei Stepanenko

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a79fecd-fd8d-437f-a074-a72acbff9f59 · outbound

This paper cites Colbrook and Alex Townsend.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook and Alex Townsend

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6f7cbc8d-ab8c-4e08-866a-83bf96e02848 · outbound

This paper cites Brunton, and Matthew J.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Brunton, and Matthew J

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 53fd23e1-b182-490b-829e-4f85a8ceff3f · outbound

This paper cites Estimating long-term behavior of periodically driven flows without trajectory integration.Nonlinearity, 30(5):1948, apr 2017.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Estimating long-term behavior of periodically driven flows without trajectory integration.Nonlinearity, 30(5):1948, apr 2017

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3dd2eea7-d2e6-491f-8d42-adbebcde749f · outbound

This paper cites Graduate Texts in Mathematics.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Graduate Texts in Mathematics

Reference 15

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bc41c342-5e61-4abd-810c-9d3bdd3172cc · outbound

This paper cites Colbrook.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Colbrook

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 873d6bce-2cee-4e88-8fcc-162f6a55ee61 · outbound

This paper cites an unresolved cited work.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Unresolved cited work

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e10b091c-25f7-4e1b-b2a3-7adb514cd840 · outbound

This paper cites On convergence of extended dynamic mode decomposition to the koopman operator.Journal of Nonlinear Science, 28(2):687–710, 2018.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism On convergence of extended dynamic mode decomposition to the koopman operator.Journal of Nonlinear Science, 28(2):687–710, 2018

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bbea7ec3-8495-4e07-aa49-86821545695b · outbound

This paper cites Nathan Kutz, Steven L.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Nathan Kutz, Steven L

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0a97a86f-0c2d-4e7d-ab2b-7ccfb951b6bd · outbound

This paper cites Applied Mathematical Sciences.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Applied Mathematical Sciences

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2aa645fd-0a38-43b1-bb08-5a8761a0aa4d · outbound

This paper cites Spectral properties of dynamical systems, model reduction and decompositions.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Spectral properties of dynamical systems, model reduction and decompositions

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b31e3570-f65e-4ae8-ad38-7c9a16bcbac0 · outbound

This paper cites Rowley, Igor Mezi´ c, Shervin Bagheri, Philipp Schlatter, and Dan S.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Rowley, Igor Mezi´ c, Shervin Bagheri, Philipp Schlatter, and Dan S

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e71b3faa-6883-4e3a-8ec6-42b84e1b3be2 · outbound

This paper cites an unresolved cited work.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 223d4984-efd2-4c06-bdb8-3f5b1fe33ceb · outbound

This paper cites Low-Reynolds-number pitching airfoil direct numerical sim- ulations, 2022.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Low-Reynolds-number pitching airfoil direct numerical sim- ulations, 2022

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b6471517-4183-41c3-a6db-b2d84463f02b · outbound

This paper cites Spectra and pseudospectra.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Spectra and pseudospectra

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 57c36bdf-2415-49d3-b744-b9c00d6cfd01 · outbound

This paper cites Tu, Clarence W.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Tu, Clarence W

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8dd5ba25-ddb9-4b2f-86ae-832e2a2c9120 · outbound

This paper cites Pointwise and uniform convergence of fourier extensions, 2019.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Pointwise and uniform convergence of fourier extensions, 2019

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8c7ab9c9-64ac-44b5-9d64-658949829c4c · outbound

This paper cites Williams, Ioannis G.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Williams, Ioannis G

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

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Unavailable: canonical work link unavailable.

Observation effdc0c5-c66b-491d-ae6e-407e6c2960cc · outbound

This paper cites Williams, Clarence W.

PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism Williams, Clarence W

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-29T02:13:07.016394Z

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Unavailable: canonical work link unavailable.

Pith citing papers

Observation fc164728-969a-4cde-a2d0-a600c71b06ae · inbound

Weak-form Extended Dynamic Mode Decomposition cites this paper.

Weak-form Extended Dynamic Mode Decomposition PRONE: Petrov-Galerkin Operator Learning Unifies DMD, SINDy & Koopmanism

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-01T01:05:37.042919Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.