Paper Citation Record · LEDGER

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

As of 21 August 2026, this Paper Citation Record lists 39 of 39 outbound references and 4 inbound Pith citation observations for arXiv:2412.03734.

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

pith.paper-citation-record.v1
2412.03734 v1

Coverage vector

measured 39 of 39 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T22:13:11.475627Z

measured 43 of 43 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 4 of 4 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-16T12:17:15.749915Z

measured 1 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

39 of 39 outbound references displayed

verified exact11
verified fuzzy7
unresolved18
parse uncertain0
malformed identifier3
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External citation measurements

2
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 7561d646-e8b9-4a63-b90c-da485f67e42d · outbound

This paper cites Allawala and J.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Allawala and J

Reference 1

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.812309Z

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 82d9da2d-f190-4096-b175-629442fa95f7 · outbound

This paper cites Allawala and J.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Allawala and J

Reference 2

Resolution: verified exact; raw_fallback, observed 2026-08-11T22:13:12.041204Z

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 947b4017-e0a0-4fae-ba94-e2c58b301fc2 · outbound

This paper cites Bittracher, M.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Bittracher, M

Reference 3

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.691568Z

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 f6b79e75-11f3-43f1-b389-539f8b04f33d · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.286124Z

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 63bd11aa-e829-4357-bc51-2cccd66bd482 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.296761Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 358c9393-7d46-4b22-ad2e-a58fefc37ea0 · outbound

This paper cites Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Enhancing Predictive Capabilities in Data-Driven Dynamical Modeling with Automatic Differentiation: Koopman and Neural ODE Approaches

Reference 6

Resolution: verified exact; local_arxiv, observed 2026-08-11T22:13:11.945240Z

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 2646b7b6-2a2e-4446-836c-70eb4f99d1e6 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 7

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.670828Z

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 4654e806-4b14-4146-8c3b-f447f259b9a8 · outbound

This paper cites Dellnitz, G.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Dellnitz, G

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.273488Z

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 cbfdd90c-cf5c-4709-a40c-dde43785f04b · outbound

This paper cites Dellnitz and O.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Dellnitz and O

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.321684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c8f0a3c5-4b06-4f2c-9709-8c04d987a419 · outbound

This paper cites Dellnitz, O.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Dellnitz, O

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.328152Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3621507d-b612-4db9-91c4-87d99e86eb52 · outbound

This paper cites Fernex, B.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Fernex, B

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.261003Z

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 54b3c8c4-95dd-492f-ab57-d5c907ae31f4 · outbound

This paper cites Froyland, Computer-assisted bounds for the rate of decay of correlations, Communications in Mathematical Physics, 189 (1997), pp.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Froyland, Computer-assisted bounds for the rate of decay of correlations, Communications in Mathematical Physics, 189 (1997), pp

Reference 13

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.642038Z

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 ebbbcec9-88f1-4aa7-8ceb-6b62c42f328f · outbound

This paper cites Froyland, O.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Froyland, O

Reference 14

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.629325Z

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 b84bf9eb-be1e-4794-a0d4-3d99ed9fc8a0 · outbound

This paper cites Giannakis , Data-driven spectral decomposition and forecasting of ergodic dynamical sys- tems, Applied and Computational Harmonic Analysis, 47 (2019), pp.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Giannakis , Data-driven spectral decomposition and forecasting of ergodic dynamical sys- tems, Applied and Computational Harmonic Analysis, 47 (2019), pp

Reference 15

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.616333Z

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 9ef9dc60-8050-4ed6-b306-084220bb48b4 · outbound

This paper cites Reduced Markovian Models of Dynamical Systems.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Reduced Markovian Models of Dynamical Systems

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.353658Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4510bca5-ddfa-43c5-bf3c-9b99c325303f · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.248407Z

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 f6ace270-3b45-431d-a437-f0e1d437c649 · outbound

This paper cites Goodfellow, Y.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Goodfellow, Y

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.233387Z

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 de4d052f-d70d-4625-9053-bfe5d0d2d68c · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.368392Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b56f9153-3785-4d90-9cdc-38cfe507d60b · outbound

This paper cites Jim´enez, A perron–frobenius analysis of wall-bounded turbulence , Journal of Fluid Mechan- ics, 968 (2023), p.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Jim´enez, A perron–frobenius analysis of wall-bounded turbulence , Journal of Fluid Mechan- ics, 968 (2023), p

Reference 20

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.593912Z

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 243ef060-9e5f-462e-a67d-d0afc8c7bb58 · outbound

This paper cites Junge and P.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Junge and P

Reference 21

Resolution: verified exact; raw_fallback, observed 2026-08-11T22:13:11.916195Z

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 ae0a57be-9d76-453c-8533-f4b7d03238d3 · outbound

This paper cites Karypis, E.-H.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Karypis, E.-H

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.216066Z

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 cad63ac0-d343-41d4-9dd4-362979f390fb · outbound

This paper cites 51–79, https://doi.org/10.3934/jcd.2016003, /article/id/ 99a4878a-5263-40bf-b4e8-bbf7c2730a2a.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations 51–79, https://doi.org/10.3934/jcd.2016003, /article/id/ 99a4878a-5263-40bf-b4e8-bbf7c2730a2a

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.387170Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6135cfe3-cf7d-462c-bc3a-ab8f14c99a38 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.200760Z

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 97d0c49b-65bf-4e3d-8a71-705a6ba3ef5b · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.184218Z

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 2e0b4444-96a0-4c23-9a61-1d72e8699352 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.164601Z

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 50e2300a-8543-4496-a8fb-b5de61f642b4 · outbound

This paper cites Mezi´c, Spectral properties of dynamical systems, model reduction and decompositions , Non- 13 linear Dynamics, 41 (2005), pp.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Mezi´c, Spectral properties of dynamical systems, model reduction and decompositions , Non- 13 linear Dynamics, 41 (2005), pp

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.150685Z

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 175dd864-4dc6-4a6e-a672-fa558d7a916a · outbound

This paper cites Mezi ´c, Analysis of fluid flows via spectral properties of the koopman operator , Annual Re- view of Fluid Mechanics, 45 (2013), pp.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Mezi ´c, Analysis of fluid flows via spectral properties of the koopman operator , Annual Re- view of Fluid Mechanics, 45 (2013), pp

Reference 28

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T22:13:12.136431Z

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 7a9bcfe1-d488-49aa-865a-a0ec49833337 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 29

Resolution: verified exact; doi, observed 2026-08-11T22:13:11.572226Z

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 5af02ca3-13da-4f7f-a9db-a27689b60a4b · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.420266Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d1662bb1-da31-4099-a009-62a34ab48055 · outbound

This paper cites Santos Guti ´errez and V.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Santos Guti ´errez and V

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.427105Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ad252ff8-a0d4-45c8-9f7c-2ce5d8345a96 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.431333Z

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Unavailable: canonical work link unavailable.

Observation 16b17609-17de-4ecd-bb28-bbbcd457f856 · outbound

This paper cites Sch ¨utte, S.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Sch ¨utte, S

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.120737Z

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 beabb105-e1e9-438a-939e-cd01f03d2767 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 34

Resolution: malformed identifier; raw_fallback, observed 2026-08-11T22:13:12.104567Z

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 581e95c0-5563-48cf-befc-0b37de219c19 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.448871Z

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Unavailable: canonical work link unavailable.

Observation 73b738b1-c9ab-400b-b7a5-d0ab8a85ba65 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 36

Resolution: malformed identifier; no resolver link, observed 2026-08-11T22:13:11.454429Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 10cccb84-c34c-4408-8749-5e4a0fc7515b · outbound

This paper cites Steinbach, G.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Steinbach, G

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T22:13:12.088589Z

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 a043ef49-fb58-4aaf-a4b0-5e479a12ac40 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 38

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.071062Z

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 4834b4be-ed47-499a-a931-01fc7e23e066 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 39

Resolution: unresolved; raw_fallback, observed 2026-08-11T22:13:12.053832Z

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 a5220c35-e6f4-4a62-b3b0-25366874d6a6 · outbound

This paper cites an unresolved cited work.

A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations Unresolved cited work

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-11T22:13:11.475627Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation da54df8c-9b15-4dda-822d-1efbd5b5cb9a · inbound

Learning dissipation and instability fields from chaotic dynamics cites this paper.

Learning dissipation and instability fields from chaotic dynamics A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-09T04:48:30.016603Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 66c9085b-65e4-4dad-bbe3-4f6b1cd527b9 · inbound

Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling cites this paper.

Predicting Forced Responses of Probability Distributions via the Fluctuation-Dissipation Theorem and Generative Modeling A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

Reference 79

Resolution: unresolved; no resolver link, observed 2026-08-16T12:17:15.749915Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3628a34d-3f62-47f3-9102-e20ed1103ce6 · inbound

A General Framework for Linking Free and Forced Fluctuations via Koopmanism cites this paper.

A General Framework for Linking Free and Forced Fluctuations via Koopmanism A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

Reference 84

Resolution: unresolved; no resolver link, observed 2026-08-15T19:35:33.391262Z

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Unavailable: canonical work link unavailable.

Observation 7b7342b6-51f3-4825-8c88-0683ced37b1b · inbound

Optimal scenario design for climate emulation cites this paper.

Optimal scenario design for climate emulation A Modified Bisecting K-Means for Approximating Transfer Operators: Application to the Lorenz Equations

Reference 61

Resolution: verified exact; arxiv_id, observed 2026-06-26T18:49:44.113792Z

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.