Paper Citation Record · LEDGER

Discovery of Nonlinear Dynamics with Automated Basis Function Generation

As of 5 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 2 inbound Pith citation observations for arXiv:2605.09696.

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

pith.paper-citation-record.v1
2605.09696 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-12T04:22:25.175453Z

measured 56 of 56 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-05T06:32:48.257954+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-05T00:51:00.428799Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-05T00:51:00.879631Z

Reference resolution

54 of 54 outbound references displayed

verified exact12
verified fuzzy19
unresolved19
parse uncertain0
malformed identifier1
metadata mismatch3

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 4b8d8e10-8b8f-4a7d-8249-43373289da25 · outbound

This paper cites Each chunk is constructed by drawing, without replacement, an index setIk of sizec=⌊m train/d⌋from the training samples: Dk = (xi, ˙xi) :i∈ I k , k= 1.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Each chunk is constructed by drawing, without replacement, an index setIk of sizec=⌊m train/d⌋from the training samples: Dk = (xi, ˙xi) :i∈ I k , k= 1

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.259646Z

Source-reported events for the cited work

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Observation 7e736ab4-6a50-4911-864b-21829d33899f · outbound

This paper cites Nested trigonometric compositions (e.g.sin(sin(·))) are explicitly forbidden via nested constraints, preventing the evolutionary search from exploiting degenerate identities.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Nested trigonometric compositions (e.g.sin(sin(·))) are explicitly forbidden via nested constraints, preventing the evolutionary search from exploiting degenerate identities

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.244619Z

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Observation c01c4101-1b3a-4b73-81ef-543dadd43bab · outbound

This paper cites All numeric con- stant prefactors are stripped, sinceSINDylearns all coefficients independently during the regression step.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation All numeric con- stant prefactors are stripped, sinceSINDylearns all coefficients independently during the regression step

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.237947Z

Source-reported events for the cited work

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Observation 939210ae-8da7-4a83-8d25-19b5cb2693b6 · outbound

This paper cites This maximizes coverage of monomial basis functions at the cost of a larger intermediate pool.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation This maximizes coverage of monomial basis functions at the cost of a larger intermediate pool

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.250612Z

Source-reported events for the cited work

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Observation 7220a7d9-bc52-4de2-a3ca-485e8168cc92 · outbound

This paper cites LetL=∅be the accepted library, initially empty.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation LetL=∅be the accepted library, initially empty

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.232081Z

Source-reported events for the cited work

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Observation bf90599b-d74a-4c7d-9739-7a471afd1ffd · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 6

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 09f8ee69-d27d-4566-8943-144c4d3b86c3 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 7

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Observation c3443401-c4ae-4027-8680-dc5e15ccc62a · outbound

This paper cites Accepta i if and only if corr vi,v j < ρ max ∀a j ∈ L,(7) whereρ max is the collinearity threshold.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Accepta i if and only if corr vi,v j < ρ max ∀a j ∈ L,(7) whereρ max is the collinearity threshold

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.241546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 91b3cadf-1199-41b5-9bfd-3d91ce421406 · outbound

This paper cites 15 The complexity-ordered traversal guarantees the simplicity bias: a complex atomai is re- tainedonlyif it provides information that no simpler already-accepted term can replicate.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation 15 The complexity-ordered traversal guarantees the simplicity bias: a complex atomai is re- tainedonlyif it provides information that no simpler already-accepted term can replicate

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.314862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 26207ec2-4fc7-4608-9f1a-0ae7b4ec1676 · outbound

This paper cites ℓq}is augmented with a constant bias term to form a library ofp=q+ 1functions.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation ℓq}is augmented with a constant bias term to form a library ofp=q+ 1functions

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.286462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 44891e17-67bb-425d-831f-c6bec59476ed · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.220846Z

Source-reported events for the cited work

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Observation 5a854278-1448-4aea-af8b-612a7ddecfdb · outbound

This paper cites A total ofBbootstrap replicates are drawn from the training set, and an independent sparse model is fitted on each replicate.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation A total ofBbootstrap replicates are drawn from the training set, and an independent sparse model is fitted on each replicate

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.318823Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 89bb212f-fefe-48e1-a2d9-5cbec3d1286e · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.269027Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7b35d3a8-15eb-43c5-bfeb-a182188151bd · outbound

This paper cites Scores on the test segment of the training trajectory serve as a secondary check for overfitting.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Scores on the test segment of the training trajectory serve as a secondary check for overfitting

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.299291Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 51ac0b41-432a-44fe-a1a0-843dcd415202 · outbound

This paper cites This strict binary threshold acts as a conservative proxy forcorrect structural identification.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation This strict binary threshold acts as a conservative proxy forcorrect structural identification

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.302877Z

Source-reported events for the cited work

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Observation f087ae2c-2b0f-4c6a-b31d-a67924a719e9 · outbound

This paper cites Simulated trajecto- ries are compared against the corresponding noise-free ground-truth trajectory, withR2 and MSE computed over the state variables.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Simulated trajecto- ries are compared against the corresponding noise-free ground-truth trajectory, withR2 and MSE computed over the state variables

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.247733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 1dc23172-5801-456b-a0bc-f2f053ad3df5 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.291158Z

Source-reported events for the cited work

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Observation 4ad72fba-0d7c-4e81-8433-d60dfa0e81a6 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.256499Z

Source-reported events for the cited work

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Observation bf6a477d-8661-40db-a6ba-cf50c9df64ab · outbound

This paper cites This is the time a practitioner must wait before a governing equation is available.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation This is the time a practitioner must wait before a governing equation is available

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.288852Z

Source-reported events for the cited work

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Observation 446cbac7-67d5-45c5-9a9d-440f6fdb5675 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 20

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7e30dcde-9419-4969-9520-1d8cd4f6033f · outbound

This paper cites Its bistable potential (α <0,β >0) concentrates trajectory density near the two equilibria, where the derivative ofx3 0 is largest and most sensitive to noise.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Its bistable potential (α <0,β >0) concentrates trajectory density near the two equilibria, where the derivative ofx3 0 is largest and most sensitive to noise

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.271954Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a29cf5a8-43f7-4397-99ae-87396ab79b7f · outbound

This paper cites Discovering Causal Relations and Equations from Data.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Discovering Causal Relations and Equations from Data

Reference 22

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:21:25.757178Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation b711c0c2-df80-4e7e-8cd6-d530da2e368e · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.296490Z

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Observation ada72467-7bf4-449f-b07f-7f1071666ccf · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 24

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Observation 0452bcb4-8d97-47d7-9766-c96333c5ea87 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.234560Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 2c4a7bf7-4c39-487c-92d9-deb09c12f21d · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.215026Z

Source-reported events for the cited work

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Observation 48671322-bc44-4fd6-a805-9fd72b10bf3c · outbound

This paper cites Zanna and T.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Zanna and T

Reference 27

Resolution: verified exact; doi, observed 2026-05-12T04:26:23.227158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 35f14593-7733-4eb0-a186-421be9a27dc5 · outbound

This paper cites Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Tractable Dendritic RNNs for Reconstructing Nonlinear Dynamical Systems

Reference 28

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:21:25.780039Z

Source-reported events for the cited work

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Observation 1109c210-3394-4954-a420-7dc450121d7a · outbound

This paper cites Métayer, A.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Métayer, A

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.218331Z

Source-reported events for the cited work

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Observation 19e89f50-445f-4884-b476-5357e4f56741 · outbound

This paper cites L., Proctor J.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation L., Proctor J

Reference 30

Resolution: verified exact; doi, observed 2026-05-12T04:26:23.221730Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a2dd6612-b821-4f91-99b8-d791c9a4edcf · outbound

This paper cites Rudy, Steven L.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Rudy, Steven L

Reference 31

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Source-reported events for the cited work

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Observation 63ae7e5c-9f7c-4d0c-a6df-b9fcdd7f7a8c · outbound

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Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 32

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Observation 4404115d-d465-4cc2-b296-1ceb7fbd9e8f · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 33

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.253622Z

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Observation 280829c7-2371-421d-abd9-98352baebca3 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 34

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Observation f9744965-bbe6-4c80-9889-742d952448ff · outbound

This paper cites Kaheman, J.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Kaheman, J

Reference 35

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Observation bcd478fe-7af7-4495-b2c4-954948e923d6 · outbound

This paper cites Champion, B.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Champion, B

Reference 36

Resolution: verified exact; doi, observed 2026-05-12T04:26:23.229696Z

Source-reported events for the cited work

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Observation 6c50bfee-1560-4959-bb19-0b464dba10ab · outbound

This paper cites Champion, P.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Champion, P

Reference 37

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Observation 3b2a7f05-e6bb-4c45-8050-2a93624143d5 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 38

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Observation f7083052-ad5e-442a-9215-31c32193a117 · outbound

This paper cites Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences473(2204), 20170009 (2017) https://doi.org/10.1098/rspa.2017.0009.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences473(2204), 20170009 (2017) https://doi.org/10.1098/rspa.2017.0009

Reference 39

Resolution: metadata mismatch; arxiv_id, observed 2026-05-12T04:26:23.216550Z

Source-reported events for the cited work

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Observation 432cd3de-6179-4d27-9dde-3d0d6cb72115 · outbound

This paper cites and Kutz, J.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation and Kutz, J

Reference 40

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Source-reported events for the cited work

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Observation 5332ab01-4437-483f-9f97-42c737e61525 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 41

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation c58b955d-44a6-48b0-82ab-b3d165c6f52d · outbound

This paper cites Distilling free-form natural laws from experimental data.Science, 324(5923):81–85, 2009.doi:10.1126/science.1165893.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Distilling free-form natural laws from experimental data.Science, 324(5923):81–85, 2009.doi:10.1126/science.1165893

Reference 42

Resolution: verified exact; doi, observed 2026-05-12T04:26:23.203798Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 7c6b4828-54be-4f66-aa90-228fdb82afbf · outbound

This paper cites Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl

Reference 43

Resolution: verified exact; arxiv_id, observed 2026-05-13T03:54:08.249097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 36c9a050-da2d-4e75-a811-a770d31d7863 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 44

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.305759Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation dcce41b8-71b6-47de-bea3-50f4ffb98ef7 · outbound

This paper cites Dong, Y.-L.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Dong, Y.-L

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.321885Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 9e14be50-a3c9-48dc-8f8a-6ce8f543d938 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 46

Resolution: verified exact; doi, observed 2026-05-12T04:26:23.209435Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 19d25c30-c1f2-4ef5-a152-3f6eaa82c8ba · outbound

This paper cites Symbolic Regression is NP-hard.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Symbolic Regression is NP-hard

Reference 47

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:21:25.803359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation a3911aa8-b7a8-496c-b702-7b7bf51989ff · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 48

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.223120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 4e876274-6b36-40ef-9e54-3f850f116bd5 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 49

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.225919Z

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No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 21c69cb2-12ee-4267-bb44-9be73bcf40f2 · outbound

This paper cites Raissi, P.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Raissi, P

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.277389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.

Observation 996e7a18-554b-4546-ba33-343c447d3e52 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 51

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.274680Z

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Observation 72db36ab-1574-4628-936d-04e9d171b2eb · outbound

This paper cites ODEFormer: Symbolic Regression of Dynamical Systems with Transformers.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation ODEFormer: Symbolic Regression of Dynamical Systems with Transformers

Reference 52

Resolution: verified exact; arxiv_id, observed 2026-05-12T06:21:25.750082Z

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Observation 099f79c7-ac73-4214-a7bc-fa06ef19f376 · outbound

This paper cites Meurer, C.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Meurer, C

Reference 53

Resolution: verified fuzzy; raw_fallback, observed 2026-05-12T15:26:39.324796Z

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Observation b4fa2fc2-5d6e-4b75-83c5-832ab8b50415 · outbound

This paper cites an unresolved cited work.

Discovery of Nonlinear Dynamics with Automated Basis Function Generation Unresolved cited work

Reference 54

Resolution: unresolved; raw_fallback, observed 2026-05-12T15:26:39.265393Z

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Pith citing papers

Observation c4a33d03-30a6-496b-a0c9-852471c805b5 · inbound

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement cites this paper.

On the post-hoc Evaluation of PDE Discovery: A Multifaceted Challenge of Scientific Advancement Discovery of Nonlinear Dynamics with Automated Basis Function Generation

Reference 80

Resolution: unresolved; no resolver link, observed 2026-07-30T13:41:05.901696Z

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Observation f147e0bd-09e2-4805-b5f0-82ed6584d4e7 · inbound

Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers cites this paper.

Verifier-Guided Model Discovery for Physical Dynamical Systems with Pretrained Symbolic Transformers Discovery of Nonlinear Dynamics with Automated Basis Function Generation

Reference 22

Resolution: metadata mismatch; local_arxiv, observed 2026-08-05T00:51:00.884444Z

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