Paper Citation Record · LEDGER

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations

As of 11 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2507.15805.

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

pith.paper-citation-record.v1
2507.15805 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:27:44.519231Z

measured 21 of 21 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

21 of 21 outbound references displayed

verified exact0
verified fuzzy18
unresolved3
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External citation measurements

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Outbound references

Observation 5680d31a-c300-4d72-8b8a-6abd1d80a5cf · outbound

This paper cites Time-Series Machine Learning Techniques for Modeling and Identification of Mecha- tronic Systems with Friction: A Review and Real Application,Electronics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Time-Series Machine Learning Techniques for Modeling and Identification of Mecha- tronic Systems with Friction: A Review and Real Application,Electronics, Vol

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:47.958188Z

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.

Observation f446fab9-5376-4e0a-84a1-b421fccf33d8 · outbound

This paper cites Formulating turbulence closures using sparse regression with embedded form invariance,Physical Review Fluids, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Formulating turbulence closures using sparse regression with embedded form invariance,Physical Review Fluids, Vol

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:47.747499Z

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

Observation 58cbf7fa-777a-4e53-90b9-6f38a3d875da · outbound

This paper cites Sparse learning of stochastic dynamical equations,The Journal of Chemical Physics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Sparse learning of stochastic dynamical equations,The Journal of Chemical Physics, Vol

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:47.445737Z

Source-reported events for the cited work

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Observation b799c9e6-7caa-44c6-b5b8-155750e817e0 · outbound

This paper cites Discovering governing equations from data by sparse identification of nonlinear dynamical systems,Proceedings of the National Academy of Sciences, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Discovering governing equations from data by sparse identification of nonlinear dynamical systems,Proceedings of the National Academy of Sciences, Vol

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:47.275622Z

Source-reported events for the cited work

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Observation da2c4beb-b40e-4b06-959b-073d0edde88b · outbound

This paper cites Data-driven discovery of coordinates and governing equations,Proceedings of the National Academy of Sciences, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Data-driven discovery of coordinates and governing equations,Proceedings of the National Academy of Sciences, Vol

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:47.045051Z

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.

Observation 29e3460f-6122-4e2f-8f41-dcfd220a6499 · outbound

This paper cites Efficient Inference of Parsimonious Phenomenological Models of Cellular Dy- namics Using S-Systems and Alternating Regression,PloS ONE, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Efficient Inference of Parsimonious Phenomenological Models of Cellular Dy- namics Using S-Systems and Alternating Regression,PloS ONE, Vol

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.796622Z

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.

Observation a9509117-2154-449f-ac66-164b9d45affb · outbound

This paper cites A Robust SINDy Approach by Combining Neural Networks and an Integral Form.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations A Robust SINDy Approach by Combining Neural Networks and an Integral Form

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T15:27:43.222582Z

Source-reported events for the cited work

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Observation 1fc93553-f755-40c7-a7f5-d49c96f16191 · outbound

This paper cites Cluster-based network model identification and control of nonlinear systems.Nonlinear Dynamics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Cluster-based network model identification and control of nonlinear systems.Nonlinear Dynamics, Vol

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.639674Z

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.

Observation b74ac678-9179-417e-b88c-5ca392ebc534 · outbound

This paper cites 87, 1, 2021.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations 87, 1, 2021

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.470330Z

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.

Observation fb1d458e-b897-40c5-96ea-6958624e3e25 · outbound

This paper cites Constrained sparse Galerkin regression,Journal of Fluid Mechanics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Constrained sparse Galerkin regression,Journal of Fluid Mechanics, Vol

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.302371Z

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.

Observation cd736953-3126-4ba9-bccc-75f9e20d02c3 · outbound

This paper cites Sparse reduced-order modeling: Sensor-based dynamics to full- state estimation.Journal of Fluid Mechanics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Sparse reduced-order modeling: Sensor-based dynamics to full- state estimation.Journal of Fluid Mechanics, Vol

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.171851Z

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.

Observation 39d0f207-17b1-4015-a64c-ee8fd414a417 · outbound

This paper cites Mathematical Biology.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Mathematical Biology

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:46.036771Z

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.

Observation 372df954-e64e-4c26-97e1-4f097ec17bd6 · outbound

This paper cites Inferring biological networks by sparse identification of nonlinear dynamics,IEEE Transactions on Molecular, Biological, and Multi-Scale Communications, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Inferring biological networks by sparse identification of nonlinear dynamics,IEEE Transactions on Molecular, Biological, and Multi-Scale Communications, Vol

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.911900Z

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.

Observation 40c82a3b-0373-42a5-95f4-98a50a6a4ca5 · outbound

This paper cites Data-driven discovery of partial differential equations, Science Advances, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Data-driven discovery of partial differential equations, Science Advances, Vol

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.738190Z

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.

Observation 61835be4-4f66-4105-8f50-0e5e80946663 · outbound

This paper cites Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations,Biophys Chem, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Temperature dependency and temperature compensation in a model of yeast glycolytic oscillations,Biophys Chem, Vol

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.557571Z

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.

Observation 4bf43616-7b95-4741-b7b8-5ac0bc4494a5 · outbound

This paper cites Learning dynamical systems and bifurcation via group sparsity,SIAM Journal on Applied Mathematics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Learning dynamical systems and bifurcation via group sparsity,SIAM Journal on Applied Mathematics, Vol

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.371267Z

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.

Observation 6c4167ed-d5d9-473b-9833-defd50a5cbb2 · outbound

This paper cites Sparse identification of truncation errors,Journal of Computational Physics, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Sparse identification of truncation errors,Journal of Computational Physics, Vol

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.234474Z

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.

Observation 210ef221-a742-4fed-9a8e-bdc71d488452 · outbound

This paper cites Sparse Discovery of Functional Relationships in ODE Systems.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Sparse Discovery of Functional Relationships in ODE Systems

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:45.069624Z

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.

Observation 0041b6b1-faab-4241-9d31-01d97d2e95d4 · outbound

This paper cites On the Convergence of the SINDy Algorithm,SIAM Journal on Scientific Computing, Vol.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations On the Convergence of the SINDy Algorithm,SIAM Journal on Scientific Computing, Vol

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:27:44.918838Z

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.

Observation d4c0f9e4-4395-4f7a-912d-56a261ea4d43 · outbound

This paper cites SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations SINDy-RL: Interpretable and Efficient Model-Based Reinforcement Learning

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T15:27:44.455987Z

Source-reported events for the cited work

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Observation ec6830ad-ee9c-4e07-bd74-5be5b775fd6e · outbound

This paper cites an unresolved cited work.

Sparse Discovery of Functional Relationships in Solutions to Systems of Differential Equations Unresolved cited work

Reference 21

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:27:44.731322Z

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.

Pith citing papers

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