Paper Citation Record · LEDGER

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles

As of 13 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2608.05522.

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

pith.paper-citation-record.v1
2608.05522 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T11:37:07.729215Z

measured 37 of 37 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 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

37 of 37 outbound references displayed

verified exact17
verified fuzzy0
unresolved13
parse uncertain0
malformed identifier1
metadata mismatch6

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 0b1fa33e-ce9b-42d5-92e7-b4b5953a3055 · outbound

This paper cites Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part 1: Theory,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Lyapunov characteristic exponents for smooth dynamical systems and for Hamiltonian systems: A method for computing all of them. Part 1: Theory,

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.609076Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 695df231-057a-400d-b04c-5306caa62c04 · outbound

This paper cites Determining Lyapunov exponents from a time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Determining Lyapunov exponents from a time series,

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.613279Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b4f91f1-0559-4997-9716-aea2526f6f37 · outbound

This paper cites Measurement of the Lyapunov spectrum from a chaotic time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Measurement of the Lyapunov spectrum from a chaotic time series,

Reference 3

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.969547Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b960cd47-2b01-47e4-8b3d-6c971f70bacd · outbound

This paper cites Lyapunov exponents from time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Lyapunov exponents from time series,

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.620575Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9f8ced24-d6b4-43ef-91a0-e612dfe70fa8 · outbound

This paper cites A practical method for calculating largest Lyapunov exponents from small data sets,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A practical method for calculating largest Lyapunov exponents from small data sets,

Reference 5

Resolution: malformed identifier; no resolver link, observed 2026-08-08T11:37:07.624546Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1888c5b5-2ab4-4384-842d-43badee293c5 · outbound

This paper cites A robust method to estimate the maximal Lyapunov exponent of a time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A robust method to estimate the maximal Lyapunov exponent of a time series,

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.628151Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b19f1f50-894d-4e96-b385-4ee3dc001886 · outbound

This paper cites Simple mathematical models with very complicated dynamics,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Simple mathematical models with very complicated dynamics,

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.632282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f6354639-9dc1-4716-8ab9-33fe1dd8b890 · outbound

This paper cites Predictability: A way to characterize complexity,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Predictability: A way to characterize complexity,

Reference 8

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.937374Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f6c30ec0-a0ff-42e5-8899-2931287899d8 · outbound

This paper cites A novel approach for estimating largest Lyapunov exponents in one-dimensional chaotic time series using machine learning,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A novel approach for estimating largest Lyapunov exponents in one-dimensional chaotic time series using machine learning,

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.638785Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b45f6f5c-9403-4331-9f9e-e84af1ecde69 · outbound

This paper cites Chaotic map with no fixed points: Entropy, implementation and control,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Chaotic map with no fixed points: Entropy, implementation and control,

Reference 10

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.922273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 7506d7a4-e9f3-47c4-8203-a5e8c5c5cd40 · outbound

This paper cites A robust method on estimation of Lyapunov exponents from a noisy time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A robust method on estimation of Lyapunov exponents from a noisy time series,

Reference 11

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.912501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation affcc9c6-82df-40a5-9da4-c715e5386084 · outbound

This paper cites Estimation of Lyapunov exponents from a time series for n-dimensional state space using nonlinear mapping,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Estimation of Lyapunov exponents from a time series for n-dimensional state space using nonlinear mapping,

Reference 12

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.902855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 60a8cea5-83aa-4982-bc6d-04714b4e7fdc · outbound

This paper cites A radial-basis-function network-based method of estimating Lyapunov exponents from a scalar time series for analyzing nonlinear systems stability,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A radial-basis-function network-based method of estimating Lyapunov exponents from a scalar time series for analyzing nonlinear systems stability,

Reference 13

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.892690Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation fb3218a8-99c2-403a-8f02-29b9e0b040f7 · outbound

This paper cites Improved assessment of orbital stability of rhythmic motion with noise,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Improved assessment of orbital stability of rhythmic motion with noise,

Reference 14

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.883096Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4b2cb4a5-aec6-4473-8084-7e5448fd010f · outbound

This paper cites Development of Floquet multiplier estimator to determine nonlinear oscillatory behavior in power system data measurement,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Development of Floquet multiplier estimator to determine nonlinear oscillatory behavior in power system data measurement,

Reference 15

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.873120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 4401a197-7910-48dd-a6e1-c2ab953b448c · outbound

This paper cites Improving empirical characteristic multiplier estimation through a change of basis,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Improving empirical characteristic multiplier estimation through a change of basis,

Reference 16

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.674289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b59d6445-bdf9-4b89-b73e-b229c4ce7c35 · outbound

This paper cites Poincar´ e maps for multi- scale physics discovery and nonlinear Floquet theory,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Poincar´ e maps for multi- scale physics discovery and nonlinear Floquet theory,

Reference 17

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.609599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 73aeda52-b4a7-43d2-914d-7182193a18db · outbound

This paper cites A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A data-driven phase and isostable reduced modeling framework for oscillatory dynamical systems,

Reference 18

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.863072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation e06d3965-bc22-43b1-be8c-00ce2ef03523 · outbound

This paper cites Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time-series data,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time-series data,

Reference 19

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.852834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 100bec85-a6e3-4ab5-b13a-ff76cc962410 · outbound

This paper cites A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles A data-driven approximation of the Koopman operator: Extending dynamic mode decomposition,

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.674972Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ab65a367-0a2e-4538-9542-4d5a642f1c9b · outbound

This paper cites Global stability analysis using the eigenfunctions of the Koopman operator,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Global stability analysis using the eigenfunctions of the Koopman operator,

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.678470Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a1ff814b-b6f1-4cd6-83e0-1c3ce33efe78 · outbound

This paper cites Data-driven transient sta- bility analysis using the Koopman operator,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Data-driven transient sta- bility analysis using the Koopman operator,

Reference 22

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.438381Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1c87a48d-cf6f-4a0d-9994-1e7ee4ded71a · outbound

This paper cites Big data-driven predictive control for nonlinear systems—A trajectory cluster-based contraction approach,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Big data-driven predictive control for nonlinear systems—A trajectory cluster-based contraction approach,

Reference 23

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.370312Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 00b3f987-4107-471a-9c02-5b2624801fd4 · outbound

This paper cites Convex data-driven contraction with Riemannian metrics,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Convex data-driven contraction with Riemannian metrics,

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.687987Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 13a15cd6-f4d2-4cae-b058-6addaa49b484 · outbound

This paper cites Supervised machine learning to estimate instabilities in chaotic systems: Estimation of local Lyapunov exponents,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Supervised machine learning to estimate instabilities in chaotic systems: Estimation of local Lyapunov exponents,

Reference 25

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.836883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 43145360-f0f2-4aa5-8772-f4116a0e1805 · outbound

This paper cites Full Lyapunov exponents spectrum with deep learning from single-variable time series,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Full Lyapunov exponents spectrum with deep learning from single-variable time series,

Reference 26

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.206189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 20bb4bb1-d9ca-4c86-8a27-80caf9a7618f · outbound

This paper cites Ambient vibration re-testing and operational modal analysis of the Humber Bridge,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Ambient vibration re-testing and operational modal analysis of the Humber Bridge,

Reference 27

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.826493Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation c8278e2a-911d-449d-8f42-07c3d47ce323 · outbound

This paper cites Ambient and free-vibration tests to improve the quantification and estimation of modal parameters in existing bridges,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Ambient and free-vibration tests to improve the quantification and estimation of modal parameters in existing bridges,

Reference 28

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.816037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b9953f7d-d2ce-4087-9c00-2476d9fc157b · outbound

This paper cites Influence of the modal damping ratio calculation method in the analysis of dynamic events obtained in structural health monitoring of bridges,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Influence of the modal damping ratio calculation method in the analysis of dynamic events obtained in structural health monitoring of bridges,

Reference 29

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.806304Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation b732ad58-a968-43c8-9665-09a18703a06a · outbound

This paper cites Intelligent automatic operational modal analysis,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Intelligent automatic operational modal analysis,

Reference 30

Resolution: metadata mismatch; raw_fallback, observed 2026-08-08T11:37:08.145874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 1386e1b7-c099-4965-9873-baebfca2f67e · outbound

This paper cites Quantitative analysis of non-equilibrium systems from short-time experimental data,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Quantitative analysis of non-equilibrium systems from short-time experimental data,

Reference 31

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.796175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 21be555e-b8f1-40c9-a6ca-04c32e977515 · outbound

This paper cites Modeling nonlinear dynamics from videos,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Modeling nonlinear dynamics from videos,

Reference 32

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.786000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation 9e696bea-b9bb-4c48-b0b8-115a6f42e7fe · outbound

This paper cites Condition monitoring of impact vibrations using observed signals and estimated principal Lyapunov exponents,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Condition monitoring of impact vibrations using observed signals and estimated principal Lyapunov exponents,

Reference 33

Resolution: verified exact; doi, observed 2026-08-08T11:37:07.775875Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.

Observation f805b670-780e-4544-a663-206106290960 · outbound

This paper cites Data-driven method for identifying the expression of the Lyapunov exponent from discrete random data,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Data-driven method for identifying the expression of the Lyapunov exponent from discrete random data,

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.719488Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b3abc0e-453c-4cd1-9188-02f268f78a88 · outbound

This paper cites Data-driven spectral analysis of the Koopman operator,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Data-driven spectral analysis of the Koopman operator,

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.722643Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 06f63feb-d7a9-441d-9b66-c079cb5b0a0f · outbound

This paper cites Modern Koopman theory for dynamical systems,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Modern Koopman theory for dynamical systems,

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.725772Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e17ad6c3-230f-4ac2-8a09-3366774ed42a · outbound

This paper cites Rigorous data-driven computation of spectral proper- ties of Koopman operators for dynamical systems,.

Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles Rigorous data-driven computation of spectral proper- ties of Koopman operators for dynamical systems,

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-08T11:37:07.729215Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.