Paper Citation Record · LEDGER

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems

As of 19 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2508.21213.

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

pith.paper-citation-record.v1
2508.21213 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T14:42:07.131810Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

29 of 29 outbound references displayed

verified exact2
verified fuzzy26
unresolved1
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation bb977efa-9119-401b-a968-2527e6d9ec25 · outbound

This paper cites Neural Lyapunov control.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Neural Lyapunov control

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.430650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f7db1b8c-e294-465b-bfca-f56be1c4b5cc · outbound

This paper cites Neural Lyapunov control of unknown nonlinear systems with stability guar- antees.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Neural Lyapunov control of unknown nonlinear systems with stability guar- antees

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.423652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 37c32ad7-c15b-44e1-9788-06e09cd68add · outbound

This paper cites Region of attraction in a power system with discrete LTCs.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Region of attraction in a power system with discrete LTCs

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.416281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ce423655-74af-45a8-98c9-2e7f0cb966b2 · outbound

This paper cites Regions of attraction for hybrid limit cycles of walking robots.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Regions of attraction for hybrid limit cycles of walking robots

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.408412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 66720065-69ca-4b8a-a939-b32dedd188e6 · outbound

This paper cites Region of attraction estimation of biological continuous boolean models.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Region of attraction estimation of biological continuous boolean models

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.401207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fba486de-9746-476b-a74c-36ba3e1b8120 · outbound

This paper cites Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Maximal Lyapunov functions and domains of attraction for autonomous nonlinear systems

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-05T14:42:07.071942Z

Source-reported events for the cited work

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Observation a5ec20d7-21d0-499a-9757-9db2adce51ac · outbound

This paper cites Towards learning and verifying maximal neural Lyapunov functions.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Towards learning and verifying maximal neural Lyapunov functions

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.389220Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 18f67b15-4bef-4859-9f93-5e32905b4493 · outbound

This paper cites Physics-informed neural network Lyapunov functions: PDE charac- terization, learning, and verification.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Physics-informed neural network Lyapunov functions: PDE charac- terization, learning, and verification

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.381817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation cf30e9bd-2710-4b71-aedf-432ddd82f7ee · outbound

This paper cites Data-driven computational methods for the domain of attraction and Zubov’s equation.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Data-driven computational methods for the domain of attraction and Zubov’s equation

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.374787Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 40746524-620c-403f-9eab-5841c9ac5462 · outbound

This paper cites Formal synthesis of Lyapunov neural networks.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Formal synthesis of Lyapunov neural networks

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.367685Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 127483e6-d7e6-42b8-b5c2-dd23c29155e2 · outbound

This paper cites Lyapunov-net: A deep neural network architecture for lyapunov function approximation.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Lyapunov-net: A deep neural network architecture for lyapunov function approximation

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.360726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4927b5cf-7e3a-4df5-8712-cc0693c72e99 · outbound

This paper cites Learning control Lyapunov functions from counterexamples and demonstrations.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Learning control Lyapunov functions from counterexamples and demonstrations

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.354049Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 43b809e6-33fc-415c-aaac-37da8e282da3 · outbound

This paper cites Tool LyZNet: A lightweight python tool for learning and verifying neural Lyapunov functions and regions of attraction.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Tool LyZNet: A lightweight python tool for learning and verifying neural Lyapunov functions and regions of attraction

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.346629Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation e36518c2-70c3-45c1-8787-05a84886cf7b · outbound

This paper cites Safe control with learned certificates: A survey of neural lyapunov, barrier, and contrac- tion methods for robotics and control.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Safe control with learned certificates: A survey of neural lyapunov, barrier, and contrac- tion methods for robotics and control

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.339590Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a41e4483-9922-4acb-8919-c97fdc95de91 · outbound

This paper cites Methods of AM Lyapunov and their application, volume 4439.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Methods of AM Lyapunov and their application, volume 4439

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.332216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 669eb2c6-3d3f-4f77-bf10-7fab014834fc · outbound

This paper cites A characterization of the domain of attraction for a locally exponentially stable stochastic system.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems A characterization of the domain of attraction for a locally exponentially stable stochastic system

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.325512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 68c9d562-94f2-4757-9ebe-2afd25e7e7ef · outbound

This paper cites Characterizing attraction probabilities via the stochastic zubov equation.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Characterizing attraction probabilities via the stochastic zubov equation

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.318742Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2a8889ca-ca43-473d-a29d-a1f643cf95da · outbound

This paper cites Zubov’s method for stochastic control systems.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Zubov’s method for stochastic control systems

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.311946Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation af323062-33b7-4e24-ae55-2320020b754b · outbound

This paper cites Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.305063Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ec54a68b-82f5-41e5-a3f0-724a230d9977 · outbound

This paper cites Neural stochastic control.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Neural stochastic control

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.297781Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8a07a288-6698-46c5-99c9-da2c079ef212 · outbound

This paper cites Stability verification in stochastic control systems via neural network supermartingales.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Stability verification in stochastic control systems via neural network supermartingales

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.291130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2e95cacc-bd5e-4dc1-9f3b-8c363ee745b6 · outbound

This paper cites Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Learning Provably Stabilizing Neural Controllers for Discrete-Time Stochastic Systems

Reference 22

Resolution: verified exact; local_arxiv, observed 2026-08-05T14:42:07.237639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d845dcde-1361-450c-95c3-4defbc9c9e87 · outbound

This paper cites dReal: An SMT solver for nonlinear theories over the reals.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems dReal: An SMT solver for nonlinear theories over the reals

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.282842Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f576639d-2b5c-4da2-927a-d34a74d317c3 · outbound

This paper cites Stochastic stability of differential equations , volume 66.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Stochastic stability of differential equations , volume 66

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.275671Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6b44a5fb-0ab7-414f-970d-adbbfbf1d3be · outbound

This paper cites Stochastic Differential Equations and Applications.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Stochastic Differential Equations and Applications

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.267551Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 909180ee-903c-4057-ad29-148ddd07fa9b · outbound

This paper cites A generalization of Zubov’s method to perturbed systems.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems A generalization of Zubov’s method to perturbed systems

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.259907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 19037f8f-5e8e-4926-94e2-05040da33ffb · outbound

This paper cites Local Lyapunov functions for nonlinear stochastic differen- tial equations by linearization.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Local Lyapunov functions for nonlinear stochastic differen- tial equations by linearization

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.252814Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation bfce8c99-63e3-4701-ba9c-42b5b0dbf2ba · outbound

This paper cites Stochastic Lyapunov-barrier functions for robust probabilistic reach-avoid-stay specifications.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Stochastic Lyapunov-barrier functions for robust probabilistic reach-avoid-stay specifications

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T14:42:07.245296Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 860a5684-1a91-4616-8fd7-d6b8c8bb1e9c · outbound

This paper cites Scalable neural network verification with branch-and-bound inferred cutting planes.

Verifying Probabilistic Regions of Attraction with Neural Lyapunov Functions for Stochastic Systems Scalable neural network verification with branch-and-bound inferred cutting planes

Reference 29

Resolution: verified exact; raw_fallback, observed 2026-08-05T14:42:07.227442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

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