Paper Citation Record · LEDGER

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems

As of 21 August 2026, this Paper Citation Record lists 34 of 34 outbound references and 3 inbound Pith citation observations for arXiv:2504.17102.

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

pith.paper-citation-record.v1
2504.17102 v1

Coverage vector

measured 34 of 34 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-16T10:58:01.590095Z

measured 37 of 37 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T05:08:49.469474Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-06-29T22:13:59.863161Z

Reference resolution

34 of 34 outbound references displayed

verified exact0
verified fuzzy26
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation afd9e65f-be67-4e69-9588-89304b5475cd · outbound

This paper cites A unified algebraic perspective on L ipschitz neural networks.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems A unified algebraic perspective on L ipschitz neural networks

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.210627Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ea3ee8e1-5318-4ef1-8055-367c23c4c70a · outbound

This paper cites Contraction theory for dynamical systems.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Contraction theory for dynamical systems

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.194612Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation d37dbc6b-c214-4bda-9ee7-4e8feab54b37 · outbound

This paper cites Neural lyapunov control.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Neural lyapunov control

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.444835Z

Source-reported events for the cited work

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Observation 79ffdbb1-2dec-4016-a539-d63112a6ec79 · outbound

This paper cites Lyapunov-stable neural-network control.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Lyapunov-stable neural-network control

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.449514Z

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Observation e31b5273-7e4b-4ede-b90d-d2920922a416 · outbound

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

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Safe control with learned certificates: A survey of neural lyapunov, barrier, and contraction methods for robotics and control

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.455080Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d044763c-ad91-45d0-b298-d1fc25760292 · outbound

This paper cites Drip: Domain refinement iteration with polytopes for backward reachability analysis of neural feedback loops.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Drip: Domain refinement iteration with polytopes for backward reachability analysis of neural feedback loops

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.158375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 888b8fc2-212f-421a-8d0d-f36b9043469a · outbound

This paper cites Efficient and accurate estimation of L ipschitz constants for deep neural networks.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Efficient and accurate estimation of L ipschitz constants for deep neural networks

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.143399Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 64212182-a749-440b-8286-1f7646cfa296 · outbound

This paper cites Computation and formal verification of neural network contraction metrics.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Computation and formal verification of neural network contraction metrics

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.470268Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation af9837b4-fdf2-42bb-9dc1-dd1027ceb930 · outbound

This paper cites Construction of a contraction metric by meshless collocation.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Construction of a contraction metric by meshless collocation

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.127820Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 45f3d6c9-57e3-4b20-bab8-87391d53725e · outbound

This paper cites Review on contraction analysis and computation of contraction metrics.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Review on contraction analysis and computation of contraction metrics

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.479745Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2171a5ea-2cb0-4ea8-9310-53f562e62753 · outbound

This paper cites Contraction metric computation using numerical integration and quadrature.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Contraction metric computation using numerical integration and quadrature

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.112419Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 537baeec-a200-4af2-8a94-b41e8af52b43 · outbound

This paper cites Training certifiably robust neural networks with efficient local L ipschitz bounds.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Training certifiably robust neural networks with efficient local L ipschitz bounds

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.096749Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ebf690a4-bdb2-446f-af33-4715dee256a0 · outbound

This paper cites Introduction to Riemannian manifolds, volume 2.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Introduction to Riemannian manifolds, volume 2

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.080979Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 28695931-dfb1-4947-9327-593e3537425a · outbound

This paper cites On contraction analysis for non-linear systems.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems On contraction analysis for non-linear systems

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.065548Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 013db361-50e0-4f5b-b6cf-b2317db855d6 · outbound

This paper cites The general problem of the stability of motion.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems The general problem of the stability of motion

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.049311Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 346d2c94-0b75-42a4-9ffe-af95093c011f · outbound

This paper cites Control contraction metrics: Convex and intrinsic criteria for nonlinear feedback design.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Control contraction metrics: Convex and intrinsic criteria for nonlinear feedback design

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.033593Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation ce466261-931c-4bcc-9ed4-fdb298db2521 · outbound

This paper cites Construction of contraction metrics for discrete-time dynamical systems using meshfree collocation.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Construction of contraction metrics for discrete-time dynamical systems using meshfree collocation

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.016107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0ab3240f-8897-4fdc-bec8-29f77dfa7c73 · outbound

This paper cites Contraction theory on riemannian manifolds.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Contraction theory on riemannian manifolds

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:02.000375Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 0efec9f5-eb0c-41e5-af20-6014e5258fcd · outbound

This paper cites Learning certified control using contraction metric.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Learning certified control using contraction metric

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.984799Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 305b78ac-da02-42d0-8376-a4d707cff25a · outbound

This paper cites o rn S R \.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems o rn S R \

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.968868Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 36ffe371-6cf2-448c-9364-969965711f1b · outbound

This paper cites Neural contraction metrics for robust estimation and control: A convex optimization approach.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Neural contraction metrics for robust estimation and control: A convex optimization approach

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.953854Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 18fa1e95-1f8d-450f-b848-7f7c0d6e29a6 · outbound

This paper cites Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.535615Z

Source-reported events for the cited work

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Observation ff262a83-e890-46cb-bb2c-87cd3816b375 · outbound

This paper cites Actor-Critic Physics-informed Neural Lyapunov Control.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Actor-Critic Physics-informed Neural Lyapunov Control

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.540186Z

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Unavailable: canonical work link unavailable.

Observation e382316d-8bdc-4c2b-a6f8-2715f9a6e129 · outbound

This paper cites Beta-CROWN : Efficient bound propagation with per-neuron split constraints for complete and incomplete neural network verification.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Beta-CROWN : Efficient bound propagation with per-neuron split constraints for complete and incomplete neural network verification

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.925894Z

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No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 7aa28b05-51fa-4126-a829-7a46c308e9e1 · outbound

This paper cites On the scalability and memory efficiency of semidefinite programs for L ipschitz constant estimation of neural networks.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems On the scalability and memory efficiency of semidefinite programs for L ipschitz constant estimation of neural networks

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.910019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 03a6973d-83ec-4d41-872a-cdf94d922727 · outbound

This paper cites Control contraction metric synthesis for discrete-time nonlinear systems.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Control contraction metric synthesis for discrete-time nonlinear systems

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.894431Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 191ec21f-5538-4a19-9ce8-bb493f880b07 · outbound

This paper cites Discrete-time contraction-based control of nonlinear systems with parametric uncertainties using neural networks.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Discrete-time contraction-based control of nonlinear systems with parametric uncertainties using neural networks

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.878708Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 16741d64-1879-4a2a-a38a-9ade68f1ab6c · outbound

This paper cites Neural lyapunov control for discrete-time systems.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Neural lyapunov control for discrete-time systems

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.863157Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 26e0d8c2-f001-4537-a944-08b69357bb83 · outbound

This paper cites Automatic perturbation analysis for scalable certified robustness and beyond.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Automatic perturbation analysis for scalable certified robustness and beyond

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-16T10:58:01.567664Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6e029ca0-9065-4896-a66c-205a5b780d6e · outbound

This paper cites Fast and Complete : Enabling complete neural network verification with rapid and massively parallel incomplete verifiers.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Fast and Complete : Enabling complete neural network verification with rapid and massively parallel incomplete verifiers

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.835739Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 82f5fdcf-d60c-473a-a41d-22f3250e8fc4 · outbound

This paper cites Lyapunov-stable neural control for state and output feedback: A novel formulation.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Lyapunov-stable neural control for state and output feedback: A novel formulation

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.818650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 2970508b-18dd-40c6-b08b-521ab9201ba8 · outbound

This paper cites Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Neural-network-based online optimal control for uncertain non-linear continuous-time systems with control constraints

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.801729Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 8b1a02e0-487d-4406-84fb-29559df68ac1 · outbound

This paper cites Efficient neural network robustness certification with general activation functions.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems Efficient neural network robustness certification with general activation functions

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.785615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a2dc0c98-3398-4e63-ba55-fc9d8c123359 · outbound

This paper cites General cutting planes for bound-propagation-based neural network verification.

Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems General cutting planes for bound-propagation-based neural network verification

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-16T10:58:01.769261Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Pith citing papers

Observation a9557176-7bb1-4bb6-a84f-29399aa6aced · inbound

Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers cites this paper.

Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllers Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems

Reference 31

Resolution: verified exact; arxiv_id, observed 2026-06-29T22:13:59.865307Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation 602441d1-0930-4876-be9c-a4b993d92a98 · inbound

Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial cites this paper.

Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorial Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems

Reference 59

Resolution: verified exact; arxiv_id, observed 2026-06-29T16:23:39.396393Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

Observation a48f1a13-8ab4-4f6f-a0ee-a04300705818 · inbound

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics cites this paper.

Tube MPC for Bilinear Koopman Models using Robust Control Contraction Metrics Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T05:08:49.469474Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.