Paper Citation Record · LEDGER

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty

As of 7 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 0 inbound Pith citation observations for arXiv:1907.11514.

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

pith.paper-citation-record.v1
1907.11514 v1

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-24T16:08:02.516636Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-07T06:34:17.273281+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

43 of 43 outbound references displayed

verified exact0
verified fuzzy41
unresolved2
parse uncertain0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5544e61e-ce07-4e26-afb5-d75e9336c141 · outbound

This paper cites Implementation of interval arithmetic in CORA 2016.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Implementation of interval arithmetic in CORA 2016

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.025733Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4d2aee76-f6b6-466e-a957-7b5a25de2d8d · outbound

This paper cites Hybridization methods for the analysis of nonlinear systems.Acta Informatica, 43(7):451–476.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Hybridization methods for the analysis of nonlinear systems.Acta Informatica, 43(7):451–476

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.047415Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 16eaefb1-f47c-43fa-9dcc-944aaaf054bb · outbound

This paper cites Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.043889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 18095606-bd16-48aa-8459-af31aed5b340 · outbound

This paper cites Veriﬁed integration of odes and ﬂows using diﬀerential algebraic methods on high-order taylor models.Reliable Computing, 4(4):361–369.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Veriﬁed integration of odes and ﬂows using diﬀerential algebraic methods on high-order taylor models.Reliable Computing, 4(4):361–369

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.040334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 42f4fff7-ba73-4963-9058-ef12f781d2f4 · outbound

This paper cites Abstraction-based parameter synthesis for multiaﬃne systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Abstraction-based parameter synthesis for multiaﬃne systems

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.021849Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b1dfbe35-ef27-47c5-84b3-4e4b319237e7 · outbound

This paper cites Flow*: An analyzer for non-linear hybrid systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Flow*: An analyzer for non-linear hybrid systems

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.029118Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 91690407-f2de-4389-8ebd-ddb19d698a08 · outbound

This paper cites Experimentingonsolvingnonlinearintegerarithmeticwithincremental linearization.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Experimentingonsolvingnonlinearintegerarithmeticwithincremental linearization

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.036112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e3301065-fb60-4568-abfa-f30f5a061113 · outbound

This paper cites Incremental linearization for satisﬁability and veriﬁcation modulo nonlinear arithmetic and transcendental functions.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Incremental linearization for satisﬁability and veriﬁcation modulo nonlinear arithmetic and transcendental functions

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.032706Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e6330328-6838-4e7a-a0ba-799e95720a42 · outbound

This paper cites Ariful Islam, Greg Byrne, Paul L.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Ariful Islam, Greg Byrne, Paul L

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.980784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation b6a823e1-3ffc-4122-8c0a-c3bcde4b8c80 · outbound

This paper cites Ariful Islam, Scott A.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Ariful Islam, Scott A

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.973151Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 33c8e0f0-fbee-44fc-92ce-556a582f0da5 · outbound

This paper cites C2E2: A veriﬁcation tool for stateﬂow models.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty C2E2: A veriﬁcation tool for stateﬂow models

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.969275Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 3fb065a0-12cd-44c5-9640-1aa71634fbef · outbound

This paper cites Eﬃcient solving of large non-linear arithmetic constraint systems with com- plex boolean structure.JSAT, 1(3-4):209–236.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Eﬃcient solving of large non-linear arithmetic constraint systems with com- plex boolean structure.JSAT, 1(3-4):209–236

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.988565Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 1bb2f0a3-61f1-40bf-b404-bb3b34e96a58 · outbound

This paper cites Veriﬁcation of hybrid systems using iterative reﬁnement.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Veriﬁcation of hybrid systems using iterative reﬁnement

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.976989Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation d0c368cb-4aa7-485b-b738-badea80a9be7 · outbound

This paper cites SpaceEx: Scalable veriﬁcation of hybrid systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty SpaceEx: Scalable veriﬁcation of hybrid systems

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.984380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 2b5ad8d4-b8d9-4ce7-8f97-3d08c5efad0b · outbound

This paper cites Eﬃcient reachability analysis for linear systems using support functions.Proc.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Eﬃcient reachability analysis for linear systems using support functions.Proc

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.958388Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation af66818e-4699-46a3-b201-6f3f0b084726 · outbound

This paper cites Fenton, James Glimm, Colas Le Guernic, Scott A.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Fenton, James Glimm, Colas Le Guernic, Scott A

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.992284Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 895037b5-0e71-4bba-874d-aee6c6d6922a · outbound

This paper cites Gulwani and A.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Gulwani and A

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.961728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4315c5bb-182c-4e99-96ca-2fbab795b2ed · outbound

This paper cites Towards formal veriﬁcation of analog and mixed-signal designs.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Towards formal veriﬁcation of analog and mixed-signal designs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.954334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation e38bf27d-02c0-4fd5-acf3-3840a191a25a · outbound

This paper cites Parallel reachability analysis of hybrid systems in xspeed.International Journal on Software Tools for Technology Transfer, to appear:1–23.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Parallel reachability analysis of hybrid systems in xspeed.International Journal on Software Tools for Technology Transfer, to appear:1–23

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.950649Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9dde8162-00b9-47c2-af4f-a9ee033a1b60 · outbound

This paper cites Model checking algorithms for analog veriﬁcation.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Model checking algorithms for analog veriﬁcation

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.007183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 29879487-cf90-4a77-a8de-034d021f6af5 · outbound

This paper cites Henzinger.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Henzinger

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.938959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 090b7375-177c-4067-99e5-eca287c667c6 · outbound

This paper cites Henzinger.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Henzinger

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.935262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ec0f2e14-de60-431b-b2a4-3735ebd5923e · outbound

This paper cites Hen- zinger.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Hen- zinger

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.943019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f58a5f6a-384f-4a88-93ef-27299a11b6b9 · outbound

This paper cites Exponential- condition-based barrier certiﬁcate generation for safety veriﬁcation of hybrid sys- tems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Exponential- condition-based barrier certiﬁcate generation for safety veriﬁcation of hybrid sys- tems

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.946639Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7e92bb21-e5a3-4406-877a-f04433fe7d61 · outbound

This paper cites an unresolved cited work.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-24T16:09:40.965486Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a09c1f5e-7b85-4cb0-ace6-9adf6c50532e · outbound

This paper cites PhD thesis, University of Twente, Enschede, Netherlands.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty PhD thesis, University of Twente, Enschede, Netherlands

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.927648Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c4e818cf-1c00-4b8f-8107-e9caf7c6013b · outbound

This paper cites Polynomial programming: Lp-relaxations also converge.SIAM Journal on Optimization, 15(2):383–393.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Polynomial programming: Lp-relaxations also converge.SIAM Journal on Optimization, 15(2):383–393

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.923607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation ff77b274-7a18-46c4-b99e-144a750ac797 · outbound

This paper cites an unresolved cited work.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-05-24T16:09:40.996211Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation cd6ac7d4-2c24-4657-9deb-0378f24a8634 · outbound

This paper cites Generating invariants for non-linear hybrid systems by linear algebraic methods.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Generating invariants for non-linear hybrid systems by linear algebraic methods

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.915915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation a7d4f31d-cea9-43ec-a642-ea98c8e3b64d · outbound

This paper cites Interval tools for ODEs and DAEs.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Interval tools for ODEs and DAEs

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.999792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 95678c07-bcbf-4461-a9c6-615cd3b3f3ae · outbound

This paper cites Hybridization for stability analysis of switched linear systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Hybridization for stability analysis of switched linear systems

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.003650Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation da0ceae2-9bbb-4e60-b182-8a9971abca36 · outbound

This paper cites Prajna and A.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Prajna and A

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.911422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation c944f508-786f-4f19-9ae9-84a08385dd74 · outbound

This paper cites Positive polynomials on compact semi-algebraic sets.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Positive polynomials on compact semi-algebraic sets

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.919911Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 0d258630-14f4-495c-b129-9eaabf7176b7 · outbound

This paper cites Xspeed: Accelerating reachability analysis on multi-core processors.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Xspeed: Accelerating reachability analysis on multi-core processors

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.931550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 985a5c46-e57b-47fc-9dce-aaf58cb9e2ae · outbound

This paper cites Hybridization based CEGAR for hybrid automata with aﬃne dynamics.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Hybridization based CEGAR for hybrid automata with aﬃne dynamics

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.900542Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 9e829ee3-b7a2-4dbe-8f2b-96fdbd4d2c17 · outbound

This paper cites Sankaranarayanan.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Sankaranarayanan

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.014188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 16e27d31-3e36-414c-864c-44bea7dfa0be · outbound

This paper cites Sankaranarayanan, H.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Sankaranarayanan, H

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.904109Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 682a60e6-6547-4077-859b-99195f10e4c2 · outbound

This paper cites Lyapunov function synthesis using handelman representations.IFAC Proceedings Volumes, 46(23):576–581.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Lyapunov function synthesis using handelman representations.IFAC Proceedings Volumes, 46(23):576–581

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.010845Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 4b82cb59-e95b-4a9e-9cf1-98992642fc23 · outbound

This paper cites Hypro: A C++ library of state set representations for hybrid systems reachability analysis.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Hypro: A C++ library of state set representations for hybrid systems reachability analysis

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:41.018394Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation f6c00843-c604-4494-a2e0-1ac75fe855e2 · outbound

This paper cites A method for invariant generation for polynomial continuous systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty A method for invariant generation for polynomial continuous systems

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.896189Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7c243cf9-d259-422f-80ad-1bc2b3fb7697 · outbound

This paper cites A Nullstellensatz and a Positivstellensatz in semialgebraic geom- etry.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty A Nullstellensatz and a Positivstellensatz in semialgebraic geom- etry

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.907828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 14a6f800-210e-44f0-b4af-9b1aacccb816 · outbound

This paper cites Taly and A.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty Taly and A

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.892299Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Observation 7fcc7aa3-ddbd-4132-a9b7-a055bf1fcca0 · outbound

This paper cites A linear programmingrelaxationbasedapproachforgeneratingbarriercertiﬁcatesofhybrid systems.

Piecewise Robust Barrier Tubes for Nonlinear Hybrid Systems with Uncertainty A linear programmingrelaxationbasedapproachforgeneratingbarriercertiﬁcatesofhybrid systems

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-05-24T16:09:40.888794Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.

Pith citing papers

No inbound Pith citation observations are available.