Paper Citation Record · LEDGER

On the Construction of Barrier Certificate: A Dynamic Programming Perspective

As of 8 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2507.17222.

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

pith.paper-citation-record.v1
2507.17222 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:06:02.464819Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-18T15:16:28.518229Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-18T15:16:32.220669Z

Reference resolution

31 of 31 outbound references displayed

verified exact1
verified fuzzy23
unresolved7
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5d3a8a18-1c85-4953-98ec-b4b4495ac7e1 · outbound

This paper cites Formal Methods for Control Synthesis: An Optimization Perspective,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Formal Methods for Control Synthesis: An Optimization Perspective,

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.071568Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a34ff6b4-a15d-4f1e-a99f-20de2a7e774d · outbound

This paper cites Automated verifica- tion and synthesis of stochastic hybrid systems: A survey,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Automated verifica- tion and synthesis of stochastic hybrid systems: A survey,

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.060430Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8b155e1b-deba-4050-b1dd-360e3406dbf4 · outbound

This paper cites Formal synthesis of controllers for safety- critical autonomous systems: Developments and challenges,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Formal synthesis of controllers for safety- critical autonomous systems: Developments and challenges,

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.050358Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a4630a5b-7b9a-4f7e-a573-0a3c748ed1c4 · outbound

This paper cites Probabilistic reacha- bility and safety for controlled discrete time stochastic hybrid systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Probabilistic reacha- bility and safety for controlled discrete time stochastic hybrid systems,

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.039161Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 81f2ca0a-ac8f-468b-9bad-f2b21a8c05b2 · outbound

This paper cites Precise approximations of the probability distribution of a markov process in time: an application to probabilistic invariance,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Precise approximations of the probability distribution of a markov process in time: an application to probabilistic invariance,

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.028250Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 1e18a27a-f51c-4f6e-9b78-9501bd878f4b · outbound

This paper cites Automata-based controller synthesis for stochastic systems: A game framework via approximate probabilistic relations,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Automata-based controller synthesis for stochastic systems: A game framework via approximate probabilistic relations,

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:03.014083Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 8f401df0-de2c-46f3-990e-7c9b70ece92f · outbound

This paper cites A framework for worst- case and stochastic safety verification using barrier certificates,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective A framework for worst- case and stochastic safety verification using barrier certificates,

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.391292Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 20c7f9a3-735c-4525-b657-ec8cad0e8996 · outbound

This paper cites Data-driven safety verification of stochas- tic systems via barrier certificates: A wait-and-judge approach,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Data-driven safety verification of stochas- tic systems via barrier certificates: A wait-and-judge approach,

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.995546Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0c8c36c0-07f0-487a-819f-8fe4c6b727ba · outbound

This paper cites Formal verification of unknown discrete-and continuous-time systems: A data- driven approach,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Formal verification of unknown discrete-and continuous-time systems: A data- driven approach,

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.984426Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c13fa1ef-04ff-4d44-9169-9ee3f4ea015d · outbound

This paper cites Stochastic safety analysis of stochastic hybrid systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Stochastic safety analysis of stochastic hybrid systems,

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.972763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation aae9912b-1180-408c-ba77-eb4074849b9f · outbound

This paper cites Probabilistic safety verification of stochastic hybrid systems using barrier certificates,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Probabilistic safety verification of stochastic hybrid systems using barrier certificates,

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.961754Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 23c5e707-8c56-4d95-82e8-dbceccfc69dc · outbound

This paper cites Finite-time regional verification of stochastic non-linear systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Finite-time regional verification of stochastic non-linear systems,

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.407067Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b42155b0-8888-4ffb-b69c-050610ab5c87 · outbound

This paper cites A barrier function approach to finite-time stochastic system verification and control,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective A barrier function approach to finite-time stochastic system verification and control,

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.410055Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59ff0725-d496-44ac-a3e5-291ffdf8af6e · outbound

This paper cites Finite-time safety and reach-avoid verification of stochastic discrete-time systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Finite-time safety and reach-avoid verification of stochastic discrete-time systems,

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.412973Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d69d4175-7b12-49c1-af9c-a20dcbcd994f · outbound

This paper cites Temporal logic verification of stochastic systems using barrier certificates,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Temporal logic verification of stochastic systems using barrier certificates,

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.938113Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 27c84220-8411-4a56-82bc-b8e712ca4643 · outbound

This paper cites Data-driven distributionally robust safety verification using barrier certificates and conditional mean embeddings,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Data-driven distributionally robust safety verification using barrier certificates and conditional mean embeddings,

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.927991Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation fc3ecddd-f06d-4f65-97f4-f50b5b3efe64 · outbound

This paper cites Distributionally robust control syn- thesis for stochastic systems with safety and reach-avoid specifications,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Distributionally robust control syn- thesis for stochastic systems with safety and reach-avoid specifications,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.421674Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0ad90407-ed41-4bd2-af76-94eab4dc1f34 · outbound

This paper cites K-inductive barrier certificates for stochastic systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective K-inductive barrier certificates for stochastic systems,

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.918072Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 0db2f545-c005-4bf2-941b-4d290fdae4c2 · outbound

This paper cites Learning control policies for stochastic systems with reach-avoid guarantees,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Learning control policies for stochastic systems with reach-avoid guarantees,

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.907345Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 30a4c199-0312-4db3-b99c-788788d049ca · outbound

This paper cites Sufficient and necessary barrier-like conditions for safety and reach-avoid verification of stochastic discrete-time systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Sufficient and necessary barrier-like conditions for safety and reach-avoid verification of stochastic discrete-time systems,

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-06T15:06:02.430711Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8197a878-3948-4014-8842-97f148a996a6 · outbound

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

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Stochastic lyapunov-barrier functions for robust probabilistic reach-avoid-stay specifications,

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.895964Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation f3f150ff-f3dd-42bd-aa4e-5d206df30048 · outbound

This paper cites Quantitative supermartingale cer- tificates,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Quantitative supermartingale cer- tificates,

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.885840Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation b180ff3e-0d9e-4712-8628-780a009975a4 · outbound

This paper cites Supermartingale certificates for quantitative omega-regular verification and control,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Supermartingale certificates for quantitative omega-regular verification and control,

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.875835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a92f0d8c-f6e9-4e63-8a34-2fc07dd7e652 · outbound

This paper cites A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions

Reference 24

Resolution: verified exact; local_arxiv, observed 2026-08-06T15:06:02.500575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 45f94600-48a9-4d5b-95f8-5be0d3145ff0 · outbound

This paper cites Bertsekas and S.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Bertsekas and S

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.865488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 319455ae-25bd-4d43-91d1-5097935a3d7c · outbound

This paper cites Verification of discrete time stochastic 10 hybrid systems: A stochastic reach-avoid decision problem,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Verification of discrete time stochastic 10 hybrid systems: A stochastic reach-avoid decision problem,

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.853922Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation c817a219-8363-4401-aa99-862a725baed7 · outbound

This paper cites an unresolved cited work.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Unresolved cited work

Reference 27

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:06:02.841696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dec798ea-01ba-454c-afb7-ddc0c21599a3 · outbound

This paper cites Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones,

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.831271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation a2de9064-553f-4dda-b539-d542012c631f · outbound

This paper cites Introducing SOS- TOOLS: A general purpose sum of squares programming solver,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Introducing SOS- TOOLS: A general purpose sum of squares programming solver,

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.820907Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 3ac79ff9-4ce6-4392-926d-6530023b6a08 · outbound

This paper cites Formal synthesis of stochastic systems via control barrier certificates,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Formal synthesis of stochastic systems via control barrier certificates,

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.810234Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation 5c2bec38-030c-48a4-a7cc-dd644b6ea952 · outbound

This paper cites Secure-by-construction synthesis for control systems,.

On the Construction of Barrier Certificate: A Dynamic Programming Perspective Secure-by-construction synthesis for control systems,

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:06:02.799948Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Pith citing papers

Observation ea4ac95d-a49f-4d2d-9a2a-e5c7707bbb24 · inbound

Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems cites this paper.

Refined Barrier Conditions for Finite-Time Safety and Reach-Avoid Guarantees in Stochastic Systems On the Construction of Barrier Certificate: A Dynamic Programming Perspective

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-18T15:16:32.224536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.