Paper Citation Record · LEDGER

Sample Efficient Certification of Discrete-Time Control Barrier Functions

As of 8 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2509.03899.

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

pith.paper-citation-record.v1
2509.03899 v1

Coverage vector

measured 37 of 37 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T10:38:50.555484Z

measured 37 of 37 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

37 of 37 outbound references displayed

verified exact1
verified fuzzy26
unresolved9
parse uncertain1
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9a477bcc-1c62-486c-a588-2742740b790a · outbound

This paper cites Discrete control barrier functions for safety-critical control of discrete systems with application to bipedal robot navigation.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Discrete control barrier functions for safety-critical control of discrete systems with application to bipedal robot navigation

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:57.345937Z

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 50608d42-f08d-4419-b694-3b8f23f30db3 · outbound

This paper cites Burdick, and Aaron D.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Burdick, and Aaron D

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:57.101657Z

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 a543b9a1-113c-4d5c-a2eb-c736e00d5854 · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:38:56.874804Z

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 e8ac7ac5-6464-45aa-a005-7739863cf334 · outbound

This paper cites Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Ames, Samuel Coogan, Magnus Egerstedt, Gennaro Notomista, Koushil Sreenath, and Paulo Tabuada

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:56.654431Z

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 207fbd85-0984-43f8-86f1-d5713a911237 · outbound

This paper cites Bertsekas.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Bertsekas

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:56.521757Z

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 3ed60094-1179-4d0f-8c10-c902162f1e3d · outbound

This paper cites Set-Theoretic Methods in Control.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Set-Theoretic Methods in Control

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:56.323984Z

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 0337ac51-f8f6-4e6c-ac16-b6f7acef742a · outbound

This paper cites Learning stability certificates from data.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Learning stability certificates from data

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:56.102183Z

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 f6161b86-49b4-4f3c-b1d2-b535e1f86b3a · outbound

This paper cites Bravo, D.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Bravo, D

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:55.729250Z

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 23931934-22b4-4aed-9ef3-f75b11b7a063 · outbound

This paper cites Computing Controlled Invariant Sets of Nonlinear Control-Affine Systems.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Computing Controlled Invariant Sets of Nonlinear Control-Affine Systems

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-05T10:38:50.810452Z

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 d2874238-036e-44db-986e-1dfe3ab48058 · outbound

This paper cites Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Byrd, Peihuang Lu, Jorge Nocedal, and Ciyou Zhu

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:55.585194Z

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 91a074f5-b15e-4c79-b2b1-51262409c25c · outbound

This paper cites Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Verification-Aided Learning of Neural Network Barrier Functions with Termination Guarantees

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-05T10:38:48.114792Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ae357e58-4659-4966-bf07-2ebf306c5e74 · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 12

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:38:55.402333Z

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 f2f4ea46-1315-4198-b676-6c3bc75cab2f · outbound

This paper cites Verification and synthesis of control barrier functions.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Verification and synthesis of control barrier functions

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:55.204881Z

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 c36a0931-1944-4945-98c9-d798eeb84174 · outbound

This paper cites Safe reinforcement learning using robust control barrier functions.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Safe reinforcement learning using robust control barrier functions

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:55.069365Z

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 70ae3c88-21a3-4ca8-974f-cca587c0914c · outbound

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

Sample Efficient Certification of Discrete-Time Control Barrier Functions Efficient and accurate estimation of lipschitz constants for deep neural networks

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:54.867975Z

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 400b0693-c8e3-4eaf-8f20-05d4610992df · outbound

This paper cites Fiacchini, T.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Fiacchini, T

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:54.723196Z

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 e8810837-5eb7-47a5-b988-7bb9967bb1ee · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:38:54.511124Z

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 140f5225-32dc-42b9-b02a-70da6e921699 · outbound

This paper cites Ad- vances in the theory of control barrier functions: Addressing practical challenges in safe control synthesis for autonomous and robotic systems.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Ad- vances in the theory of control barrier functions: Addressing practical challenges in safe control synthesis for autonomous and robotic systems

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:54.319984Z

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 aeda2798-d890-42dd-8fda-97a2cc6a9e76 · outbound

This paper cites On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models.

Sample Efficient Certification of Discrete-Time Control Barrier Functions On the Effectiveness of Interval Bound Propagation for Training Verifiably Robust Models

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-05T10:38:48.767788Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 477006be-f4e6-4835-9994-a10547d540ff · outbound

This paper cites Kerrigan.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Kerrigan

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:54.149061Z

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 3212b559-850e-4aec-9a52-4543a38a2407 · outbound

This paper cites Adam: A Method for Stochastic Optimization.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Adam: A Method for Stochastic Optimization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-05T10:38:48.931742Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f7fafec5-da3a-4b90-bd2e-a6bbbbac7b9f · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:38:53.934414Z

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 624bafca-f192-40a0-9e0e-2d41c5ed53ab · outbound

This paper cites Empirical Bernstein Bounds and Sample-Variance Penalization.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Empirical Bernstein Bounds and Sample-Variance Penalization

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:53.712417Z

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 04ec13a2-08eb-46d4-9c75-0ae678b45f65 · outbound

This paper cites Mitchell, A.M.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Mitchell, A.M

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:53.491616Z

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 144570ef-9124-4331-a416-6b4c35891fc2 · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-05T10:38:53.272781Z

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 63f05136-8bf6-4c25-a59e-3a4e8d16fbe1 · outbound

This paper cites Fast verification of control barrier functions via linear programming.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Fast verification of control barrier functions via linear programming

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:53.057179Z

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 e7c16805-2e86-40a7-b22e-1e672eaf6528 · outbound

This paper cites Vboc: Learning the viability boundary of a robot manipulator us- ing optimal control.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Vboc: Learning the viability boundary of a robot manipulator us- ing optimal control

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:52.793885Z

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 f8f60cd5-8cbe-4a81-b3c1-cb855bee91b7 · outbound

This paper cites Scalable computation of robust control invariant sets of nonlinear systems.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Scalable computation of robust control invariant sets of nonlinear systems

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:52.552162Z

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 ff101eac-e63e-4b1d-8342-4c5311c05c82 · outbound

This paper cites Shakhesi.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Shakhesi

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:52.334683Z

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 8403dd79-2b66-43bf-a667-0578c22450ce · outbound

This paper cites Strong and Leila J.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Strong and Leila J

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:52.113480Z

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 8ea0de3c-efcc-4b04-8604-359e9b547851 · outbound

This paper cites Intriguing properties of neural networks.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Intriguing properties of neural networks

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-05T10:38:50.020529Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 327bf6f1-6d42-4070-9a70-29c158665a61 · outbound

This paper cites Dimarogonas.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Dimarogonas

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:51.826906Z

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 bd5e3e35-228c-4cd6-a484-f72755fbaeaa · outbound

This paper cites Predictive control barrier functions: Enhanced safety mechanisms for learning- based control.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Predictive control barrier functions: Enhanced safety mechanisms for learning- based control

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:51.636142Z

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 21986006-437c-4d3b-8a4c-1e69aed09719 · outbound

This paper cites Safety verification and controller synthesis for systems with input constraints.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Safety verification and controller synthesis for systems with input constraints

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:51.426867Z

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 adc4b2ed-6bd0-4890-a5fb-1b3218a8ed3c · outbound

This paper cites Safety-critical model predictive control with discrete-time control barrier func- tion.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Safety-critical model predictive control with discrete-time control barrier func- tion

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:51.199076Z

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 9bb434f6-3bac-4ed0-8663-04d06c0aef27 · outbound

This paper cites Exact verification of relu neural control barrier functions.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Exact verification of relu neural control barrier functions

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-05T10:38:51.016557Z

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 dc603502-b4a4-4df9-871f-e95409e06cbf · outbound

This paper cites an unresolved cited work.

Sample Efficient Certification of Discrete-Time Control Barrier Functions Unresolved cited work

Reference 1350

Resolution: parse uncertain; raw_fallback, observed 2026-08-05T10:38:55.928430Z

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.