Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T05:02:47.236543Z
Paper Citation Record · LEDGER
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares
As of 20 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2506.09164.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
22 of 22 outbound references displayed
- verified exact1
- verified fuzzy15
- unresolved6
- parse uncertain0
- malformed identifier0
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External citation measurements
No source-named external measurement is stored.
Outbound references
Observation d26101ec-49f2-41b6-9b0b-5b3b83c0fea3 · outbound
This paper cites A framework for worst-case and stochastic safety verification using barrier certificates,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares A framework for worst-case and stochastic safety verification using barrier certificates,
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.473135Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 78573147-bd84-4daa-9b61-cf79976e7a15 · outbound
This paper cites A barrier function approach to finite-time stochastic system verification and control,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares A barrier function approach to finite-time stochastic system verification and control,
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:02:47.170645Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4d8f7e79-35e9-4c36-bfd2-2a9c1d93dca2 · outbound
This paper cites Safety certification for stochastic systems via neural barrier functions,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Safety certification for stochastic systems via neural barrier functions,
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.454909Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f06ec18c-1f4c-4b7b-9872-ca7afa2302ac · outbound
This paper cites Piecewise Stochastic Barrier Functions.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Piecewise Stochastic Barrier Functions
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:02:47.177415Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 41eab634-1e9c-4eb5-9944-1133dd532ba1 · outbound
This paper cites Formal synthesis of stochastic systems via control barrier certificates,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Formal synthesis of stochastic systems via control barrier certificates,
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.444825Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation a728a644-cfef-4f26-a1ee-e735605be5de · outbound
This paper cites Some np-complete problems in quadratic and nonlinear programming,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Some np-complete problems in quadratic and nonlinear programming,
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.434639Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation f5ee11e4-3b1e-4f9e-a281-b7b833f75442 · outbound
This paper cites A nullstellensatz and a positivstellensatz in semialgebraic geometry,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares A nullstellensatz and a positivstellensatz in semialgebraic geometry,
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.425254Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 110b9fea-f2e3-4d1d-b5bb-b68ac03a972b · outbound
This paper cites Convergent bounds for the range of multivariate polynomials,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Convergent bounds for the range of multivariate polynomials,
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.414006Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation fac0322d-61f0-4e5c-a95d-ad0cce198ffb · outbound
This paper cites Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Linear relaxations of polynomial positivity for polynomial lyapunov function synthesis,
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.403569Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 782d7dfa-87c8-420c-9b4f-d283e9bcede3 · outbound
This paper cites Formal abstraction of general stochastic systems via noise partitioning,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Formal abstraction of general stochastic systems via noise partitioning,
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:02:47.196688Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5436876c-0155-4c0c-95a7-23719c40b220 · outbound
This paper cites Abstraction-based synthesis for stochastic systems with omega-regular objectives,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Abstraction-based synthesis for stochastic systems with omega-regular objectives,
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.385225Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 8788d6f2-fd40-46ee-af28-a1c7d5281e5d · outbound
This paper cites Efficiency through uncertainty: Scalable formal synthesis for stochastic hybrid systems,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Efficiency through uncertainty: Scalable formal synthesis for stochastic hybrid systems,
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.372885Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation ad9a38b4-6ea8-4aa9-8126-6ffa1930e0a7 · outbound
This paper cites A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares A Unifying Perspective for Safety of Stochastic Systems: From Barrier Functions to Finite Abstractions
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:02:47.206915Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1b360f33-1ea2-4355-ae85-b03f20bf1df2 · outbound
This paper cites Learning control policies for stochastic systems with reach-avoid guarantees,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Learning control policies for stochastic systems with reach-avoid guarantees,
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.362322Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 5133c3d7-07b6-49f4-bd0c-952bb3c16e64 · outbound
This paper cites Fast verification of control barrier functions via linear programming,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Fast verification of control barrier functions via linear programming,
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.352260Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4908490e-7633-43fc-b05f-715c5a1c80fd · outbound
This paper cites Counterexample to global convergence of DSOS and SDSOS hierarchies.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Counterexample to global convergence of DSOS and SDSOS hierarchies
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T05:02:47.265950Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 2a5a6461-b0c5-400e-9f27-880626eca74b · outbound
This paper cites On the complexity of putinar’s positivstel- lensatz,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares On the complexity of putinar’s positivstel- lensatz,
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.342467Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 754e7223-9528-422c-9e04-31c29cc0f49a · outbound
This paper cites Safety guarantees for neural network dynamic systems via stochastic barrier functions,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Safety guarantees for neural network dynamic systems via stochastic barrier functions,
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.331517Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 4d44b4c7-dce3-4597-afc6-190adff5f531 · outbound
This paper cites Semidefinite programming,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Semidefinite programming,
Reference 19
- Resolution
- unresolved
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Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2ffdf7bc-f6aa-43c7-ad6c-d90dfa74f2cd · outbound
This paper cites Über die analytische darstellbarkeit sogenannter willkür- licher functionen einer reellen veränderlichen,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Über die analytische darstellbarkeit sogenannter willkür- licher functionen einer reellen veränderlichen,
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.314797Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Observation 299bdc31-5d16-4a51-8624-7f4942c5ef88 · outbound
This paper cites an unresolved cited work.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares Unresolved cited work
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T05:02:47.233592Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 944dab85-6253-4eac-9331-2c4c62a2005b · outbound
This paper cites The bernstein algorithm,.
On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares The bernstein algorithm,
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T05:02:47.297565Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.
Pith citing papers
No inbound Pith citation observations are available.