Paper Citation Record · LEDGER

On Polynomial Stochastic Barrier Functions: Bernstein Versus Sum-of-Squares

As of 14 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.

pith.paper-citation-record.v1
2506.09164 v1

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:02:47.236543Z

measured 22 of 22 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

22 of 22 outbound references displayed

verified exact1
verified fuzzy15
unresolved6
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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 2026-08-14T06:32:32.682623+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

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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 2026-08-14T06:32:32.682623+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

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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

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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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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

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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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+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; no resolver link, observed 2026-08-07T05:02:47.226329Z

Source-reported events for the cited work

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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 2026-08-14T06:32:32.682623+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 2026-08-14T06:32:32.682623+00:00.

Pith citing papers

No inbound Pith citation observations are available.