Paper Citation Record · LEDGER

Convergence rates for polynomial optimization on set products

As of 20 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 3 inbound Pith citation observations for arXiv:2505.18580.

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

pith.paper-citation-record.v1
2505.18580 v4

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:41:02.341243Z

measured 41 of 41 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-28T05:59:12.615897Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-02T08:26:48.473076Z

Reference resolution

38 of 38 outbound references displayed

verified exact2
verified fuzzy25
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d0b1eec9-d38e-4529-be92-3bd1a19b7f92 · outbound

This paper cites Order $p$ quantum Wasserstein distances from couplings.

Convergence rates for polynomial optimization on set products Order $p$ quantum Wasserstein distances from couplings

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:57.736306Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation be8835a2-1ceb-4036-9c13-3484370bcfd1 · outbound

This paper cites Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de finetti theorems.

Convergence rates for polynomial optimization on set products Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de finetti theorems

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:57.796274Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bd5be6f5-a511-43e3-93fb-471efb791ede · outbound

This paper cites On the effective Putinar's Positivstellensatz and moment approximation.

Convergence rates for polynomial optimization on set products On the effective Putinar's Positivstellensatz and moment approximation

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:08.011971Z

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 ea771ae7-934d-4625-8bfb-2402f46a5b8e · outbound

This paper cites Degree bounds for Putinar’s Positivstellensatz on the hypercube.

Convergence rates for polynomial optimization on set products Degree bounds for Putinar’s Positivstellensatz on the hypercube

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:07.811643Z

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 f40f996c-5115-48ee-860d-457abcb6aa09 · outbound

This paper cites Approximating the order 2 quantum Wasserstein distance using the moment-SOS hierarchy.

Convergence rates for polynomial optimization on set products Approximating the order 2 quantum Wasserstein distance using the moment-SOS hierarchy

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:07.603783Z

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 9f741e50-cd31-408c-9b2b-9d82db397b8b · outbound

This paper cites The quantum Wasserstein distance of order 1.

Convergence rates for polynomial optimization on set products The quantum Wasserstein distance of order 1

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:58.101728Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 166a0ea5-5fc5-4f2c-b6be-328815927693 · outbound

This paper cites Distinguishing separable and entangled states.

Convergence rates for polynomial optimization on set products Distinguishing separable and entangled states

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:07.391516Z

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 2dd8a4eb-9579-49b7-a367-4601a1ca0e61 · outbound

This paper cites The sum-of-squares hierarchy on the sphere and applications in quantum information theory.

Convergence rates for polynomial optimization on set products The sum-of-squares hierarchy on the sphere and applications in quantum information theory

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:07.146574Z

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 adc26857-f9ea-43f4-b01b-aadcbc466777 · outbound

This paper cites Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube.

Convergence rates for polynomial optimization on set products Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube

Reference 9

Resolution: verified exact; raw_fallback, observed 2026-08-07T14:41:02.978828Z

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 6d213809-f924-4c3c-86ea-446f96f1b9e6 · outbound

This paper cites Bounding the separable rank via polynomial optimization.

Convergence rates for polynomial optimization on set products Bounding the separable rank via polynomial optimization

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:06.869088Z

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 911905a6-a3e5-4fb3-84e2-f20c5a122bd7 · outbound

This paper cites The Effective Countable Generalized Moment Problem.

Convergence rates for polynomial optimization on set products The Effective Countable Generalized Moment Problem

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:58.468499Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 46197f9e-7c37-4d67-ae36-50660515b5c0 · outbound

This paper cites The Moment-SOS Hierarchy: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear PDEs , volume 4.

Convergence rates for polynomial optimization on set products The Moment-SOS Hierarchy: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear PDEs , volume 4

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:06.668885Z

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 ac32cd04-dd71-4e88-a526-4def6e3990a4 · outbound

This paper cites Optimality conditions for homogeneous polynomial optimization on the unit sphere.

Convergence rates for polynomial optimization on set products Optimality conditions for homogeneous polynomial optimization on the unit sphere

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:06.417174Z

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 e012bbc4-8069-431f-b03a-03c1c4262bc9 · outbound

This paper cites Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets.

Convergence rates for polynomial optimization on set products Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:06.226648Z

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 44e2e0dc-ad65-4754-812e-33c5962bdf22 · outbound

This paper cites Convergence rates of moment-sum-of-squares hierarchies for optimal control problems.

Convergence rates for polynomial optimization on set products Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:06.031550Z

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 30110be3-f976-4d00-8e34-fce81b60e7ff · outbound

This paper cites Convergence rates for sums-of-squares hierarchies with correlative sparsity.

Convergence rates for polynomial optimization on set products Convergence rates for sums-of-squares hierarchies with correlative sparsity

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:05.786761Z

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 dc7a03de-37cc-452a-8e51-cf14fb13e3f1 · outbound

This paper cites Global optimization with polynomials and the problem of moments.

Convergence rates for polynomial optimization on set products Global optimization with polynomials and the problem of moments

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:59.095347Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 62b13d58-42ff-47ba-962a-812bc75f5e2d · outbound

This paper cites A new look at nonnegativity on closed sets and polynomial optimization.

Convergence rates for polynomial optimization on set products A new look at nonnegativity on closed sets and polynomial optimization

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:59.201037Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44f07b24-f9f6-42b2-b17a-bd9777468d55 · outbound

This paper cites A hierarchy of eigencomputations for polynomial optimization on the sphere.

Convergence rates for polynomial optimization on set products A hierarchy of eigencomputations for polynomial optimization on the sphere

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-07T14:41:02.651484Z

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 6fce822e-9438-4a75-9ad7-e68f325743a9 · outbound

This paper cites An effective version of Schm \"u dgen’s Positivstellensatz for the hypercube.

Convergence rates for polynomial optimization on set products An effective version of Schm \"u dgen’s Positivstellensatz for the hypercube

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:05.580218Z

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 80420d08-0aab-4d39-bf0e-3c03407dc4fc · outbound

This paper cites An Overview of Convergence Rates for Sum of Squares Hierarchies in Polynomial Optimization.

Convergence rates for polynomial optimization on set products An Overview of Convergence Rates for Sum of Squares Hierarchies in Polynomial Optimization

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:59.592839Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 38cb8a4f-46de-45f7-a6f1-f5b48ae7a88e · outbound

This paper cites On the complexity of Putinar--Vasilescu's Positivstellensatz.

Convergence rates for polynomial optimization on set products On the complexity of Putinar--Vasilescu's Positivstellensatz

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:05.366007Z

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 8d8a7894-543a-4288-8023-916962d78739 · outbound

This paper cites Magron and J.

Convergence rates for polynomial optimization on set products Magron and J

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:05.174361Z

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 ee76a0bb-85cc-4f04-980e-ed72bbfa0e47 · outbound

This paper cites an unresolved cited work.

Convergence rates for polynomial optimization on set products Unresolved cited work

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-07T14:40:59.976684Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3782ff65-60e1-4d77-8451-732af0444d8e · outbound

This paper cites Optimality conditions and finite convergence of lasserre's hierarchy.

Convergence rates for polynomial optimization on set products Optimality conditions and finite convergence of lasserre's hierarchy

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.993901Z

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 5d418e83-be97-427d-9402-4241a6ce6efe · outbound

This paper cites Moment and Polynomial Optimization.

Convergence rates for polynomial optimization on set products Moment and Polynomial Optimization

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.886130Z

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 0c7b2783-aa5a-4680-9e62-ac553d192e1d · outbound

This paper cites On the complexity of Putinar's Positivstellensatz.

Convergence rates for polynomial optimization on set products On the complexity of Putinar's Positivstellensatz

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.807713Z

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 26bd2366-cbd7-4170-9e8f-613d2b02077b · outbound

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

Convergence rates for polynomial optimization on set products Positive polynomials on compact semi-algebraic sets

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-07T14:41:00.565405Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44ba0b5a-7926-4294-8f5d-6903249eccf4 · outbound

This paper cites Introduction to Radon transforms , volume 160.

Convergence rates for polynomial optimization on set products Introduction to Radon transforms , volume 160

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.656579Z

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 c91d6aa4-240f-432f-9cd5-8dbbaa9c5c27 · outbound

This paper cites The K -moment problem for compact semi-algebraic sets.

Convergence rates for polynomial optimization on set products The K -moment problem for compact semi-algebraic sets

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.464932Z

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 e77f0e14-523d-4e6d-b367-1ebc945a618a · outbound

This paper cites On the complexity of S chm \"u dgen's P ositivstellensatz.

Convergence rates for polynomial optimization on set products On the complexity of S chm \"u dgen's P ositivstellensatz

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.286667Z

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 66f568e8-8f96-4bc8-9173-2a965b04e542 · outbound

This paper cites Sum-of-squares hierarchies for binary polynomial optimization.

Convergence rates for polynomial optimization on set products Sum-of-squares hierarchies for binary polynomial optimization

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:04.103979Z

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 6d8dd5d8-7b63-499a-a843-1aa11a7fade4 · outbound

This paper cites Sum-of-squares hierarchies for polynomial optimization and the C hristoffel-- D arboux kernel.

Convergence rates for polynomial optimization on set products Sum-of-squares hierarchies for polynomial optimization and the C hristoffel-- D arboux kernel

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:03.921815Z

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 e0bcf7c1-7a72-4d0f-8525-562d3582b8ff · outbound

This paper cites Specialized effective Positivstellens \"a tze for improved convergence rates of the moment-SOS hierarchy.

Convergence rates for polynomial optimization on set products Specialized effective Positivstellens \"a tze for improved convergence rates of the moment-SOS hierarchy

Reference 34

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:03.746432Z

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 5af5874c-6d7e-4848-9993-15c5b11b3f8d · outbound

This paper cites Orthogonal P olynomials.

Convergence rates for polynomial optimization on set products Orthogonal P olynomials

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:03.512861Z

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 824280ef-1114-4e50-bed4-42d49dd47281 · outbound

This paper cites Tchakaloff.

Convergence rates for polynomial optimization on set products Tchakaloff

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-07T14:41:02.014661Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f3b8c937-dbbd-49ea-8a9a-c8b9ab3283e0 · outbound

This paper cites Semidefinite programming.

Convergence rates for polynomial optimization on set products Semidefinite programming

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-07T14:41:02.148337Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eeb0c8d8-f0e6-448e-9424-335575fb872f · outbound

This paper cites Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in R ^ d.

Convergence rates for polynomial optimization on set products Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in R ^ d

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T14:41:03.319511Z

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

Observation e9e4f46c-80de-47ee-8c5c-c808a22cb17a · inbound

Degree Bounds for Positivstellens\"atze of general semialgebraic sets cites this paper.

Degree Bounds for Positivstellens\"atze of general semialgebraic sets Convergence rates for polynomial optimization on set products

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-05T02:15:26.741847Z

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 d544bbc0-75c2-49b6-87bf-929d1800f849 · inbound

Degree Bounds for Positivstellens\"atze of general semialgebraic sets cites this paper.

Degree Bounds for Positivstellens\"atze of general semialgebraic sets Convergence rates for polynomial optimization on set products

Reference 24

Resolution: verified exact; arxiv_id, observed 2026-06-05T02:15:26.741847Z

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 0062f8b1-18cb-4831-b967-4bf173ec499a · inbound

Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra cites this paper.

Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra Convergence rates for polynomial optimization on set products

Reference 59

Resolution: verified exact; local_arxiv, observed 2026-07-02T08:26:48.474270Z

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.