{"as_of":"2026-08-09T14:20:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:55d12f2ad6bc0f0f8009e563c2d3351ec8abe6c240f66317f856c142636e7670","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T14:41:02.341243Z","state":"measured"},{"denominator":41,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":41,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":3,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":3,"source":"paper_references, paper_reference_links","source_observed_at":"2026-06-28T05:59:12.615897Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-02T08:26:48.473076Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"cited_work":{"arxiv_id":"2505.18580","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.18580","snapshot_observed_at":"2026-07-02T08:26:48.473076Z","title":"Convergence rates for polynomial optimization on set products","venue":"math.OC","work_id":"7ccab9c9-2316-4221-bd53-b7c0d197fa21","year":2025},"citing_paper":{"arxiv_id":"2605.15821","last_updated":"2026-05-20T09:17:38Z","snapshot_observed_at":"2026-08-03T18:05:51.471208Z","submitted_at":"2026-05-15T10:19:31Z","title":"Degree Bounds for Positivstellens\\\"atze of general semialgebraic sets","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-20T17:33:39.453045Z"},"links":{"cited_paper":"/paper/2505.18580","citing_paper":"/paper/2605.15821"},"observation_digest":"sha256:c253e92b05781bccdf0908d95fd5e7f2d349878000bf9cd63f4f727e58f525e5","observation_id":"e9e4f46c-80de-47ee-8c5c-c808a22cb17a","resolution":{"observed_at":"2026-06-05T02:15:26.741847Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"cited_work":{"arxiv_id":"2505.18580","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.18580","snapshot_observed_at":"2026-07-02T08:26:48.473076Z","title":"Convergence rates for polynomial optimization on set products","venue":"math.OC","work_id":"7ccab9c9-2316-4221-bd53-b7c0d197fa21","year":2025},"citing_paper":{"arxiv_id":"2605.15821","last_updated":"2026-05-20T09:17:38Z","snapshot_observed_at":"2026-08-03T18:05:51.471208Z","submitted_at":"2026-05-15T10:19:31Z","title":"Degree Bounds for Positivstellens\\\"atze of general semialgebraic sets","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-21T08:00:10.454697Z"},"links":{"cited_paper":"/paper/2505.18580","citing_paper":"/paper/2605.15821"},"observation_digest":"sha256:053db3baee9f56ec73702d41dcd2c0bad8cf04201a138e78097e78fdec2b3926","observation_id":"d544bbc0-75c2-49b6-87bf-929d1800f849","resolution":{"observed_at":"2026-06-05T02:15:26.741847Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"cited_work":{"arxiv_id":"2505.18580","doi":null,"metadata_source":"pith","pith_arxiv_id":"2505.18580","snapshot_observed_at":"2026-07-02T08:26:48.473076Z","title":"Convergence rates for polynomial optimization on set products","venue":"math.OC","work_id":"7ccab9c9-2316-4221-bd53-b7c0d197fa21","year":2025},"citing_paper":{"arxiv_id":"2606.04940","last_updated":"2026-06-03T14:30:52Z","snapshot_observed_at":"2026-07-06T23:44:57.208389Z","submitted_at":"2026-06-03T14:30:52Z","title":"Convergence rates of Sum-of-Hermitian-Squares Hierarchies for the Pauli algebra","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-06-28T05:59:12.615897Z"},"links":{"cited_paper":"/paper/2505.18580","citing_paper":"/paper/2606.04940"},"observation_digest":"sha256:2d0f5f090707335c3c6a107b9477927d364936216e2cdbdb3fa97fe0ccdc4f9c","observation_id":"0062f8b1-18cb-4831-b967-4bf173ec499a","resolution":{"observed_at":"2026-07-02T08:26:48.474270Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2505.18580/citation-record","integrity":"/paper/2505.18580/integrity","json":"/paper/2505.18580/citation-record.json","paper":"/paper/2505.18580"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2402.16477","last_updated":"2025-03-11T22:46:01Z","snapshot_observed_at":"2026-07-06T17:35:28.271209Z","submitted_at":"2024-02-26T10:48:46Z","title":"Order $p$ quantum Wasserstein distances from couplings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.16477","snapshot_observed_at":"2026-08-07T14:40:57.736306Z","title":"Order p quantum W asserstein distances from couplings","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:57.736306Z"},"links":{"cited_paper":"/paper/2402.16477","citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:b796d6f42b5c522f7e3af174832b40eaf5a337b7861bd6d919e9560d3d9715d2","observation_id":"d0b1eec9-d38e-4529-be92-3bd1a19b7f92","resolution":{"observed_at":"2026-08-07T14:40:57.736306Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:57.796274Z","title":"Moment-sos and spectral hierarchies for polynomial optimization on the sphere and quantum de finetti theorems","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:57.796274Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:6140818290d3e77e5dc8fe3010b792a727b0d747400f7cb96597f8ee20d2e59c","observation_id":"be8835a2-1ceb-4036-9c13-3484370bcfd1","resolution":{"observed_at":"2026-08-07T14:40:57.796274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:07.927179Z","title":"On the effective Putinar's Positivstellensatz and moment approximation","venue":null,"work_id":"e076312b-80a3-46a4-a620-0f9347c27e33","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:57.849178Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:36a81f9b45831823146e96e4c59d45998dd8364dcfcbbe1f5ef9b81675e62547","observation_id":"bd5be6f5-a511-43e3-93fb-471efb791ede","resolution":{"observed_at":"2026-08-07T14:41:08.011971Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:07.727246Z","title":"Degree bounds for Putinar’s Positivstellensatz on the hypercube","venue":null,"work_id":"e859b071-59a9-4eb1-8001-ee265f455c7b","year":2024},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:57.932339Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:94bd7ddab565770431d00fba5c6ec74a8afd97967c3f176002e0e67b777fb0d6","observation_id":"ea771ae7-934d-4625-8bfb-2402f46a5b8e","resolution":{"observed_at":"2026-08-07T14:41:07.811643Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:07.483819Z","title":"Approximating the order 2 quantum Wasserstein distance using the moment-SOS hierarchy","venue":null,"work_id":"39f62dac-9782-47c7-ad0c-377da4088907","year":2025},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.027293Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:72b0933d1bab22ad49747a2529b77e2cfa2f4a9a3b420a4e2efcfd1abc1f3058","observation_id":"f40f996c-5115-48ee-860d-457abcb6aa09","resolution":{"observed_at":"2026-08-07T14:41:07.603783Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:58.101728Z","title":"The quantum Wasserstein distance of order 1","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.101728Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:3a84ddf906378d2f486e5bd31ab350860e1fa10d74a904ad82907617994eb7c7","observation_id":"9f741e50-cd31-408c-9b2b-9d82db397b8b","resolution":{"observed_at":"2026-08-07T14:40:58.101728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:07.260290Z","title":"Distinguishing separable and entangled states","venue":null,"work_id":"54373770-3e82-4d37-b39f-2bed63f809ed","year":2002},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.184739Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:5ed5391a5b10180ec52401b93331731d86cd2cf92d53e25ebeea0e100a8712d3","observation_id":"166a0ea5-5fc5-4f2c-b6be-328815927693","resolution":{"observed_at":"2026-08-07T14:41:07.391516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:07.044415Z","title":"The sum-of-squares hierarchy on the sphere and applications in quantum information theory","venue":null,"work_id":"76f6e93d-3a4a-4717-8db1-4a35b40e1bcc","year":2021},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.259397Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:59f166a5f8a2a80ba7e4bebacdcab6e9ee09745b64205aaf841d316939e99311","observation_id":"2dd8a4eb-9579-49b7-a367-4601a1ca0e61","resolution":{"observed_at":"2026-08-07T14:41:07.146574Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2505.00544","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:02.894809Z","title":"Revisiting the convergence rate of the Lasserre hierarchy for polynomial optimization over the hypercube","venue":null,"work_id":"002a996c-988c-4a06-8eec-45898e1b7979","year":2025},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.326181Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:3c80a14979e17b5fc1b2b6bdc6e48643f68455c12cc0718e9a64e4d4075d0d8b","observation_id":"adc26857-f9ea-43f4-b01b-aadcbc466777","resolution":{"observed_at":"2026-08-07T14:41:02.978828Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:06.787774Z","title":"Bounding the separable rank via polynomial optimization","venue":null,"work_id":"f25e0b59-882c-4250-b224-4de9af6d8c11","year":2022},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.410233Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:1d3425f6f495331a97d54dfddad697d60db089ca5f8b9a070210daef639b5e1a","observation_id":"6d213809-f924-4c3c-86ea-446f96f1b9e6","resolution":{"observed_at":"2026-08-07T14:41:06.869088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2501.09385","last_updated":"2025-09-01T12:42:54Z","snapshot_observed_at":"2026-07-06T20:21:50.886212Z","submitted_at":"2025-01-16T08:55:19Z","title":"The Effective Countable Generalized Moment Problem","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2501.09385","snapshot_observed_at":"2026-08-07T14:40:58.468499Z","title":"The Effective Generalized Moment Problem","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.468499Z"},"links":{"cited_paper":"/paper/2501.09385","citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:f04ada606e2d3cf9c096656b7d6f6efdd7b1c7e9f13693c709840387cc234fac","observation_id":"911905a6-a3e5-4fb3-84e2-f20c5a122bd7","resolution":{"observed_at":"2026-08-07T14:40:58.468499Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:06.530264Z","title":"The Moment-SOS Hierarchy: Lectures In Probability, Statistics, Computational Geometry, Control And Nonlinear PDEs , volume 4","venue":null,"work_id":"d7577a5e-f229-44a8-ac2a-82944dc2bbbc","year":2020},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.532108Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:81897d7e9689c5579078bb3a8346f2fe2e26ae25554d02c805abda68631fe61c","observation_id":"46197f9e-7c37-4d67-ae36-50660515b5c0","resolution":{"observed_at":"2026-08-07T14:41:06.668885Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:06.347193Z","title":"Optimality conditions for homogeneous polynomial optimization on the unit sphere","venue":null,"work_id":"7d40fd63-e24e-447f-8042-b412c4c9212d","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.537950Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:c003e0cbf580df0e5c2568005f1222bc34f612b7355d68c3e763040993798c29","observation_id":"ac32cd04-dd71-4e88-a526-4def6e3990a4","resolution":{"observed_at":"2026-08-07T14:41:06.417174Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:06.149253Z","title":"Convergence rates of moment-sum-of-squares hierarchies for volume approximation of semialgebraic sets","venue":null,"work_id":"8d29785b-cc58-400c-b454-f6b088256086","year":2018},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.621175Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:90f681945abe41a1762b0983a0e555b48e7cf90187e952a7d81fc8737308202b","observation_id":"e012bbc4-8069-431f-b03a-03c1c4262bc9","resolution":{"observed_at":"2026-08-07T14:41:06.226648Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:05.899667Z","title":"Convergence rates of moment-sum-of-squares hierarchies for optimal control problems","venue":null,"work_id":"9d8705d1-5d9d-4a71-95f1-b38ea241a22b","year":2017},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.780879Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:a8f15e8204c875baf830883790cd0e96c2759da6ca25d3740b04e8c91aa82a6e","observation_id":"44e2e0dc-ad65-4754-812e-33c5962bdf22","resolution":{"observed_at":"2026-08-07T14:41:06.031550Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:05.698134Z","title":"Convergence rates for sums-of-squares hierarchies with correlative sparsity","venue":null,"work_id":"08284c9d-a69a-4ff1-978f-7f9d8b39edc4","year":2025},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:58.937123Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:f71719b9c26683079f3da3821d914db0ede98b01951cca0b4c6e5af3148e8cec","observation_id":"30110be3-f976-4d00-8e34-fce81b60e7ff","resolution":{"observed_at":"2026-08-07T14:41:05.786761Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:59.095347Z","title":"Global optimization with polynomials and the problem of moments","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.095347Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:ac630b08279c60a9ca9f82da632d383c5f09a7805ed94ac78c5ef003eab6fbe3","observation_id":"dc7a03de-37cc-452a-8e51-cf14fb13e3f1","resolution":{"observed_at":"2026-08-07T14:40:59.095347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:59.201037Z","title":"A new look at nonnegativity on closed sets and polynomial optimization","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.201037Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:8b988f58a797a25c55137dcfae088dd6d0b1a9ad5d1704c54f04b19486601caa","observation_id":"62b13d58-42ff-47ba-962a-812bc75f5e2d","resolution":{"observed_at":"2026-08-07T14:40:59.201037Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.17827","last_updated":"2025-07-13T23:22:49Z","snapshot_observed_at":"2026-07-06T16:39:16.652626Z","submitted_at":"2023-10-27T00:28:12Z","title":"A hierarchy of eigencomputations for polynomial optimization on the sphere","version":3},"cited_work":{"arxiv_id":"2310.17827","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.17827","snapshot_observed_at":"2026-08-07T14:41:02.546343Z","title":"A hierarchy of eigencomputations for polynomial optimization on the sphere","venue":"math.OC","work_id":"51779277-4239-467f-b56c-8c17a2f17980","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.359567Z"},"links":{"cited_paper":"/paper/2310.17827","citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:49a9fd94a7906370b4aea497c114bbb95c5066c68eedf17ff526dc920d1b827a","observation_id":"44f07b24-f9f6-42b2-b17a-bd9777468d55","resolution":{"observed_at":"2026-08-07T14:41:02.651484Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:05.486113Z","title":"An effective version of Schm \\\"u dgen’s Positivstellensatz for the hypercube","venue":null,"work_id":"ad37d996-11b6-4440-9ede-b3cdeb2f160d","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.486797Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:f8adcdd9c7c6cb17bce84a539198beb89333de849b198aa4027ebff52854ca31","observation_id":"6fce822e-9438-4a75-9ad7-e68f325743a9","resolution":{"observed_at":"2026-08-07T14:41:05.580218Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2408.04417","last_updated":"2025-01-15T11:45:31Z","snapshot_observed_at":"2026-07-06T18:58:22.457329Z","submitted_at":"2024-08-08T12:44:48Z","title":"An Overview of Convergence Rates for Sum of Squares Hierarchies in Polynomial Optimization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.04417","snapshot_observed_at":"2026-08-07T14:40:59.592839Z","title":"An Overview of Convergence Rates for Sum of Squares Hierarchies in Polynomial Optimization","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.592839Z"},"links":{"cited_paper":"/paper/2408.04417","citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:7f169ebbb1bc54d147ad4238cbfa76faf1eea42936948391b5e02265bce8a324","observation_id":"80420d08-0aab-4d39-bf0e-3c03407dc4fc","resolution":{"observed_at":"2026-08-07T14:40:59.592839Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:05.285096Z","title":"On the complexity of Putinar--Vasilescu's Positivstellensatz","venue":null,"work_id":"78c04742-00a6-4f7c-8456-5c12d13a0e3f","year":2022},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.718155Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:cd2d0f9a1663f5e15285cff988b67b46dde8ff14437e8c4372d56040b17da7f7","observation_id":"38cb8a4f-46de-45f7-a6f1-f5b48ae7a88e","resolution":{"observed_at":"2026-08-07T14:41:05.366007Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:05.076280Z","title":"Magron and J","venue":null,"work_id":"49201a88-e6df-4d7a-bd2d-69a5b2656b0f","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.833750Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:5f278ec9578ae3bc034f1b8fb98754ac8208e32c72efbb4cb9b26d12d55c71cd","observation_id":"8d8a7894-543a-4288-8023-916962d78739","resolution":{"observed_at":"2026-08-07T14:41:05.174361Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:40:59.976684Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T14:40:59.976684Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:377ea0587630812de1f9cb7d0ef4f980b15fe151310a7e6ec01dd7d2d6c9e211","observation_id":"ee76a0bb-85cc-4f04-980e-ed72bbfa0e47","resolution":{"observed_at":"2026-08-07T14:40:59.976684Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.941393Z","title":"Optimality conditions and finite convergence of lasserre's hierarchy","venue":null,"work_id":"31cae247-92a6-49bd-b408-ca3ec25cf0dc","year":2014},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.130058Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:655da2add9a2c4214e36b6f4bdaf4111c20acf333f4dff112da6083e9ae05ae9","observation_id":"3782ff65-60e1-4d77-8451-732af0444d8e","resolution":{"observed_at":"2026-08-07T14:41:04.993901Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.863117Z","title":"Moment and Polynomial Optimization","venue":null,"work_id":"052d27aa-7312-49ea-8926-c0124655c0fc","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.246745Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:eeef376094fc5528c994968ac9560c739fbe2deccd9045dc1bc6ddc539f2ee00","observation_id":"5d418e83-be97-427d-9402-4241a6ce6efe","resolution":{"observed_at":"2026-08-07T14:41:04.886130Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.746238Z","title":"On the complexity of Putinar's Positivstellensatz","venue":null,"work_id":"d3c684f8-e42d-46d2-82d7-0c0366b0aa66","year":2007},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.412064Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:4e72d65af8c83f22d4ed9e701f5fe3ed9605cb0823055dfa3ec5688253d67f60","observation_id":"0c7b2783-aa5a-4680-9e62-ac553d192e1d","resolution":{"observed_at":"2026-08-07T14:41:04.807713Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:00.565405Z","title":"Positive polynomials on compact semi-algebraic sets","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.565405Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:ad44bfd9b46fe6992a5af7c4064e8a7426c4690e7921cc644a7db89cec91a487","observation_id":"26bd2366-cbd7-4170-9e8f-613d2b02077b","resolution":{"observed_at":"2026-08-07T14:41:00.565405Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.566548Z","title":"Introduction to Radon transforms , volume 160","venue":null,"work_id":"5136fa04-2701-4bb4-9668-b7edba25672e","year":2015},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.749585Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:9641b6b6248469f6bf07470843f6b1f4fa5b1d6bb2b58f1429fa93dff0dfc807","observation_id":"44ba0b5a-7926-4294-8f5d-6903249eccf4","resolution":{"observed_at":"2026-08-07T14:41:04.656579Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.385894Z","title":"The K -moment problem for compact semi-algebraic sets","venue":null,"work_id":"7214e76c-58d5-4384-a7d4-9bb5e5c6cc96","year":1991},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:00.911958Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:9f3a2641a4217fd099b421f3cf51a651f6ff9e0717f49b715ed6d31b3656165a","observation_id":"c91d6aa4-240f-432f-9cd5-8dbbaa9c5c27","resolution":{"observed_at":"2026-08-07T14:41:04.464932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.195903Z","title":"On the complexity of S chm \\\"u dgen's P ositivstellensatz","venue":null,"work_id":"eea3b398-97ce-41c7-9b2e-b609a0c6f71f","year":2004},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:01.121465Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:04b91dd15919c192580be018d91079393b79daf764772b206dcc1e45d1e32e56","observation_id":"e77f0e14-523d-4e6d-b367-1ebc945a618a","resolution":{"observed_at":"2026-08-07T14:41:04.286667Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:04.015356Z","title":"Sum-of-squares hierarchies for binary polynomial optimization","venue":null,"work_id":"ad6b9801-a2b3-4f7a-8120-32435a8c6b86","year":2023},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:01.310769Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:1e0d696e7f7fe18b7cff6f0e4436f9387cc3a88e5f4e405bf3770c462d6438d1","observation_id":"66f568e8-8f96-4bc8-9173-2a965b04e542","resolution":{"observed_at":"2026-08-07T14:41:04.103979Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:03.840849Z","title":"Sum-of-squares hierarchies for polynomial optimization and the C hristoffel-- D arboux kernel","venue":null,"work_id":"c8222bdd-1c5f-47e7-aad9-5ace2a41104c","year":2022},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:01.513983Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:829bdb7a771f1e17f15feb7698941a0de737ebec6ba6bef262db1c765cb85d32","observation_id":"6d8dd5d8-7b63-499a-a843-1aa11a7fade4","resolution":{"observed_at":"2026-08-07T14:41:03.921815Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:03.627223Z","title":"Specialized effective Positivstellens \\\"a tze for improved convergence rates of the moment-SOS hierarchy","venue":null,"work_id":"d2b24283-d245-4047-974c-6c0fd86bdb69","year":2024},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:01.731283Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:e0ea7220ed57099a895981a6f4cf94bca4daae7df17f012011242032910f5766","observation_id":"e0bcf7c1-7a72-4d0f-8525-562d3582b8ff","resolution":{"observed_at":"2026-08-07T14:41:03.746432Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:03.434513Z","title":"Orthogonal P olynomials","venue":null,"work_id":"d5fad9d3-b279-4259-9a45-e8b5c73c9cd7","year":1975},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:01.882716Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:e166e1116300b8eeab5d3a038864afced6f43bbcd1c41399dfc9a4d4e9f66b43","observation_id":"5af5874c-6d7e-4848-9993-15c5b11b3f8d","resolution":{"observed_at":"2026-08-07T14:41:03.512861Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:02.014661Z","title":"Tchakaloff","venue":null,"work_id":null,"year":1957},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:02.014661Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:754f1f7357ad050b4acbc85889ade3ec7de0bc9b6d006136b9a2e0d92d5811c6","observation_id":"824280ef-1114-4e50-bed4-42d49dd47281","resolution":{"observed_at":"2026-08-07T14:41:02.014661Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:02.148337Z","title":"Semidefinite programming","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:02.148337Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:205d780e42b30d324c0743006c87a706bb605f55a8828c1456af666796a55944","observation_id":"f3b8c937-dbbd-49ea-8a9a-c8b9ab3283e0","resolution":{"observed_at":"2026-08-07T14:41:02.148337Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T14:41:03.187579Z","title":"Summability of Fourier orthogonal series for Jacobi weight functions on the simplex in R ^ d","venue":null,"work_id":"3e4b25f8-4141-4439-a764-41fb20ef847a","year":1998},"citing_paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products","version":4},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-07T14:41:02.341243Z"},"links":{"citing_paper":"/paper/2505.18580"},"observation_digest":"sha256:7c89b61e48918d48884a0c4368a35042af608ef6b72bfdc2db0688dd40d1e1c8","observation_id":"eeb0c8d8-f0e6-448e-9424-335575fb872f","resolution":{"observed_at":"2026-08-07T14:41:03.319511Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2505.18580","last_updated":"2026-06-03T22:19:35Z","latest_version":4,"primary_category":"math.OC","snapshot_observed_at":"2026-08-07T14:27:07.851029Z","submitted_at":"2025-05-24T08:09:17Z","title":"Convergence rates for polynomial optimization on set products"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":11,"verified_exact":2,"verified_fuzzy":25},"total_outbound_references":38},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 3 inbound Pith citation observations for arXiv:2505.18580."}