{"as_of":"2026-08-11T19:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:93dc05a8b0cd7291198884f4080d4c16171a0d2f9298d79fdb26caf44c2e24cc","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:27:57.771191Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-23T03:35:08.104608Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-23T03:35:20.640442Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"cited_work":{"arxiv_id":"2507.00572","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.00572","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"On the Convergence Rates of Moment- SOS Hierarchies Approximation of Truncated Moment Sequences","venue":null,"work_id":"decb8d25-8f4e-4bcd-a52d-100dd8a1d507","year":null},"citing_paper":{"arxiv_id":"2502.09102","last_updated":"2026-04-06T10:56:19Z","snapshot_observed_at":"2026-08-09T18:51:34.960982Z","submitted_at":"2025-02-13T09:21:53Z","title":"Sum-of-Squares Hierarchy for the Gromov Wasserstein Problem","version":4},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-23T03:35:08.104608Z"},"links":{"cited_paper":"/paper/2507.00572","citing_paper":"/paper/2502.09102"},"observation_digest":"sha256:14d8d3bf716da934dc84d5b265cf0b58a82db6c8f1d864ab444156cf178f7d3f","observation_id":"d338845b-3c7d-47d8-99ec-43cf0d4879d3","resolution":{"observed_at":"2026-05-23T03:35:20.643573Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.00572/citation-record","integrity":"/paper/2507.00572/integrity","json":"/paper/2507.00572/citation-record.json","paper":"/paper/2507.00572"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:27:57.681568Z","title":"write newline","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.681568Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:0f9a0eb62ef576ac66591c1c9169810413c1239ec663108babb88e5b5f3d1f80","observation_id":"d066fb08-fa98-4bad-96c6-0199bceaafde","resolution":{"observed_at":"2026-08-06T21:27:57.681568Z","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":"2026-08-06T21:27:58.033108Z","title":"Handbook on Semidefinite, Conic and Polynomial Optimization , volume 166","venue":null,"work_id":"e85a6101-c169-4f92-b727-f3bd537aec54","year":2011},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.685842Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:2d4d36933071f6811e965c76b6ed6df9e98d740c98043eb4264e8b66baf7dd2f","observation_id":"04af3fe8-8055-4355-ac5d-5be5382bf33a","resolution":{"observed_at":"2026-08-06T21:27:58.035879Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:58.026240Z","title":"Real Algebraic Geometry","venue":null,"work_id":"62b650a7-3f6e-45cb-a635-2237ccd58c2f","year":1998},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.688727Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:be3ecdf56f13b2507e9bd66477e1e525ff0ead769f3ea46cb40592da29b91d06","observation_id":"d2cea1fd-986b-418a-bbac-7b55a90bec59","resolution":{"observed_at":"2026-08-06T21:27:58.028661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:58.017436Z","title":"Characterizations of ojasiewicz inequalities: subgradient flows, talweg, convexity","venue":null,"work_id":"4c6cfa41-876e-4bd8-acba-6636c0356b07","year":2010},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.692740Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:21d4f4e9431957e0da5dbc8943af87fab3aac9b431dd59abd8ac85bd7cf1ccca","observation_id":"5ead0cb2-d2e3-45ab-8508-7194eb9ad192","resolution":{"observed_at":"2026-08-06T21:27:58.020622Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:58.009841Z","title":"Bertsekas","venue":null,"work_id":"c59f7187-ca0b-4f0c-904e-0ee1a4a9083b","year":2015},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.695650Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:30262e0178942e4e3a6b93aee45be1c8fc48f46b6d0b7275583fdc5490f83b58","observation_id":"4100fa0d-59d8-4251-a194-841ada6bb819","resolution":{"observed_at":"2026-08-06T21:27:58.012684Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:58.002492Z","title":"On the effective Putinar 's Positivstellensatz and moment approximation","venue":null,"work_id":"fba1633c-c1bd-4c18-99c7-ecc3f77fc0df","year":2023},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.699057Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:eafa466875046dfc682687b4632c81dbc65545c5db3ca4e5b8182ee781c10c84","observation_id":"c33f7629-244a-40c5-b1c5-4000c3f25583","resolution":{"observed_at":"2026-08-06T21:27:58.004952Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.994779Z","title":"On Łojasiewicz inequalities and the effective P utinar’s P ositivstellensatz","venue":null,"work_id":"8f21adce-2a1a-431f-a6ba-a3d300e98e33","year":2025},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.701966Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:2e6ebe751ed39ee6748e29622f8271782fe771dbf211928ae89f86e0839cfa2e","observation_id":"43314fc3-0243-4918-8841-816aaedcedb5","resolution":{"observed_at":"2026-08-06T21:27:57.997362Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.986224Z","title":"The distance to a polyhedron","venue":null,"work_id":"77f6f8cb-30c3-47c5-bd87-8d7abb6aeb9d","year":1992},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.704561Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:d25193f3b10369d7e6d250e1108597426e31018130cc0a9b143bc8b7318153cb","observation_id":"ff98c22a-01ac-4b7a-9684-d7b13348dbbe","resolution":{"observed_at":"2026-08-06T21:27:57.988823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.978016Z","title":"The proof of Tchakaloff 's Theorem","venue":null,"work_id":"c13e1f7a-61c2-47ef-a05e-a80a2039bafe","year":2006},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.707022Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:79ecdae6bdc7f5e944ce4affef65e3a63781382d7f5b22b5ecd16be1ee90bd1f","observation_id":"d78e5f5e-ec0a-4435-94bf-65a257117f98","resolution":{"observed_at":"2026-08-06T21:27:57.980645Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.970807Z","title":"Drusvyatskiy, A","venue":null,"work_id":"dc06d9c8-36f6-4aa5-bcd8-3a13914fdf87","year":2015},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.709770Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:553fd0be3e82e83037f18d6d0e70ec836c181c5921c828f1f90aaad1d9ce212c","observation_id":"a9aaaf12-8f44-4802-a1fe-92e0e33f1f4d","resolution":{"observed_at":"2026-08-06T21:27:57.973941Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.963650Z","title":"Error bounds for some semidefinite programming approaches to polynomial minimization on the hypercube","venue":null,"work_id":"a9c94823-43ca-4a69-b4da-2453b4c4eaa0","year":2010},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.712366Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:fbb7d3391a58ba204e1420020580e9c5b38a5e36656152de6b18af3879f75b42","observation_id":"cb15d214-69f0-4385-850c-c014c1f74aa0","resolution":{"observed_at":"2026-08-06T21:27:57.966104Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.956313Z","title":"The sum-of-squares hierarchy on the sphere and applications in quantum information theory","venue":null,"work_id":"cad4ea7d-16db-4cf1-bdae-28d9a99ef51f","year":2021},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.714756Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:a025d9637679c12fca9d2a3ac8dff41111394b8e0d699c60ab921e0cb9b944b4","observation_id":"0e8d234c-c725-43cc-912c-c80cf0c5ce86","resolution":{"observed_at":"2026-08-06T21:27:57.958896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.948641Z","title":"Sparse sums of squares on finite abelian groups and improved semidefinite lifts","venue":null,"work_id":"15f3a91c-e61c-4df8-853f-d2d666ec53e5","year":2016},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.717228Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:6ed02d1c92f2d09b5b43b256fc3316c04f43ccab70144e5b9bba061dc3bfc007","observation_id":"d26c3ac3-7e78-4c68-902e-10edd8ee6711","resolution":{"observed_at":"2026-08-06T21:27:57.951889Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2301.10332","last_updated":"2023-01-24T22:25:46Z","snapshot_observed_at":"2026-08-07T00:30:56.588797Z","submitted_at":"2023-01-24T22:25:46Z","title":"Square distance functions are Polyak-{\\L}ojasiewicz and vice-versa","version":1},"cited_work":{"arxiv_id":"2301.10332","doi":null,"metadata_source":"pith","pith_arxiv_id":"2301.10332","snapshot_observed_at":"2026-08-06T21:27:57.800687Z","title":"Square distance functions are Polyak-{\\L}ojasiewicz and vice-versa","venue":"math.OC","work_id":"8dbc302f-13a7-4b35-9526-4a72b9a5f2c4","year":2023},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.719828Z"},"links":{"cited_paper":"/paper/2301.10332","citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:44549feb7e31750d259a4da2c85d962c9896e614e3b7e29490fb814e6fcd740f","observation_id":"81b1738a-27d2-4c3c-9967-e6e28382f7a6","resolution":{"observed_at":"2026-08-06T21:27:57.805744Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.940164Z","title":"Strong duality in L asserre's hierarchy for polynomial optimization","venue":null,"work_id":"8429d6aa-1d8f-4afd-9b3a-eecf96db8d0a","year":2016},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.722624Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:6ad706f76202d609f227f1a5a860d1c4bc092644f574335e0581ee2361ad4367","observation_id":"926dab74-9cae-47eb-9969-f6970f3b7f0a","resolution":{"observed_at":"2026-08-06T21:27:57.943425Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.931574Z","title":"Convergence rates of RLT and Lasserre -type hierarchies for the generalized moment problem over the simplex and the sphere","venue":null,"work_id":"fe55ed1f-0b37-43fd-a09d-561f06056e9b","year":2022},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.724940Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:9b16926199118693e37dfcfa5f6b39c32ead98de55c2fae6f4c7f64a1f2e3d38","observation_id":"2fe8691d-34a4-4b71-8b26-4de5c69b9951","resolution":{"observed_at":"2026-08-06T21:27:57.934802Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.922500Z","title":"Global optimization with polynomials and the problem of moments","venue":null,"work_id":"11756bad-bd63-4d50-8c3f-e5c5b0134960","year":2001},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.727232Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:e908ab1c3320604c98e533a38af2a973b087a0de764f8804a40acc84ec1313ff","observation_id":"5a00db82-8efd-47c7-9201-d89414ff0386","resolution":{"observed_at":"2026-08-06T21:27:57.925726Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.914163Z","title":"Lasserre","venue":null,"work_id":"20038bd1-491c-4e19-8710-df928bbf469d","year":2005},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.730491Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:615ab6623b786dc09df051a0c184066d06a425f1e569e46a354f7e091ce4b074","observation_id":"4a9b9e3e-d3aa-40f8-a2f4-6ec1383690f4","resolution":{"observed_at":"2026-08-06T21:27:57.916998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.905724Z","title":"Moments, Positive Polynomials and their Applications , volume 1","venue":null,"work_id":"c92b4115-ada4-43b7-8270-068d0b017e45","year":2009},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.734121Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:a2731d9ff178f4379e4c6fefc8233185e06b0310ea42f6530b8e197e0c1632fc","observation_id":"98297900-ea68-4185-90f0-572015875306","resolution":{"observed_at":"2026-08-06T21:27:57.908225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.899522Z","title":"A new look at nonnegativity on closed sets and polynomial optimization","venue":null,"work_id":"fadb6ece-edd1-492d-a2f2-8ca6ee1c6d43","year":2011},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.737077Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:db671c7dae70895f41fcf6e95066405fa34771912fd8738a990376f0af95b35e","observation_id":"5621e1d5-959b-4aaa-9e3d-7eb5315e4d54","resolution":{"observed_at":"2026-08-06T21:27:57.901994Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.893224Z","title":"An Introduction to Polynomial and Semi-algebraic Optimization , volume 52","venue":null,"work_id":"ed163f1b-106d-46cc-95fb-33e63c84d352","year":2015},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.740690Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:11ccf18736af3f0c01a753e441f02b61cb4116ffb7c09e762645b9ca7e717809","observation_id":"f1083ea0-cd41-4950-bd64-a884ca7510b2","resolution":{"observed_at":"2026-08-06T21:27:57.895562Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.885139Z","title":"An effective version of S chm \\\"u dgen’s P ositivstellensatz for the hypercube","venue":null,"work_id":"1a7b5579-79f1-47ed-9c40-56f596a9b603","year":2023},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.743279Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:51411c73cf0dbed5a3ad7c2e6929473f3fd1da2c78bb6ebd8ef62cbb64f23b3e","observation_id":"8ed531de-eab3-46bc-a50d-f7b223242afc","resolution":{"observed_at":"2026-08-06T21:27:57.888350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.877680Z","title":"On the complexity of Putinar 's Positivstellensatz","venue":null,"work_id":"e15718c9-2f6a-420f-a3ca-f352e56d3beb","year":2007},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.745478Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:0afc4be2184668f32767011005386b06865fd1096493283a78920a72a04fd984","observation_id":"fd2cdce8-7803-4912-b624-38f40215cf13","resolution":{"observed_at":"2026-08-06T21:27:57.880624Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.871224Z","title":"Positive polynomials on compact semi-algebraic sets","venue":null,"work_id":"765eadbd-14df-46b6-bada-a741b04b726f","year":1993},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.748837Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:8bc498ef450a386c5d6e6311ac80e57292629e0d54aa0e2d2d125af4c36896d9","observation_id":"a1ea9ad0-d1bc-41c9-b00f-da3b18c03a85","resolution":{"observed_at":"2026-08-06T21:27:57.873585Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.863583Z","title":"A note on Tchakaloff 's theorem","venue":null,"work_id":"b0bc5334-d8db-4c85-bc4b-92a4aebd3f6a","year":1997},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.752317Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:12d0d98176301f6f78763f67fece4fd82de8fe1d6d85574c8989190e338d40d9","observation_id":"189d1ef3-63f4-4827-80fd-2e20b79382bf","resolution":{"observed_at":"2026-08-06T21:27:57.866466Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.855261Z","title":"Tyrrell Rockafellar and Roger J.-B","venue":null,"work_id":"d8abcfba-30c2-40a8-a602-c6bd5d032d45","year":1998},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.755425Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:e111f60c1f4f251e9ad7e1838bc99706b0a126791a004274bd62394822b54b38","observation_id":"692c5857-89d2-4d86-bb6b-0d46a71a7a46","resolution":{"observed_at":"2026-08-06T21:27:57.858782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.845745Z","title":"On the complexity of Schm \\\"u dgen 's Positivstellensatz","venue":null,"work_id":"180c4cc0-205e-44c2-881c-22a360fde5ec","year":2004},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.758482Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:b3770ffd75f3563b97eb34e135ce3efab074c7e0342b3ffaf4a3fade4b687998","observation_id":"cfaf2945-2494-4885-ade4-1857f6545246","resolution":{"observed_at":"2026-08-06T21:27:57.850006Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.835989Z","title":"Near-optimal analysis of Lasserre 's univariate measure-based bounds for multivariate polynomial optimization","venue":null,"work_id":"e88af346-463f-4055-9783-ef300e1b356c","year":2021},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.761314Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:5b0d98c589fc669eba51f34907eda97db325b9b6d462b28ee99408c0cf58b12a","observation_id":"ff3f76cb-fc0c-48e4-b9be-9ef82809ab07","resolution":{"observed_at":"2026-08-06T21:27:57.839344Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.04610","last_updated":"2024-04-07T17:44:41Z","snapshot_observed_at":"2026-07-06T12:06:32.421413Z","submitted_at":"2021-11-08T16:29:48Z","title":"Sum-of-squares hierarchies for polynomial optimization and the Christoffel-Darboux kernel","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.04610","snapshot_observed_at":"2026-08-06T21:27:57.763730Z","title":"Sum-of-squares hierarchies for polynomial optimization and the C hristoffel- D arboux kernel","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.763730Z"},"links":{"cited_paper":"/paper/2111.04610","citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:c51557c8a064cbefeca2b357805610cbbcf595e44a435a51ed0420dd34b0b6dc","observation_id":"92ffdf7f-a623-456c-bf19-71c31bdf61b0","resolution":{"observed_at":"2026-08-06T21:27:57.763730Z","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":"2026-08-06T21:27:57.828272Z","title":"u dgen and Konrad Schm \\","venue":null,"work_id":"c51fba5e-39c9-4a2f-9f16-fd0036860a34","year":2017},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.766334Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:eb415e753823888bd5308e85c587d449a245b493ec329cf42cc2a16879fc31ae","observation_id":"a6b43bdf-e149-4e11-b1f1-34f4cc1e3699","resolution":{"observed_at":"2026-08-06T21:27:57.831088Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.821032Z","title":"Exact semidefinite programming relaxations with truncated moment matrix for binary polynomial optimization problems","venue":null,"work_id":"379649f0-bf4e-40ac-afd9-d3fcd65f5206","year":2017},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.769040Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:61c35d4318015a7fee87ba90e30d026b0f7e761082155da62d86ecb3de88499f","observation_id":"f754f378-d77e-4ab8-b221-9b03893224c1","resolution":{"observed_at":"2026-08-06T21:27:57.823837Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+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":"2026-08-06T21:27:57.811560Z","title":"The restricted strong convexity revisited: analysis of equivalence to error bound and quadratic growth","venue":null,"work_id":"3c4ebf12-a056-49af-86c7-f72465d1378b","year":2017},"citing_paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-06T21:27:57.771191Z"},"links":{"citing_paper":"/paper/2507.00572"},"observation_digest":"sha256:19074531d2fb379553134b1189ce40f0baf07d5ddece9ad7735b6ab232594cba","observation_id":"45f0bec9-e12a-4eaa-9859-704a304c5a2f","resolution":{"observed_at":"2026-08-06T21:27:57.815378Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.00572","last_updated":"2025-07-01T08:46:31Z","latest_version":1,"primary_category":"math.OC","snapshot_observed_at":"2026-08-10T22:20:34.173157Z","submitted_at":"2025-07-01T08:46:31Z","title":"On the convergence rates of moment-SOS hierarchies approximation of truncated moment sequences"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":2,"verified_exact":1,"verified_fuzzy":29},"total_outbound_references":32},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 11 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2507.00572."}