{"as_of":"2026-08-08T20:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d52ce7efa38aca7b69f30933fe4b83d58d6a86f2e07a9601c658f941c7be782d","coverage":[{"denominator":54,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":54,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T07:12:24.844427Z","state":"measured"},{"denominator":55,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":55,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-08-04T07:12:20.887011Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.26574","snapshot_observed_at":"2026-08-04T07:12:20.887011Z","title":"important","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:20.887011Z"},"links":{"cited_paper":"/paper/2510.26574","citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:71180409adb2d9cde26ec6f106738ba02270aaad21d61e717d81862eeaf4e8e7","observation_id":"80757b26-195d-4136-9d78-d96e47edbe81","resolution":{"observed_at":"2026-08-04T07:12:20.887011Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2510.26574/citation-record","integrity":"/paper/2510.26574/integrity","json":"/paper/2510.26574/citation-record.json","paper":"/paper/2510.26574"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.26574","snapshot_observed_at":"2026-08-04T07:12:20.887011Z","title":"important","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:20.887011Z"},"links":{"cited_paper":"/paper/2510.26574","citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:71180409adb2d9cde26ec6f106738ba02270aaad21d61e717d81862eeaf4e8e7","observation_id":"80757b26-195d-4136-9d78-d96e47edbe81","resolution":{"observed_at":"2026-08-04T07:12:20.887011Z","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":"2026-08-04T07:12:20.941462Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:20.941462Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:a3b2f5dcf6c2f6f383c131dab21bfd5722ad1a99483d533afde3f67741d82b55","observation_id":"d85c11d4-2a88-4ce7-b734-30f8fe3a815e","resolution":{"observed_at":"2026-08-04T07:12:20.941462Z","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":"2026-08-04T07:12:20.998899Z","title":"We consider again a kernel functionk:X×X→Rsatisfying the assumptions listed in Section 1.1","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:20.998899Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:3570d5c6d3bae7a6224e06cc70cfb8f1fc26a7aa30619c2ff18a5fb3aac81efc","observation_id":"01793924-380d-428e-aa8f-ddd5908320fd","resolution":{"observed_at":"2026-08-04T07:12:20.998899Z","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":"2026-08-04T07:12:21.051310Z","title":"importance","venue":null,"work_id":null,"year":2048},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.051310Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:cbbda1e718ce3f98b4066dc6b121c0fe9eec19848bd3424f3427eefbe889cc91","observation_id":"a67bef84-1424-474d-87de-d4924250280b","resolution":{"observed_at":"2026-08-04T07:12:21.051310Z","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":"2026-08-04T07:12:21.120061Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.120061Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:d09e6d7bafb55cce94fc7be78d85630d72d22c8f7c698ab69f9be4843bdf34be","observation_id":"971d47f1-fefa-4c77-bcba-11054713d418","resolution":{"observed_at":"2026-08-04T07:12:21.120061Z","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":"2026-08-04T07:12:21.181166Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.181166Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:facf6f4947a0da1fccf582e39b62da271bf9f5800a44b1ab5289dbb413e52409","observation_id":"85fe8e7e-fae4-4a29-82e4-dd1d2cec1bf1","resolution":{"observed_at":"2026-08-04T07:12:21.181166Z","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":"2026-08-04T07:12:21.243605Z","title":"Aubry, R","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.243605Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:66da975039ba89632f441441425cf41923731de58f9ff22f570d6e9c4e17321a","observation_id":"394d2ebf-942a-40bb-a80c-a44e035075f1","resolution":{"observed_at":"2026-08-04T07:12:21.243605Z","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":"2026-08-04T07:12:21.363619Z","title":"Belabbas and P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.363619Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:575c39c5892d4ef20a87f4969dd20b081ddc2fc39b9c218ccd9e5a0e17bb83f8","observation_id":"b349f8eb-e754-46ca-8704-d0087874cf2d","resolution":{"observed_at":"2026-08-04T07:12:21.363619Z","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":"2026-08-04T07:12:21.429854Z","title":"Belabbas and P","venue":null,"work_id":null,"year":1906},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.429854Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:ab9bf6460d52ccf30bfe9cd4f3454073ba5a456e94db8dbb418a1a0b37d45f8c","observation_id":"3620cc91-aa7b-497b-b499-374eed06722d","resolution":{"observed_at":"2026-08-04T07:12:21.429854Z","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":"2026-08-04T07:12:21.493131Z","title":"Belabbas and P","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.493131Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:fe3ae843fe009e35836e4bc71378c78c92e0b7fee122eec402811f8b79c56328","observation_id":"677ff230-9614-4300-bcd7-596a4ac95a23","resolution":{"observed_at":"2026-08-04T07:12:21.493131Z","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":"2026-08-04T07:12:21.551178Z","title":"Berkooz, P","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.551178Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:31eef991d540ce3140f3fdd975804f6137370b29ec646fcdf6cd2510de79116e","observation_id":"7a92fb52-015c-45e6-a9be-7f6011f52f7a","resolution":{"observed_at":"2026-08-04T07:12:21.551178Z","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":"2026-08-04T07:12:21.615501Z","title":"Berry and J","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.615501Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:fa9e7d4893c7a8146ab319113360ba05a1f7fd364683ec07dc8eb563b7c79d18","observation_id":"2c93aff9-dc30-4c51-825a-1696746d4475","resolution":{"observed_at":"2026-08-04T07:12:21.615501Z","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":"2026-08-04T07:12:21.665513Z","title":"Berry and T","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.665513Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:8243d3480d3fcaaf5dae1636d7a5706238e0a31bd47ccd1eba3b972572b827a3","observation_id":"014c9d8d-d072-4753-9d6c-3aace28a055b","resolution":{"observed_at":"2026-08-04T07:12:21.665513Z","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":"2026-08-04T07:12:21.714832Z","title":"Canuto, Y","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.714832Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:fc2d51217afb8c75296fe52dddf6a1ff7116ad906224a289c0dcc8019281787f","observation_id":"61efe849-ec5f-496c-b5c0-af01b693e99c","resolution":{"observed_at":"2026-08-04T07:12:21.714832Z","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":"2026-08-04T07:12:21.793515Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.793515Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:f10b82a26b38895d4964a2525bfadefdbd5300fcad9e2178a5361ae54fa20f81","observation_id":"26254176-555a-4c00-a82f-a2dc3559ebfa","resolution":{"observed_at":"2026-08-04T07:12:21.793515Z","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":"2026-08-04T07:12:21.848128Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.848128Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:85d38fb400ce56ce6691a51af9ede0cc404a09d8822524eb2a48307ef5fec5fe","observation_id":"10de4b85-b5a8-48e1-b270-e89e72206691","resolution":{"observed_at":"2026-08-04T07:12:21.848128Z","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":"2026-08-04T07:12:21.895615Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.895615Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:9381ba8626e685443b6ddc24c37c79b1f7928213ace8785099096943de5ac388","observation_id":"f727c45d-fc4e-497c-a0a6-ae28a753fe6d","resolution":{"observed_at":"2026-08-04T07:12:21.895615Z","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":"2026-08-04T07:12:21.996390Z","title":null,"venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:21.996390Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:e0b72db1cd5da90e9e732a62335377cb8c5b4f8787c21b342a6e3edb27cdb0b4","observation_id":"35c0bc33-66f9-4392-80c1-50dd6c8f619b","resolution":{"observed_at":"2026-08-04T07:12:21.996390Z","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":"2026-08-04T07:12:22.068059Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.068059Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:9a00382a8610896257eaad3294be44a7f87daed79e0d69e3c6ecdd19d542d7ad","observation_id":"de79a793-cc3b-4ea4-bbfc-3453ceca1160","resolution":{"observed_at":"2026-08-04T07:12:22.068059Z","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":"2026-08-04T07:12:22.186887Z","title":null,"venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.186887Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:00298adb59a11c3b167380add9aa0f8519b752a4add6487a4200641b113ed77c","observation_id":"de7c7bc9-2158-4944-8938-20664daebe47","resolution":{"observed_at":"2026-08-04T07:12:22.186887Z","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":"2026-08-04T07:12:22.263866Z","title":"Cvitanovic, R","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.263866Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:cc80f61b8da051504623e7bdc23b0a95175f2161922c7c0944459affa8f0e681","observation_id":"1db22618-3569-41d1-aac7-083a36e1a498","resolution":{"observed_at":"2026-08-04T07:12:22.263866Z","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":"2026-08-04T07:12:22.328471Z","title":"Das and D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.328471Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:a84c14305dcfe3cd78517ec5350902c71e2468d9ac7824ea2a0655fe8dbc9317","observation_id":"23095bb3-94cb-4456-9939-bc3a301668b7","resolution":{"observed_at":"2026-08-04T07:12:22.328471Z","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":"2026-08-04T07:12:22.430486Z","title":"Drineas, M","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.430486Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:dfda3eebef24b5727e0dad302e17e715400ec0e352d316f83850d500ad3222b7","observation_id":"6061e325-daa7-4686-8882-3c90790abccc","resolution":{"observed_at":"2026-08-04T07:12:22.430486Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2410.03969","last_updated":"2025-04-06T01:54:34Z","snapshot_observed_at":"2026-07-06T19:28:12.480864Z","submitted_at":"2024-10-04T23:21:37Z","title":"Embrace rejection: Kernel matrix approximation by accelerated randomly pivoted Cholesky","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2410.03969","snapshot_observed_at":"2026-08-04T07:12:22.531779Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.531779Z"},"links":{"cited_paper":"/paper/2410.03969","citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:4537bd4bbd6e920566bf92c06009bbf8188d28da3158ae359cc7f7b3d75e9958","observation_id":"7a37bc64-043e-4c22-9639-2b5974f40103","resolution":{"observed_at":"2026-08-04T07:12:22.531779Z","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":"2026-08-04T07:12:22.632197Z","title":"Fowlkes, S","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.632197Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:1afd8fc75eb6645c6a23aaac177585074919115b7a7eb7a0be2bc5cd82fa3e09","observation_id":"6566eb0f-6290-4e03-9a43-be9d01ca82ea","resolution":{"observed_at":"2026-08-04T07:12:22.632197Z","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":"2026-08-04T07:12:22.706598Z","title":"Fowlkes, S","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.706598Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:f33a22558d61512fcfbf1c58c10e6e9bd653bb8cf61b01580f00b8216565c652","observation_id":"d0f483a4-0c77-4c10-aee8-b2c7f70222a8","resolution":{"observed_at":"2026-08-04T07:12:22.706598Z","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":"2026-08-04T07:12:22.783569Z","title":"Freeman, D","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.783569Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:7c1b9190db432dd83b3b7a73e4821eb114526c99f05d3f23264247dc6d0af74c","observation_id":"74797053-6e78-47ef-9d88-5f7b34507036","resolution":{"observed_at":"2026-08-04T07:12:22.783569Z","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":"2026-08-04T07:12:22.871155Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.871155Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:a42e9a146fb90b3f7f925083c697448624ef208ece8f8b897e8ac2152f0dbca3","observation_id":"e0ce7d3e-5e59-4033-bd4d-b6e6d8ff9f63","resolution":{"observed_at":"2026-08-04T07:12:22.871155Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1707.07269","last_updated":"2018-10-30T09:48:51Z","snapshot_observed_at":"2026-07-06T05:52:17.418793Z","submitted_at":"2017-07-23T09:32:55Z","title":"Large sample analysis of the median heuristic","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1707.07269","snapshot_observed_at":"2026-08-04T07:12:22.974535Z","title":"Garreau, W","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:22.974535Z"},"links":{"cited_paper":"/paper/1707.07269","citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:e80f697bf0e9385848bc5fbd100058f628e4579d51edd6ae33321ce616dd177c","observation_id":"1448380b-7db0-41ec-9588-03586d162930","resolution":{"observed_at":"2026-08-04T07:12:22.974535Z","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":"2026-08-04T07:12:23.048767Z","title":"Giannakis","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.048767Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:91d7515018a0926e56a2508f2afa8ae41ae676db4c57888bbe5231c2603ce4f4","observation_id":"d8db64c1-03ba-43e3-9b95-9b142c6213d2","resolution":{"observed_at":"2026-08-04T07:12:23.048767Z","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":"2026-08-04T07:12:23.156395Z","title":"Giannakis, A","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.156395Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:86d5df9608481c4e4ebefbd3a930f42d60ca8eb257b3ace4bc582bed5f912fdd","observation_id":"32a7df0a-eb98-4d71-b395-79d9c01b2aa4","resolution":{"observed_at":"2026-08-04T07:12:23.156395Z","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":"2026-08-04T07:12:23.256199Z","title":"Giraud, J","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.256199Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:086bed78cd95f52376695476064d9afa2fefec4ff611a7c228739a9918f3cf24","observation_id":"f8867913-9c66-4486-9d4e-3098472d120a","resolution":{"observed_at":"2026-08-04T07:12:23.256199Z","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":"2026-08-04T07:12:23.331426Z","title":"Halko, P.-G","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.331426Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:be63bb816ba3a9593a481b55bdb76b394a6221d5a580e12ff35ef29d94b03d92","observation_id":"ecf69c7b-fade-490a-baaf-b95ebfeb3c83","resolution":{"observed_at":"2026-08-04T07:12:23.331426Z","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":"2026-08-04T07:12:23.390634Z","title":"Hinze and S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.390634Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:2b5962576c90a58ab84a802f9a725644145e16b5fe189937ca9aa1a5d2f46f80","observation_id":"cd3ef066-bbb9-4dfd-9dd9-7ffd2339ee6b","resolution":{"observed_at":"2026-08-04T07:12:23.390634Z","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":"2026-08-04T07:12:23.474630Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.474630Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:a7078f799b8e808525132dbb05c80446de2a508822afb1f860972a68da208f70","observation_id":"dcf144e5-7a78-437e-8199-84eca5be4aa8","resolution":{"observed_at":"2026-08-04T07:12:23.474630Z","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":"2026-08-04T07:12:23.559069Z","title":"Kassam and L","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.559069Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:a59bb831a209ba175ed09f4c195eb58236730ed576e3c640abc5e9984a8f7571","observation_id":"c4967fbd-d255-4dff-ae6a-861eeaeacbff","resolution":{"observed_at":"2026-08-04T07:12:23.559069Z","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":"2026-08-04T07:12:23.649126Z","title":null,"venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.649126Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:496a6de62ee499c948db0b555ec55326a0b21bc64c53651f1ef622febf28ac23","observation_id":"0af0f88a-0690-4e43-a1fb-4f29678299ec","resolution":{"observed_at":"2026-08-04T07:12:23.649126Z","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":"2026-08-04T07:12:23.729615Z","title":"Kumar, M","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.729615Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:098403da2c6d43df003109e8eecec07a8337b309819450886c06c1cd7eaf2459","observation_id":"650517e2-1b17-4e79-8bba-054cd7069cc3","resolution":{"observed_at":"2026-08-04T07:12:23.729615Z","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":"2026-08-04T07:12:23.816250Z","title":"Kuramoto and T","venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.816250Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:7d1bd8877d35253b03a8d8d8bbd1b972b0bc33ddb9eea45cb399637b3086a228","observation_id":"142b0db9-0dc7-4439-86ed-af37595f297d","resolution":{"observed_at":"2026-08-04T07:12:23.816250Z","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":"2026-08-04T07:12:23.903984Z","title":"Langone and J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.903984Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:16e8a972bce389a93e535a6f0ce0dd5af8454300817eacd6f5a7ea2525c1d964","observation_id":"383ed132-c92b-4b2f-8c8f-b953a0964e57","resolution":{"observed_at":"2026-08-04T07:12:23.903984Z","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":"2026-08-04T07:12:23.950919Z","title":"Martinsson and J","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:23.950919Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:100f0a29b1267195b66d094c6179a631cb16893f4f3779f6dd245a4961911494","observation_id":"a75c9785-7092-488c-a144-64fe77d16e38","resolution":{"observed_at":"2026-08-04T07:12:23.950919Z","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":"2026-08-04T07:12:24.041239Z","title":"Nakatsukasa and J","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.041239Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:cedbc73376b0a27910a7b2d59e736791c2b68b500dfd61bc9e53b6b87a58d59c","observation_id":"e99e2e5b-a98b-4211-8e39-0292ed5a6aaa","resolution":{"observed_at":"2026-08-04T07:12:24.041239Z","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":"2026-08-04T07:12:24.127217Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.127217Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:63f1819d4518128b2a865ee3a1c01183b9fa81b8f23bd3651b67be00250d457b","observation_id":"a83fc4ba-59f2-4785-93c7-04a1b2bd7d6a","resolution":{"observed_at":"2026-08-04T07:12:24.127217Z","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":"2026-08-04T07:12:24.210154Z","title":null,"venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.210154Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:7a562d7f9e24dd9e52c2d735eba8d75f4f63fc518b623d5e42f58c9d2e51a6ab","observation_id":"c837df9f-0c3d-4a4e-8b6f-06885d8ead46","resolution":{"observed_at":"2026-08-04T07:12:24.210154Z","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":"2026-08-04T07:12:24.293529Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.293529Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:d441a0e2f9adfa545e1677d7e36799549f7555885f8c1993ea578f2e057095a4","observation_id":"20c5b1f2-d567-4667-8bfc-37b5dae1e965","resolution":{"observed_at":"2026-08-04T07:12:24.293529Z","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":"2026-08-04T07:12:24.348368Z","title":"Sch¨ olkopf and A","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.348368Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:42e98f86397e750f413741f7d9218f983b3c4b33d05a3bb3e173801e9254c486","observation_id":"72efebbc-dd76-42e8-a7e8-352e220a5a61","resolution":{"observed_at":"2026-08-04T07:12:24.348368Z","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":"2026-08-04T07:12:24.435289Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.435289Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:fccb4b0101bbe41c311988eb2d8ad0576456fd3ae62198775a6982c1d5190d19","observation_id":"1d48bdcc-d8f6-454a-a98c-39d249629e0d","resolution":{"observed_at":"2026-08-04T07:12:24.435289Z","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":"2026-08-04T07:12:24.504124Z","title":"Temam.Infinite-dimensional dynamical systems in mechanics and physics","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.504124Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:bc6259c2c60a1e9e9876e9ef2f637c78ea36d293cb497ad6b2c53a20354cbdc9","observation_id":"ec7fe4f1-4b55-47e9-82f5-121c5e42e006","resolution":{"observed_at":"2026-08-04T07:12:24.504124Z","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":"2026-08-04T07:12:24.559405Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.559405Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:247b94d13ded7e8cca609274b8a2b9f9823dcdb61d2cd99c7dcf2ae00f9f0954","observation_id":"b6cd90ee-faaa-42cc-a13c-5d5317751d37","resolution":{"observed_at":"2026-08-04T07:12:24.559405Z","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":"2026-08-04T07:12:24.625751Z","title":"Udell and A","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.625751Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:82b0b2f393e1fdc7ff15294263712152924e912a6f61111acf7b5fc24b765a0e","observation_id":"03d90329-1b77-4f9d-aa7c-abb18c6a4a62","resolution":{"observed_at":"2026-08-04T07:12:24.625751Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07519","last_updated":"2026-03-16T16:31:13Z","snapshot_observed_at":"2026-08-07T15:47:52.586016Z","submitted_at":"2025-05-12T13:00:36Z","title":"Quantum mechanical closure of partial differential equations with symmetries","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.07519","snapshot_observed_at":"2026-08-04T07:12:24.675622Z","title":"Vales, D","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.675622Z"},"links":{"cited_paper":"/paper/2505.07519","citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:4318e451344986b22d610481f9c48db970597cef9cdf5c727db90e1a010a7a3e","observation_id":"2facb92a-4028-4ebb-94db-697826b7e1e2","resolution":{"observed_at":"2026-08-04T07:12:24.675622Z","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":"2026-08-04T07:12:24.737018Z","title":"Von Luxburg","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.737018Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:6cb88bb6f4c4e94824c04581c0d7e3642ab147f36c87d7e438e74df116c9d5e1","observation_id":"b31ce40c-7ef9-48b9-bfcd-bad3ca558e2f","resolution":{"observed_at":"2026-08-04T07:12:24.737018Z","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":"2026-08-04T07:12:24.791079Z","title":"Williams, M","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.791079Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:54a9ae3dc0b04603f3207130a22e3313e5fedb1035ca05067b80813f40defd48","observation_id":"0da8ecaa-a2c8-4f4e-b431-c771a4e6c1bb","resolution":{"observed_at":"2026-08-04T07:12:24.791079Z","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":"2026-08-04T07:12:24.844427Z","title":"Zelnik-Manor and P","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation","version":3},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-04T07:12:24.844427Z"},"links":{"citing_paper":"/paper/2510.26574"},"observation_digest":"sha256:ab8e9d7b6c4bbc7aa27c4c5d5bc614db6109099b6594198fed037f6a89f7faee","observation_id":"4173c763-bec4-41de-a915-c78cc55fa5a2","resolution":{"observed_at":"2026-08-04T07:12:24.844427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.26574","last_updated":"2026-06-27T16:33:03Z","latest_version":3,"primary_category":"math.NA","snapshot_observed_at":"2026-08-08T11:07:56.354299Z","submitted_at":"2025-10-30T15:01:19Z","title":"Accelerated decomposition of bistochastic kernel matrices by low rank approximation"},"reference_resolution":{"displayed":54,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":54,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":54},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 1 inbound Pith citation observation for arXiv:2510.26574."}