{"as_of":"2026-08-14T14:24:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:c4261683c39f811d49e005476f60f92b054b16af7f86738c625f1c754514af3d","coverage":[{"denominator":35,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":35,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-04T11:57:44.182927Z","state":"measured"},{"denominator":36,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":36,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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":"2026-08-11T04:18:41.039692Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-11T04:18:41.341338Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"cited_work":{"arxiv_id":"2510.03670","doi":null,"metadata_source":"pith","pith_arxiv_id":"2510.03670","snapshot_observed_at":"2026-08-11T04:18:41.341338Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","venue":"math.NA","work_id":"21edf473-4544-480e-aa07-e4c128c5141b","year":2025},"citing_paper":{"arxiv_id":"2608.07798","last_updated":"2026-08-07T22:41:56Z","snapshot_observed_at":"2026-08-13T23:21:20.345455Z","submitted_at":"2026-08-07T22:41:56Z","title":"A splitting mixed finite element method for a stochastic Keller-Segel system with multiplicative noise","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T04:18:41.039692Z"},"links":{"cited_paper":"/paper/2510.03670","citing_paper":"/paper/2608.07798"},"observation_digest":"sha256:0a8934900b817f85fb8f9f8450481a1382e7580aa8a0870c3cac00e8b3a0cb97","observation_id":"26c93638-5afe-40ec-ad31-fc9ddd95198e","resolution":{"observed_at":"2026-08-11T04:18:41.349321Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2510.03670/citation-record","integrity":"/paper/2510.03670/integrity","json":"/paper/2510.03670/citation-record.json","paper":"/paper/2510.03670"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-04T11:57:44.040586Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.040586Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:fa81db2fe322cde8b647e0422ff8d3e3772820a1a3a76a32bf19a6c2022afb48","observation_id":"4f36a179-3f4d-46a2-b43b-0e8cc1165e61","resolution":{"observed_at":"2026-08-04T11:57:44.040586Z","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":"2026-08-04T11:57:44.045836Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.045836Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:e9a32dffa644a334c90c5376bee7669e7279de637b185173f1b6c1e2761ca7a3","observation_id":"bb4f6f37-1aaa-4360-98d0-a25952b56741","resolution":{"observed_at":"2026-08-04T11:57:44.045836Z","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":"2026-08-04T11:57:44.050273Z","title":"Akrivis and Y.-s","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.050273Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:3ad0d1ba81f26eb65db3d7f7156e2f61977ef37a037669647b71147179b4c272","observation_id":"e74608c3-49fb-4fb2-b189-d463c9ad0481","resolution":{"observed_at":"2026-08-04T11:57:44.050273Z","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":"2026-08-04T11:57:44.054766Z","title":"Anders, M","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.054766Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:f27cbd62d2b771d2a445664fc41e732de9978141d0e0064fc9cab90c18647b59","observation_id":"4b5210b8-caca-4084-9f34-ce17debb2723","resolution":{"observed_at":"2026-08-04T11:57:44.054766Z","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":"2026-08-04T11:57:44.059194Z","title":null,"venue":null,"work_id":null,"year":1988},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.059194Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:f1f5739dd6e157e4df3cbef45972077311dc4757a589f5add7e11cbf8d1abf1b","observation_id":"05527a79-6a5e-4e6c-ac2c-6aba8969f96e","resolution":{"observed_at":"2026-08-04T11:57:44.059194Z","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":"2026-08-04T11:57:44.063381Z","title":"Bessaih and A","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.063381Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:087b39eaae0191e6c05eb33be635fb3647d57bf556038ddac49b3cefd0957a10","observation_id":"5798fb9d-7b61-4721-9b2b-8101be9212ad","resolution":{"observed_at":"2026-08-04T11:57:44.063381Z","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":"2026-08-04T11:57:44.068124Z","title":"Breit and A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.068124Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:80599cd52dce23e8f6cae037417972a31253deae80b2778b0d98773d97b0c6d9","observation_id":"12018b6e-0ff5-4605-bd8a-354a36cc5c91","resolution":{"observed_at":"2026-08-04T11:57:44.068124Z","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":"2026-08-04T11:57:44.072287Z","title":"Carelli and A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.072287Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:6aac9150b324af0820a32f5f599ee63f46e38fbab8c416cba8fc77443f6b48e7","observation_id":"b52fffe9-62e2-4360-ac6e-0e8b884912e3","resolution":{"observed_at":"2026-08-04T11:57:44.072287Z","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":"2026-08-04T11:57:44.076928Z","title":null,"venue":null,"work_id":null,"year":1976},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.076928Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:19ab5ca69a2dcb501f022a8e1ce4c46059ef72cfd16027eff625d94611329d88","observation_id":"331391a7-6dda-4b81-bec1-602d8d3ce98c","resolution":{"observed_at":"2026-08-04T11:57:44.076928Z","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":"2026-08-04T11:57:44.080722Z","title":"Collet, J.-P","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.080722Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:80babeafa53240600be068b35c9be6c5a21968df00a98eb7caeade0790f89b14","observation_id":"2616f962-b976-4424-a8fd-73fc26a16d59","resolution":{"observed_at":"2026-08-04T11:57:44.080722Z","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":"2026-08-04T11:57:44.085253Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.085253Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:4810f30d9b67bd9f01b4bce434c40392972b09befcc0df80a0368607988341a1","observation_id":"080168e6-70f4-44a8-bb2f-86965427c1b9","resolution":{"observed_at":"2026-08-04T11:57:44.085253Z","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":"2026-08-04T11:57:44.090361Z","title":null,"venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.090361Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:2c0971f9c0d5255d6d5e5debdfa93588d852fc9db1da103c8c374e81705b5d6f","observation_id":"282e3144-28f6-4419-a2df-32f7e078d8f0","resolution":{"observed_at":"2026-08-04T11:57:44.090361Z","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":"2026-08-04T11:57:44.094869Z","title":"Duan and V","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.094869Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:4cbe4d1fd9bf9e2f5ec46545ed55ab269b00dc7304018eda773fc10a67c3a779","observation_id":"5b058280-0f9b-40a4-bb85-b613a4cffa39","resolution":{"observed_at":"2026-08-04T11:57:44.094869Z","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":"2026-08-04T11:57:44.099714Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.099714Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:898407bfcb87d18742ed32860a47f35b366e86337d6afa11bba7c22ce0000355","observation_id":"897f3f29-8ac4-43f0-a57b-a6adf13a8ceb","resolution":{"observed_at":"2026-08-04T11:57:44.099714Z","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":"2026-08-04T11:57:44.103728Z","title":"Feng and L","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.103728Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:9eb2fddc56385d0cf8ab29f4550a9f74cc56a0230e6c8cd408ac3db3b9cb8ecd","observation_id":"f5fdd193-868d-44e6-a5f4-4e7308b08333","resolution":{"observed_at":"2026-08-04T11:57:44.103728Z","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":"2026-08-04T11:57:44.109081Z","title":"Feng and L","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.109081Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:edba80243f81d40e9950d6e87b60934c71005352a2c4896bdfc860450119168a","observation_id":"053f7291-3ed0-4885-abba-981d415fcb86","resolution":{"observed_at":"2026-08-04T11:57:44.109081Z","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":"2026-08-04T11:57:44.113199Z","title":"Ferrario","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.113199Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:61702070a74922c178393249d647fde57204f51d26fb2fb196f8835d1b72be88","observation_id":"32132ab1-6701-47c1-b3bd-8bf3568c0e14","resolution":{"observed_at":"2026-08-04T11:57:44.113199Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2508.01794","last_updated":"2026-08-03T03:00:14Z","snapshot_observed_at":"2026-08-06T23:27:50.587765Z","submitted_at":"2025-08-03T15:11:48Z","title":"Exponential mixing for the stochastic Kuramoto-Sivashinsky equation on the 1D torus","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2508.01794","snapshot_observed_at":"2026-08-04T11:57:44.117195Z","title":"Gao and H","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.117195Z"},"links":{"cited_paper":"/paper/2508.01794","citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:c277c6625beb07c8f773dd457715095e4b788b24c7bfd9dd8d17ff4203fa3b63","observation_id":"ad8ef26b-6c8b-43d5-aeb8-2e8d85b139c8","resolution":{"observed_at":"2026-08-04T11:57:44.117195Z","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":"2026-08-04T11:57:44.121344Z","title":null,"venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.121344Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:a310025a85533911f810dd838eccdf256e8bc4bb7611d652060e1456b64a4ad2","observation_id":"8861ca00-401d-4afc-910a-3f68107540cb","resolution":{"observed_at":"2026-08-04T11:57:44.121344Z","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":"2026-08-04T11:57:44.125159Z","title":"Khater and R","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.125159Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:67e144d1a16f6b6095cb00176e2af67d69317747f1b3f7f53381dfb895cec96e","observation_id":"4feacf6b-c8c4-4e09-a56f-2ae42173cde8","resolution":{"observed_at":"2026-08-04T11:57:44.125159Z","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":"2026-08-04T11:57:44.129286Z","title":"Kruse and M","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.129286Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:e1b71c92cfb282b77e9a50e60ce8d8dc3b5c0e3f9b77823e3ab95aaf640c6169","observation_id":"9c26057d-e3fd-475d-8aef-98b48a520548","resolution":{"observed_at":"2026-08-04T11:57:44.129286Z","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":"2026-08-04T11:57:44.133013Z","title":"Kuramoto","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.133013Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:50e87c96f0a06d00361e73decb322fd8c2eb9aba927889124e2d22377fb68268","observation_id":"8298828b-0cf5-49a3-85b5-ae3157ea9645","resolution":{"observed_at":"2026-08-04T11:57:44.133013Z","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":"2026-08-04T11:57:44.136862Z","title":null,"venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.136862Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:3b3b909b491a7e0af263ee7f5e60e663c0e147176e6724e60d1418735e0149c2","observation_id":"1ebeedcb-fa2c-4b1e-8883-daa0441184a5","resolution":{"observed_at":"2026-08-04T11:57:44.136862Z","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":"2026-08-04T11:57:44.140739Z","title":"Larios and V","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.140739Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:061a58428bcb8646baf77de8573f666626d82b681effc087942c73b9dc012594","observation_id":"4b3279e3-345f-41fc-96b0-32da0e45e524","resolution":{"observed_at":"2026-08-04T11:57:44.140739Z","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":"2026-08-04T11:57:44.144430Z","title":"Lopez-Marcos","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.144430Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:c2d3564b91d3533e3b26c4881caad14e05a349eed00d23b4c8a023c5bea923df","observation_id":"19caf69c-909c-4374-8010-8543af6dddf9","resolution":{"observed_at":"2026-08-04T11:57:44.144430Z","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":"2026-08-04T11:57:44.148088Z","title":"Mackenzie and A","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.148088Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:e0c7e0d42e32bb72281129c7e409f4d7c3f808a8add251e760f2227aaabc3ef1","observation_id":"340c8eb8-0254-4341-b556-4c5adcb383b6","resolution":{"observed_at":"2026-08-04T11:57:44.148088Z","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":"2026-08-04T11:57:44.151897Z","title":"Manickam, K","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.151897Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:97e087aeea3cbe51741f947ff457734232ec3f6682dc8f8d3d144576cc39186e","observation_id":"50c0a888-6add-4849-bb3f-2a2c478bdec4","resolution":{"observed_at":"2026-08-04T11:57:44.151897Z","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":"2026-08-04T11:57:44.155585Z","title":null,"venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.155585Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:ac2133f1c64289766b7b152e95fc440a4565ee0c0d3cbd55efaadf0a5eac5d73","observation_id":"6aa122da-3275-4c6d-b232-600a45ccb361","resolution":{"observed_at":"2026-08-04T11:57:44.155585Z","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":"2026-08-04T11:57:44.159995Z","title":"Nicolaenko, B","venue":null,"work_id":null,"year":1985},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.159995Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:ba6ac35ddb560a0bbef091645146c24a6ba62220eb6409f19b883ec0d6962e29","observation_id":"fa50112e-149c-47d2-8d32-32e2b5428649","resolution":{"observed_at":"2026-08-04T11:57:44.159995Z","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":"2026-08-04T11:57:44.163832Z","title":"Printems","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.163832Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:c4e7138cc13af0896753beb8fd2d3ab804634570f5949da681280d287e25c910","observation_id":"f506d1dd-b04f-4900-b1be-7a04e3d1d5f5","resolution":{"observed_at":"2026-08-04T11:57:44.163832Z","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":"2026-08-04T11:57:44.167612Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.167612Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:5ee3772776e6c14febc24e920f253a6b930b6c693ea5bd1fe785db35cca24258","observation_id":"12643048-4728-415b-9c56-234d3ad281d7","resolution":{"observed_at":"2026-08-04T11:57:44.167612Z","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":"2026-08-04T11:57:44.171523Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.171523Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:e38cb56d4b679eafc200519e11e51e65960aabb7e5b31ebb58f4d58ab41f81cd","observation_id":"6117fe20-1a09-411d-8830-6a3bc7a77c89","resolution":{"observed_at":"2026-08-04T11:57:44.171523Z","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":"2026-08-04T11:57:44.175223Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.175223Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:cb15bbe9a6e8f26f1f3d6146583b96441c9cb893f5967e754d3db68e78e1887a","observation_id":"0475e9b2-2818-4a39-96fb-9d982d09b3b8","resolution":{"observed_at":"2026-08-04T11:57:44.175223Z","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":"2026-08-04T11:57:44.179209Z","title":"Wu, S.-b","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.179209Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:96422ecd37a221b709218cc81b42d53b08ef2933f7e20cf781905463fec87d52","observation_id":"50ec82f5-3300-4dbe-89ad-10a50229dd80","resolution":{"observed_at":"2026-08-04T11:57:44.179209Z","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":"2026-08-04T11:57:44.182927Z","title":"Xu and C.-W","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-04T11:57:44.182927Z"},"links":{"citing_paper":"/paper/2510.03670"},"observation_digest":"sha256:8564bf6d33c341d1ff092ed867e5d9504049bf9ce8fec1198c0504b9f6b6c394","observation_id":"3d6029d0-1294-425f-bf48-402da4859cf6","resolution":{"observed_at":"2026-08-04T11:57:44.182927Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2510.03670","last_updated":"2026-07-29T01:35:23Z","latest_version":3,"primary_category":"math.NA","snapshot_observed_at":"2026-08-06T22:54:09.637418Z","submitted_at":"2025-10-04T04:52:04Z","title":"Fully discrete finite element methods for the stochastic Kuramoto-Sivashinsky equation with multiplicative noise"},"reference_resolution":{"displayed":35,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":35,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":35},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 1 inbound Pith citation observation for arXiv:2510.03670."}