{"as_of":"2026-08-15T01:44:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:237e12b6132fc15109eebf9f94338139578ddbd5be96eb7ee34f3c7a6c32c102","coverage":[{"denominator":38,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":38,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:48:39.253984Z","state":"measured"},{"denominator":40,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":40,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T18:30:18.520914Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-07-03T15:58:38.234754Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"cited_work":{"arxiv_id":"2507.07538","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07538","snapshot_observed_at":"2026-07-03T15:58:38.234754Z","title":null,"venue":null,"work_id":"bf7d1106-6ec8-42c1-8d1e-07ca85f54c84","year":null},"citing_paper":{"arxiv_id":"2606.12820","last_updated":"2026-06-11T02:34:08Z","snapshot_observed_at":"2026-08-06T14:22:03.611023Z","submitted_at":"2026-06-11T02:34:08Z","title":"Averaging principles for nonautonomous multiscale McKean-Vlasov stochastic systems","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-06-27T06:14:00.409291Z"},"links":{"cited_paper":"/paper/2507.07538","citing_paper":"/paper/2606.12820"},"observation_digest":"sha256:4655dc0c252a38f4d492127533935bd0226909c5a84c94052008fdbfdaeabb24","observation_id":"04cebb95-3006-4874-8932-e93fe06f74c9","resolution":{"observed_at":"2026-07-03T15:58:38.236075Z","resolver_source":"arxiv_id","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"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.07538","snapshot_observed_at":"2026-08-07T18:30:18.520914Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2608.06011","last_updated":"2026-08-06T13:15:33Z","snapshot_observed_at":"2026-08-14T01:21:24.109495Z","submitted_at":"2026-08-06T13:15:33Z","title":"Strong averaging principle for multiscale time-inhomogeneous SDEs with multiplicative $\\alpha$-stable noises","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-07T18:30:18.520914Z"},"links":{"cited_paper":"/paper/2507.07538","citing_paper":"/paper/2608.06011"},"observation_digest":"sha256:e280051203fb0fa651833cbb89ec695f209e98c90583668264448a2e2730e2f5","observation_id":"aa5ed481-07e3-469b-bfe8-fcbbd21d060e","resolution":{"observed_at":"2026-08-07T18:30:18.520914Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2507.07538/citation-record","integrity":"/paper/2507.07538/integrity","json":"/paper/2507.07538/citation-record.json","paper":"/paper/2507.07538"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:47.128178Z","title":null,"venue":null,"work_id":"d6d729b5-4e07-43ff-9025-46507b5c5df4","year":2017},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.351348Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:d93cb38438cad504e743c14a1993bccbca16afaec961d64c7688b3c335784c38","observation_id":"12cbc2ba-39c2-42b8-b975-20127bbcc44e","resolution":{"observed_at":"2026-08-06T18:48:47.200720Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.867057Z","title":"Bertram, J","venue":null,"work_id":"d1ec46d4-94e7-4871-8cf2-4a34c74cdcaf","year":2017},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.396412Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:c08731ca752c1c3ed5ea791351a6fbade03435bf3604d0e443489987ac098a91","observation_id":"790319dc-fa18-4f0d-b79b-f85038346c6f","resolution":{"observed_at":"2026-08-06T18:48:47.015456Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.769252Z","title":"Bogoliubov, Y.A","venue":null,"work_id":"b3d5d641-15d8-4e37-aa3b-cc058b0d7b37","year":1961},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.475458Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:18425e4ff30731e367f55d01ad09f046b781b78677ae7e4faf0b2d4a3b326b30","observation_id":"ece96972-01f8-46e1-84c6-35c738d7f0d6","resolution":{"observed_at":"2026-08-06T18:48:46.811114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.674987Z","title":"Bréhier, Strong and weak orders in averaging for SPDEs.Stochastic Process","venue":null,"work_id":"b77afb54-bc8c-48c2-a8ac-f185448f517d","year":2012},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.566170Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:8bb474f77727bbf4ea3f2538534b2616dc2bbd214dff38792fb0e2a9dd97795d","observation_id":"91533cbd-3fad-44a2-b494-11bae8215f59","resolution":{"observed_at":"2026-08-06T18:48:46.712503Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.496083Z","title":"Cerrai, A Khasminskii type averaging principle for stochastic reaction-diffusion equations.Ann","venue":null,"work_id":"3f194e31-1160-4e32-9798-a5f6a1778d90","year":2009},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.641488Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:3f5a95ffa00d9409f7e0532ae3ec66ae5a996323dd56f41a5db97f2d5d97cfbc","observation_id":"8207f9e3-e2bb-4198-9eef-47a758dfbd73","resolution":{"observed_at":"2026-08-06T18:48:46.613448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.315255Z","title":"Cerrai, M","venue":null,"work_id":"1ab9bd6b-edc8-418c-89a9-eba1f2e8d623","year":2009},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.727970Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:cb7231dc8d75779d037386cc2a678ac995e95f2ef313660331ee20cac7642c9c","observation_id":"b305698b-af3a-4b68-a632-dd48b337bc03","resolution":{"observed_at":"2026-08-06T18:48:46.374773Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:46.055720Z","title":"Cerrai, A","venue":null,"work_id":"14bbd375-d659-4a60-af0e-a3cecf83bf05","year":2017},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.797829Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:c17fa6e3907380c5c28a45c131024d5dfd0a11ebbb66189fcc0b003d18e67fca","observation_id":"6c6a144d-96b2-46a0-8277-e91a8ad74a09","resolution":{"observed_at":"2026-08-06T18:48:46.206429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:45.911750Z","title":null,"venue":null,"work_id":"372e525a-decc-467a-a7a1-0669d59c4d3f","year":2020},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:35.890876Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:8cddd0d2f33a21fe48c7d86724929a7d6e387358486e939cb4c6946490ece929","observation_id":"33532d44-a0f8-43b3-bcb9-810ba2559728","resolution":{"observed_at":"2026-08-06T18:48:45.956791Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:45.698954Z","title":"Cheng, Z","venue":null,"work_id":"22512726-2525-4d66-935f-618b70d00ba2","year":2021},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.029101Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:9435ccceb64bd17e805c401bde9d8d7db602cb82f8d33f6a1eafff3bfc1ca86e","observation_id":"4fa2f6c5-3038-40e8-ae9b-0d624ad2c596","resolution":{"observed_at":"2026-08-06T18:48:45.860414Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:45.429153Z","title":"Cheng and Z","venue":null,"work_id":"c499f31a-a700-4601-b615-d7bf4dd0bf50","year":2023},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.144289Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:18ecba645ee015317aec0ec035a6fb22f032e1e9d4ade43dfe0fd4953294bd24","observation_id":"a411216c-3162-4a25-917a-12d7b97ef02f","resolution":{"observed_at":"2026-08-06T18:48:45.561571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:45.245549Z","title":"Da Prato, M","venue":null,"work_id":"b5635f52-576c-4b4a-ad3b-a9c4ddbc6b15","year":2006},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.237834Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:64a3f9190e172cb482191d1fbe31a627e759d694e23559e3140aa6104154a957","observation_id":"639dc575-631f-47b7-a898-ba50d0eda8c0","resolution":{"observed_at":"2026-08-06T18:48:45.320834Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:44.970698Z","title":"Da Prato, M","venue":null,"work_id":"070bc397-7331-4262-a142-482971f96efd","year":2008},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.376686Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:5eb1a9bea30502f6bf3fb30f63dc167a7dd0bd8ba42f8413c283875b5db0d4c9","observation_id":"884806ea-7762-4c77-b57c-963df5f7f8e5","resolution":{"observed_at":"2026-08-06T18:48:45.122691Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:44.706939Z","title":"Da Prato and C","venue":null,"work_id":"18f383c6-559d-43a7-a6d6-6b0e4817da9d","year":1995},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.463710Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:c17aa02e285b3040f5a49f5be747498a5162e5483a84ff4d050619ef24a202f8","observation_id":"816c3037-ecd3-45cb-a883-a4de1b9a2032","resolution":{"observed_at":"2026-08-06T18:48:44.846862Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:44.524977Z","title":null,"venue":null,"work_id":"d47a9967-55e0-4119-9d19-78dd196a2fc5","year":2014},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.582053Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:cd8140d0c76a287c4125bde8591ebbf01a527d83cb2c7efc1d810d74f8add5a7","observation_id":"54ffe656-524f-4c34-8b36-982ad2ce28c1","resolution":{"observed_at":"2026-08-06T18:48:44.612032Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:44.405725Z","title":null,"venue":null,"work_id":"a0cf5b43-9193-401e-b5e7-aaa5804ea7b4","year":2018},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.703545Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:c909eaf839adc03a526520412e1c6cd2a7d29c461f84894adf25678e1defd73a","observation_id":"917756b6-19f3-4283-9d27-ff9129d4f400","resolution":{"observed_at":"2026-08-06T18:48:44.468577Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:44.182723Z","title":"E, and B","venue":null,"work_id":"871ac239-8a86-4f4c-afd5-2fbace43aaac","year":2003},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.820080Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:42c576e239463b797df41b8991d4ae0862a10134232734529fe6d2cc217024ec","observation_id":"e34a2cf0-3ea8-426a-98b7-e3648f682201","resolution":{"observed_at":"2026-08-06T18:48:44.292213Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:43.956813Z","title":"Freidlin, A.D","venue":null,"work_id":"5cba4785-ebd7-43ac-a50d-0e2b7c9cfe22","year":null},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:36.937353Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:116d8bdb6ffe30d35d2a92003c1388f8018caf84a5818520dcfdcb56c15c19f8","observation_id":"f7f6d9dc-fb0e-4435-91f2-dcf3515fd661","resolution":{"observed_at":"2026-08-06T18:48:44.075854Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:43.701233Z","title":null,"venue":null,"work_id":"5ae6c66d-ecf5-44ad-864d-d325cdf0468b","year":2015},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.086691Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:ea9ba655cfda3ef299aae6a9e9ccc14d5a5e4036f920ce338e70c7388337a383","observation_id":"b94eb8af-1e95-45a4-9e4c-8e176f9c5bdf","resolution":{"observed_at":"2026-08-06T18:48:43.802718Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:43.441560Z","title":"Galtier, G","venue":null,"work_id":"6d48e739-67bd-46f2-96d0-d66572b0513b","year":2012},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.184200Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:e1f58e02c705a0883d0889411b7a5d89cde226f8091f9dc93f7a0711dcc67aa0","observation_id":"f086b82c-03f2-4028-8342-af5ccc916303","resolution":{"observed_at":"2026-08-06T18:48:43.637776Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:43.159110Z","title":null,"venue":null,"work_id":"13949458-a0a6-410b-8892-08ee48702100","year":2025},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.334357Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:ee3aa0ddc09c4a148ca1ffb6f17792d5cce9712ab8b728ed932c9f95717a31d4","observation_id":"b545bc2f-e90f-4f56-9bb5-dcca3438bf27","resolution":{"observed_at":"2026-08-06T18:48:43.293660Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:42.932155Z","title":"Khasminskii, On the principle of averaging the Itô stochastic differential equations.Kibernetica4 (1968), 260-279","venue":null,"work_id":"09293cd0-a24e-463b-a664-9ca513078fdd","year":1968},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.443660Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:5a7533521ed8d0c49beff4a018c4c25a5dbad88af208982f5de1379c995411dd","observation_id":"35bcecc1-2c90-4d89-8c60-66ffa06e44b7","resolution":{"observed_at":"2026-08-06T18:48:43.017301Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:42.779346Z","title":null,"venue":null,"work_id":"87e37f9a-5126-4fa4-94b2-1f446dea98f3","year":2023},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.533088Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:a739f1d5ef420db135dfc8f05ad1e98bdd1d417370518e31cb84ab607b503d7b","observation_id":"14899cff-09ce-4f9d-879e-aa6f42f10382","resolution":{"observed_at":"2026-08-06T18:48:42.851271Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:42.513323Z","title":null,"venue":null,"work_id":"18ebf153-c6c7-4e34-b3ac-6f6c8381d5fc","year":2008},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.669318Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:f6872da12df9150c6a821c32d7f5d3bbcb1d0bd5d2121e07f8d5b2ef94d73f96","observation_id":"e08b0cf4-91e1-422d-86cf-dccbb2769f92","resolution":{"observed_at":"2026-08-06T18:48:42.644963Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:42.243215Z","title":null,"venue":null,"work_id":"550b4f9f-ff10-49ef-b523-d5b4c424ca13","year":2017},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.767671Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:5584f5a134b54802e834c78de7f7539cfa249a787d57f79efe63066a70dc844b","observation_id":"ceea17b2-d525-439a-8a17-10e27ece026c","resolution":{"observed_at":"2026-08-06T18:48:42.382324Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:42.047615Z","title":"Priola, J","venue":null,"work_id":"516f8d77-008c-4cc1-8973-6753913c8c07","year":2011},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.876101Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:0984829df87e12a6bd85aaa51dde4514c86555d81c0490317484783d054850d0","observation_id":"5882b7d7-c3e3-4916-a771-1aa2a3078dbf","resolution":{"observed_at":"2026-08-06T18:48:42.108137Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:41.779649Z","title":"Priola, A","venue":null,"work_id":"b87f7335-5fb9-4b83-82d2-76f90df6c6a2","year":2012},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:37.977485Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:cf04e8d68bdb9df45237519d795d8ef94c63029632962002837d02a09982dabf","observation_id":"c4e39b65-6187-43a5-b8d3-a9e9d4730292","resolution":{"observed_at":"2026-08-06T18:48:41.930600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:41.546776Z","title":null,"venue":null,"work_id":"febf26fe-ed4a-413a-8ce2-80739ec183d9","year":2022},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.095346Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:78671720521b4898e33dc1bb3bd1a6f60930c220c6d4286431d98e32d99961b8","observation_id":"ca4a9c12-8bc2-475d-9834-016efb92bd5e","resolution":{"observed_at":"2026-08-06T18:48:41.665060Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":{"arxiv_id":"2412.09850","last_updated":"2024-12-13T04:39:58Z","snapshot_observed_at":"2026-08-14T05:11:50.802375Z","submitted_at":"2024-12-13T04:39:58Z","title":"Averaging principles for time-inhomogeneous multi-scale SDEs via nonautonomous Poisson equations","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.09850","snapshot_observed_at":"2026-08-06T18:48:38.224848Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.224848Z"},"links":{"cited_paper":"/paper/2412.09850","citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:0cc7d82d9f56e3d3b88ad947a77c3edff543939bb47b34cdcc70b6678a745a2e","observation_id":"fef26e99-47c6-4a3f-a7f2-250f3c6caae2","resolution":{"observed_at":"2026-08-06T18:48:38.224848Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.18558","last_updated":"2025-06-23T12:08:43Z","snapshot_observed_at":"2026-08-06T23:13:40.972713Z","submitted_at":"2025-06-23T12:08:43Z","title":"Averaging principles for time-inhomogeneous multi-scale SDEs with partially dissipative coefficients","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.18558","snapshot_observed_at":"2026-08-06T18:48:38.319815Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.319815Z"},"links":{"cited_paper":"/paper/2506.18558","citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:f67e844a6a0ae4463429d979c2ceee3afcad3bcb9766c4336c5ae95bab93761a","observation_id":"f35e3422-94fb-463b-bbd1-49d9be5dc416","resolution":{"observed_at":"2026-08-06T18:48:38.319815Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:41.331538Z","title":null,"venue":null,"work_id":"69efabee-4760-4a70-ba47-c10c3cbc28a9","year":2022},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.481680Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:e129792354192388122fe1019ce1b8b43dacaea52494baa153969933751f96e0","observation_id":"ee05d4c6-d191-45e5-989c-85774099010b","resolution":{"observed_at":"2026-08-06T18:48:41.471552Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:41.095650Z","title":"Sun and Y","venue":null,"work_id":"32cd1b05-dc36-4aab-ac77-331e8d6c9bd0","year":2023},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.622746Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:5e9f8d560ff814695910a62681fc4d125bdf164f0ccb235ce27400423fa61623","observation_id":"5bf9cf7e-c43e-443c-8801-dfb35323dcfc","resolution":{"observed_at":"2026-08-06T18:48:41.168601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:40.765929Z","title":"Sun and J","venue":null,"work_id":"9c431ad5-d9e4-435b-acd2-9fbb2421aa06","year":2020},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.692434Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:3a4add2ac2f580400433baf8a8d29cdf5717afdfadc7d9141d570cbc621985b4","observation_id":"c6d0beed-12a9-4888-a764-db6759022671","resolution":{"observed_at":"2026-08-06T18:48:40.924302Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:40.510715Z","title":"Uda, Averaging principle for stochastic differential equations in the random periodic regime,Stochastic Pro- cess","venue":null,"work_id":"ff149ce1-dc9b-4a25-8298-cb3ec6594664","year":2021},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.803769Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:dc14ca4c9d9d1a21bc9dd9fefea7b5c36972ed594589450fa18fd19bdc392ba7","observation_id":"d0d6b592-b6ca-4044-97f1-f14b15ecdaf8","resolution":{"observed_at":"2026-08-06T18:48:40.650871Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:40.301826Z","title":"Wainrib, Double averaging principle for periodically forced slow-fast stochastic systems,Electron","venue":null,"work_id":"b9439e72-d1f5-4098-bfa9-3a9cf30aef8d","year":2013},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.902160Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:734ab0a9f22e1cb2f920ec9c88aca511d73cffcaf18cb73127a9f488842b1594","observation_id":"0221a05c-d12b-4945-b500-73552ba1e64e","resolution":{"observed_at":"2026-08-06T18:48:40.389398Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:40.157443Z","title":"Wang, A.J","venue":null,"work_id":"7e7956bd-65bd-42bc-a874-f5a08f56b2e2","year":2012},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:38.986951Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:09b97a1cb85d4ef6ad7831b9ae70dd2b94d5d72be922ab289037952cf285a872","observation_id":"ba478c99-afa9-41b1-9d89-a1a544edce91","resolution":{"observed_at":"2026-08-06T18:48:40.215670Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:39.910152Z","title":null,"venue":null,"work_id":"106c2bb2-f8e7-40ec-8beb-c9d5187fecc3","year":2016},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:39.063999Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:801d9e6cac156a8147f310d71eff6fda7ec520c464424a1e3517624cb81043e6","observation_id":"8f08fdd8-370b-430d-8674-cdf219d3036a","resolution":{"observed_at":"2026-08-06T18:48:40.052878Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:39.652352Z","title":null,"venue":null,"work_id":"d6e8efe1-c0f6-4e2f-872c-ef34e476482b","year":2015},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:39.184720Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:51e276417fe7079d25d758b4c6a2af97b64447dee5d74ae86c7c3fcf1909a360","observation_id":"76ddec3c-5448-4ace-bb46-d64a93b2ec01","resolution":{"observed_at":"2026-08-06T18:48:39.758921Z","resolver_source":"raw_fallback","status":"unresolved"},"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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:48:39.455863Z","title":"Xu, Ergodicity of the stochastic real Ginzburg-Landau equation driven byα-stable noises.Stochastic Process","venue":null,"work_id":"ffab6b37-06ba-42ad-a5fb-f3db1b721bc9","year":2013},"citing_paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T18:48:39.253984Z"},"links":{"citing_paper":"/paper/2507.07538"},"observation_digest":"sha256:e2af83f05bee98c80216f0d8d568cd3e20eaf49929306f52108e5b9d532eb948","observation_id":"06610736-8f02-420e-9d00-66f6aeb5b36f","resolution":{"observed_at":"2026-08-06T18:48:39.525853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"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"}}],"paper":{"arxiv_id":"2507.07538","last_updated":"2025-07-10T08:34:26Z","latest_version":1,"primary_category":"math.PR","snapshot_observed_at":"2026-08-06T18:35:55.988048Z","submitted_at":"2025-07-10T08:34:26Z","title":"Strong averaging principle for nonautonomous slow-fast SPDEs driven by $\\alpha$-stable processes"},"reference_resolution":{"displayed":38,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":15,"verified_exact":0,"verified_fuzzy":23},"total_outbound_references":38},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 2 inbound Pith citation observations for arXiv:2507.07538."}