{"as_of":"2026-08-15T17:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ddf280aa996de705171b7eaabe009cee2d92a2a04e6e271a03369727785f861c","coverage":[{"denominator":23,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":23,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T21:17:57.954454Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2411.09058/citation-record","integrity":"/paper/2411.09058/integrity","json":"/paper/2411.09058/citation-record.json","paper":"/paper/2411.09058"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:17:58.343820Z","title":"Averaging 2d stochastic wave equation","venue":null,"work_id":"afc1a82b-2b18-488e-b873-dbda21ee64b1","year":2021},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.842809Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:372d19e95bd1a99e06d4f6ca81bc941dda49a37d8cbdc6f61b00b910c100e706","observation_id":"5992c64b-288c-492c-b80e-21bd600d5096","resolution":{"observed_at":"2026-08-12T21:17:58.349384Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.325372Z","title":"Central limit theorems for spatial averages of the stochastic heat equation via M alliavin- S tein's method","venue":null,"work_id":"e7667cb5-a11c-45a4-96db-6c86ac6ad20f","year":2023},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.848541Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:de0e8798a91903b60167ead2610eb25a176a81006a521a54e27652d32753eab6","observation_id":"f620acf9-bbaa-4045-81a8-1a1fa0f2e2e2","resolution":{"observed_at":"2026-08-12T21:17:58.330873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.309487Z","title":"Universality in marginally relevant disordered systems","venue":null,"work_id":"afcd9ada-356c-4f28-9edc-61502274884b","year":2017},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.853416Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:65e2bf95e15e34319c73f392729f799fb84edac1f6f27175912f238e2e70b599","observation_id":"e3252826-3023-4fe8-b171-d18de1934167","resolution":{"observed_at":"2026-08-12T21:17:58.314529Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.292686Z","title":"The critical 2d stochastic heat flow","venue":null,"work_id":"a355a7a7-e3a1-4888-af8b-27cb8babd707","year":2023},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.858687Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:866beff824b978c42aef60fa7b08d889b71bff568b323c6ace39169fa4255582","observation_id":"b8465e41-93f7-4e35-af4a-6629ac1bae51","resolution":{"observed_at":"2026-08-12T21:17:58.298391Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.276740Z","title":null,"venue":null,"work_id":"ac70e9b0-b810-4e72-ba75-a776f5edc792","year":1999},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.864472Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:59d485e114cfa6915422a1b84f2354abb1a394c7836b81f4c0f8c589cc288483","observation_id":"fb25e30c-7da4-4428-91e0-e3ea5ba94c1c","resolution":{"observed_at":"2026-08-12T21:17:58.281345Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.11380","last_updated":"2025-03-12T12:59:29Z","snapshot_observed_at":"2026-08-13T18:05:59.443457Z","submitted_at":"2021-09-23T13:51:22Z","title":"Flow equation approach to singular stochastic PDEs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2109.11380","snapshot_observed_at":"2026-08-12T21:17:57.870967Z","title":"Flow equation approach to singular stochastic pdes","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.870967Z"},"links":{"cited_paper":"/paper/2109.11380","citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:8bb16bdbb511b4a27b7aabf1a595d7df14e55ee141106cbd7d1c86577eaa79de","observation_id":"86c4fa4a-a17b-4567-a79b-06236afab351","resolution":{"observed_at":"2026-08-12T21:17:57.870967Z","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":"2026-08-12T21:17:58.260828Z","title":"A Central Limit Theorem for the stochastic wave equation with fractional noise","venue":null,"work_id":"13ada591-22ac-4935-a55f-e491d2e6a732","year":2020},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.876906Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:6d0f2e4224e07069c01df0fb0af44ad2447108c71812d4126b3ac6fdbcb3c724","observation_id":"1ceaad64-4f65-48d5-82d5-c57ba42848e5","resolution":{"observed_at":"2026-08-12T21:17:58.265896Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2303.09811","last_updated":"2025-01-15T16:54:44Z","snapshot_observed_at":"2026-08-13T12:22:52.121380Z","submitted_at":"2023-03-17T07:43:26Z","title":"Fluctuations of stochastic PDEs with long-range correlations","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2303.09811","snapshot_observed_at":"2026-08-12T21:17:57.882597Z","title":"Fluctuations of stochastic pdes with long-range correlations","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.882597Z"},"links":{"cited_paper":"/paper/2303.09811","citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:e9b360d2d44395e5a694ca3e57e5159b56ed1e86469bbe2cb681b0bb19f1fc78","observation_id":"8a298717-ee55-43e4-9546-c8a552c8b705","resolution":{"observed_at":"2026-08-12T21:17:57.882597Z","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":"2026-08-12T21:17:57.887634Z","title":"Paracontrolled distributions and singular PDE s","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.887634Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:4179acd79ea24be5fd5a98bbd059c58aaee9404b69e684495ceba2a6d84ceb5e","observation_id":"010d1fe6-50f7-4a45-91c4-3320c19fabbf","resolution":{"observed_at":"2026-08-12T21:17:57.887634Z","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":"2026-08-12T21:17:58.234158Z","title":"Fluctuations of a nonlinear stochastic heat equation in dimensions three and higher","venue":null,"work_id":"f222a90c-ed13-4f67-820a-cab381667207","year":2020},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.892171Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:abc95068c839cb71c65d8db5c65cf4d4d30ec8f64fd5bfb564834669ad9ba27e","observation_id":"c56eea84-1782-4d5f-87c2-b6905008be4d","resolution":{"observed_at":"2026-08-12T21:17:58.239655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.217905Z","title":"urgen G\\","venue":null,"work_id":"8fd1ef4d-78aa-4d49-8681-16d4fba5c165","year":2015},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.897801Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:2c563112419eec462562bbd60034dc25bc47e9f6e97e1c7923707dd4057d5cd9","observation_id":"15c296ea-f0db-47c0-bce5-7b0297aad604","resolution":{"observed_at":"2026-08-12T21:17:58.222800Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-12T21:17:57.902525Z","title":"A theory of regularity structures","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.902525Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:b604d289da2788a17ecce8f9abea07ae75f292ba80b8272f2299102c56308dd4","observation_id":"c83c3603-e9e1-4d5d-9238-88978ac7aa6e","resolution":{"observed_at":"2026-08-12T21:17:57.902525Z","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":"2026-08-12T21:17:58.191510Z","title":"A central limit theorem for the stochastic heat equation","venue":null,"work_id":"1cb4b7a2-d235-4224-90b9-e3dc15f1c370","year":2020},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.907406Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:7a42df10b0475eb1b8ab6016a7a1a92922c3ff63db7d34a75438f455d35ce35d","observation_id":"91dd284c-8c25-4e07-99de-72602da6d750","resolution":{"observed_at":"2026-08-12T21:17:58.197051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.174955Z","title":"Gaussian fluctuations for the stochastic heat equation with colored noise","venue":null,"work_id":"0786c957-8d86-49df-98ba-e07f4df9aefe","year":2020},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.912720Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:ae88b044f55ba756c8c3721cfd5b46f6b2a0d91457b7108506205c0fe1ba8593","observation_id":"b3e66154-d869-494f-b934-2701029017bd","resolution":{"observed_at":"2026-08-12T21:17:58.180608Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.159782Z","title":"Foundations of Stochastic Differential Equations in Infinite Dimensional Spaces , volume 47 of CBMS-NSF Regional Conference Series in Applied Mathematics","venue":null,"work_id":"2bdc71af-ce1a-4e8f-b0be-cbf74f99b0bf","year":1984},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.917237Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:229610faee0de3d0dc83f54bd48b57e73660adcf3ffb96c55f04fdb5a2990c4b","observation_id":"7ebfca34-cfea-4c65-a546-5b2b6d3cdeaf","resolution":{"observed_at":"2026-08-12T21:17:58.164799Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.143986Z","title":"Limit theorems for time-dependent averages of nonlinear stochastic heat equations","venue":null,"work_id":"2c2d6542-ce15-4568-91ad-10083e95a558","year":2022},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.921529Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:aeb9cd613bf850a37375ead43c12df5b52848866ed7827cf9d2b51d46194a92c","observation_id":"08766887-e309-4cac-8ab6-8c49961cb8a7","resolution":{"observed_at":"2026-08-12T21:17:58.149149Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.126664Z","title":null,"venue":null,"work_id":"385b65eb-f7bc-415c-ae66-832bfbfe6550","year":1972},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.925842Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:3c654a8425b55d436ef37f10e0f4daf796a715bb419bd4ebdeccdb213ce4d89f","observation_id":"b8625a96-2f09-4eae-b457-30390d331b77","resolution":{"observed_at":"2026-08-12T21:17:58.132497Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.109465Z","title":"A singular parabolic A nderson model","venue":null,"work_id":"0b750e19-8886-40c6-8520-98d9b66ce8ef","year":2004},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.930120Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:5d70550e5f18020f8356cff9f3b7bcb90a6a2cd8d8eeb70b1d7d0403f653be8d","observation_id":"bc175f06-2c03-4aa8-96db-672dff6d8bbe","resolution":{"observed_at":"2026-08-12T21:17:58.114488Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.092715Z","title":"Spatial averages for the parabolic A nderson model driven by rough noise","venue":null,"work_id":"3b635c37-345b-49a0-8076-693700d543ac","year":2021},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.935502Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:bd209ad026d7db6f75249750ef77aae4e1d6ff75787b2ce096fca71ada3d463b","observation_id":"d5e9844d-74b1-41ff-ba73-7b1ee0578f31","resolution":{"observed_at":"2026-08-12T21:17:58.098093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.077624Z","title":"The M alliavin calculus and related topics","venue":null,"work_id":"631d58cd-9a06-4c9e-b4bb-b04072043a40","year":1995},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.940645Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:dfeaa163ca4d31b148cdf7f439f3843fe5090a6cc960b426d0c4da7eda7d8fed","observation_id":"eee71f00-928c-4728-995a-c4e56775c730","resolution":{"observed_at":"2026-08-12T21:17:58.082037Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.060795Z","title":"Quantitative central limit theorems for the parabolic A nderson model driven by colored noises","venue":null,"work_id":"35b77e6d-3bd9-476d-92f4-7e95214087b7","year":2022},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.945465Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:4678829b61f681814b7d501e23c7d5b847af13e3c06c12093d2d218f23015477","observation_id":"3981d785-e49d-46c4-a302-b124f4fd7233","resolution":{"observed_at":"2026-08-12T21:17:58.066725Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+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":"2026-08-12T21:17:58.041760Z","title":"Averaging G aussian functionals","venue":null,"work_id":"517752c1-cef0-4bba-bfa3-8a2a60222a0d","year":2020},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.950037Z"},"links":{"citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:8616900d46ab9a81c8182817c3718a9d633ceecd52246832954cae20147dcd56","observation_id":"63d0ed8e-3044-4a5b-bb00-24630c9cc4e3","resolution":{"observed_at":"2026-08-12T21:17:58.048552Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2103.11039","last_updated":"2024-03-26T20:23:42Z","snapshot_observed_at":"2026-08-13T19:54:59.277824Z","submitted_at":"2021-03-19T22:03:23Z","title":"A priori bounds for quasi-linear SPDEs in the full sub-critical regime","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2103.11039","snapshot_observed_at":"2026-08-12T21:17:57.954454Z","title":"A priori bounds for quasi-linear spdes in the full sub-critical regime","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation","version":2},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-12T21:17:57.954454Z"},"links":{"cited_paper":"/paper/2103.11039","citing_paper":"/paper/2411.09058"},"observation_digest":"sha256:3cd0b1785d5adc2176af3aeec8d1891fffa7ca915a341f0370fb95b760cb39a7","observation_id":"3f134c4e-0dca-48ca-85c5-899e2f265c3f","resolution":{"observed_at":"2026-08-12T21:17:57.954454Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2411.09058","last_updated":"2026-06-15T19:24:40Z","latest_version":2,"primary_category":"math.PR","snapshot_observed_at":"2026-08-15T12:00:23.823861Z","submitted_at":"2024-11-13T22:34:54Z","title":"Time-dependent averages of a critical long-range stochastic heat equation"},"reference_resolution":{"displayed":23,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":0,"verified_fuzzy":16},"total_outbound_references":23},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 23 of 23 outbound references and 0 inbound Pith citation observations for arXiv:2411.09058."}