{"as_of":"2026-08-14T08:51:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fa07faf8a0ca94dd47a07c5066f49108b668009953d0fb5f0646b1240f13172f","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T21:26:32.326207Z","state":"measured"},{"denominator":13,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":13,"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":"2026-08-06T20:52:49.340628Z","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":"2026-08-06T20:52:50.570941Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"cited_work":{"arxiv_id":"2507.00771","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.00771","snapshot_observed_at":"2026-08-06T20:52:50.570941Z","title":"Generic vanishing theory in positive characteristic","venue":"math.AG","work_id":"b2a2bce9-9d12-447f-b5ef-47fcbe072a5a","year":2025},"citing_paper":{"arxiv_id":"2507.01797","last_updated":"2025-07-02T15:19:23Z","snapshot_observed_at":"2026-08-10T00:44:36.781528Z","submitted_at":"2025-07-02T15:19:23Z","title":"On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:52:49.340628Z"},"links":{"cited_paper":"/paper/2507.00771","citing_paper":"/paper/2507.01797"},"observation_digest":"sha256:15ee76566bd0de9b6fa5525301d83d20209bf24a8073ce477263828b6bc637cf","observation_id":"884e2fe1-cbd9-4336-a203-39ee567f78d0","resolution":{"observed_at":"2026-08-06T20:52:50.670993Z","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/2507.00771/citation-record","integrity":"/paper/2507.00771/integrity","json":"/paper/2507.00771/citation-record.json","paper":"/paper/2507.00771"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.01797","last_updated":"2025-07-02T15:19:23Z","snapshot_observed_at":"2026-08-10T00:44:36.781528Z","submitted_at":"2025-07-02T15:19:23Z","title":"On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension","version":1},"cited_work":{"arxiv_id":"2507.01797","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.01797","snapshot_observed_at":"2026-08-06T21:26:32.608892Z","title":"On the Euler characteristic of weakly ordinary varieties of maximal Albanese dimension","venue":"math.AG","work_id":"92711770-0b72-4d90-97ba-508bd0482ea7","year":2025},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:31.900827Z"},"links":{"cited_paper":"/paper/2507.01797","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:b81a749498452b732e4935afa3ccba040287e45d032bdb3b8965e8a4f593e4f5","observation_id":"7594ad7f-b235-4fdd-8795-c8894965aa45","resolution":{"observed_at":"2026-08-06T21:26:32.644761Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2312.13456","last_updated":"2026-05-24T14:45:58Z","snapshot_observed_at":"2026-08-13T04:57:15.801431Z","submitted_at":"2023-12-20T22:15:19Z","title":"The Frobenius--stable version of the Grauert--Riemenschneider vanishing theorem fails","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.13456","snapshot_observed_at":"2026-08-06T21:26:31.925841Z","title":"[Bha12] B","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:31.925841Z"},"links":{"cited_paper":"/paper/2312.13456","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:86798c77d81176a9a6d70f591453f545b832013844a5b057cea8fd477e2e53f0","observation_id":"55edb1d9-37fe-4ec6-89f8-365091ad19d7","resolution":{"observed_at":"2026-08-06T21:26:31.925841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.15491","last_updated":"2026-07-01T15:16:13Z","snapshot_observed_at":"2026-08-13T05:58:27.772052Z","submitted_at":"2025-06-18T14:28:25Z","title":"On Gorenstein $\\mathbb{Q}_p$-rational threefold and fourfold singularities","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.15491","snapshot_observed_at":"2026-08-06T21:26:31.992066Z","title":"[BS13] Manuel Blickle and Karl Schwede.p −1-linear maps in algebra and geometry","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:31.992066Z"},"links":{"cited_paper":"/paper/2506.15491","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:658bb850f42ea676b7c14c2b491f262a52b1dd64290b1693bd51a3726b9032d0","observation_id":"378717bf-4f32-4334-84ce-b12c872e1d23","resolution":{"observed_at":"2026-08-06T21:26:31.992066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.02157","last_updated":"2023-05-03T14:45:44Z","snapshot_observed_at":"2026-08-13T11:50:02.933916Z","submitted_at":"2023-05-03T14:45:44Z","title":"The Demailly--Peternell--Schneider conjecture is true in positive characteristic","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.02157","snapshot_observed_at":"2026-08-06T21:26:32.085624Z","title":"[Fil18] S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.085624Z"},"links":{"cited_paper":"/paper/2305.02157","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:be9848d9b6ffa46b9e255f36cb6b1e6a2354576042fc84e2628701e7b6c80231","observation_id":"909ebb89-85b3-45ae-b591-78f3efda5bf9","resolution":{"observed_at":"2026-08-06T21:26:32.085624Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:33.153077Z","title":null,"venue":null,"work_id":"86ee6341-0d88-4a54-a1b9-2ac5fa6224f2","year":2018},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.224529Z"},"links":{"citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:9a4ab3b3d0883c7e740bc08a23c2d195226bce13e8f45b2ff86cab73de40cb41","observation_id":"498f27a8-e7f1-44d9-a567-57b5102a4b4b","resolution":{"observed_at":"2026-08-06T21:26:33.227414Z","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":"2026-08-06T21:26:33.304063Z","title":"[HP02] C","venue":null,"work_id":"668fbd29-740c-4257-baca-750e0cec089b","year":1987},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":1989,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.177383Z"},"links":{"citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:211c85af6aeb1ee8c53b06710b0d6f83822f33d3f0899cd320cf52fa11173712","observation_id":"11fb567a-8998-40c2-a8bc-2e60bdcaafc7","resolution":{"observed_at":"2026-08-06T21:26:33.336637Z","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":"2026-08-06T21:26:32.980561Z","title":null,"venue":null,"work_id":"534bbf21-5c48-4c9d-9231-7282176c77de","year":1974},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2008,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.287269Z"},"links":{"citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:75ac289f785dd89350eeebf1f46bc13dbf73ba81f2cd30c29804b255510303bb","observation_id":"3cdbdb99-540d-4b3a-b906-391302cc980b","resolution":{"observed_at":"2026-08-06T21:26:33.068754Z","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":"2026-08-06T21:26:33.420257Z","title":null,"venue":null,"work_id":"a0875862-9cc5-4639-8d4f-9fd75099bfdd","year":1982},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.131443Z"},"links":{"citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:c58ec97e62edae94bb8be93f02646d3a2f322b00fc9641fdf4cd4398ca22f4e1","observation_id":"8ce2a4a0-d248-484d-9d0b-229b4127aca1","resolution":{"observed_at":"2026-08-06T21:26:33.478599Z","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":"2212.09245","last_updated":"2023-05-15T00:36:14Z","snapshot_observed_at":"2026-08-13T13:19:16.737492Z","submitted_at":"2022-12-19T04:37:20Z","title":"Numerical Kodaira dimension of algebraic fiber spaces in positive characteristic","version":3},"cited_work":{"arxiv_id":"2212.09245","doi":null,"metadata_source":"pith","pith_arxiv_id":"2212.09245","snapshot_observed_at":"2026-08-06T21:26:32.492361Z","title":"Numerical Kodaira dimension of algebraic fiber spaces in positive characteristic","venue":"math.AG","work_id":"07aee97d-1e2a-4751-91ad-94fe591b77f3","year":2022},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2022,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.045343Z"},"links":{"cited_paper":"/paper/2212.09245","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:e0a63cfbd666eb102cf608fcc68267b78dff52204ee3b4bf867306a360eba0cd","observation_id":"b2cb0717-b327-4161-b9b7-1ee0f5034337","resolution":{"observed_at":"2026-08-06T21:26:32.519259Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2306.05378","last_updated":"2025-06-16T10:32:15Z","snapshot_observed_at":"2026-08-13T11:20:54.021283Z","submitted_at":"2023-06-08T17:17:23Z","title":"Duality between Cartier crystals and perverse $\\mathbb{F}_p$-sheaves, and application to generic vanishing","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2306.05378","snapshot_observed_at":"2026-08-06T21:26:31.832347Z","title":"[Bau25a] J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:31.832347Z"},"links":{"cited_paper":"/paper/2306.05378","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:cee66090b7dc9e9fc64c9fb0932b7fc998f005b73c138b5c6438c133cb020f55","observation_id":"63bb1b71-f216-4320-a76e-9e5e9f41b681","resolution":{"observed_at":"2026-08-06T21:26:31.832347Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.02608","last_updated":"2024-08-20T18:29:50Z","snapshot_observed_at":"2026-08-12T23:30:08.210142Z","submitted_at":"2024-07-02T18:50:55Z","title":"Terminal 3-folds that are not Cohen-Macaulay","version":2},"cited_work":{"arxiv_id":"2407.02608","doi":null,"metadata_source":"pith","pith_arxiv_id":"2407.02608","snapshot_observed_at":"2026-08-06T21:26:32.374725Z","title":"Terminal 3-folds that are not Cohen-Macaulay","venue":"math.AG","work_id":"ce215f8a-ac72-48e7-8ea5-f31714a960ec","year":2024},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2024,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:32.326207Z"},"links":{"cited_paper":"/paper/2407.02608","citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:13e4afa220eb76ce26a5594da7cdb0483decd1e9dadefd42453e42f8569e0751","observation_id":"e173194c-94c0-4a34-be6e-00e2203c8407","resolution":{"observed_at":"2026-08-06T21:26:32.438853Z","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"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2510.19706","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T21:26:32.800405Z","title":"[Bau25b] J","venue":null,"work_id":"f24a522b-af01-40af-a85b-ef589267b95e","year":null},"citing_paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic","version":2},"reference_index":2025,"source":"pdf_text","source_observed_at":"2026-08-06T21:26:31.866752Z"},"links":{"citing_paper":"/paper/2507.00771"},"observation_digest":"sha256:84eddb5c903268d57d068202a9d23b761694838a0c59ace08f58b683777f0796","observation_id":"af0493f0-fb6d-460c-8a70-8e6c4d938533","resolution":{"observed_at":"2026-08-06T21:26:32.887153Z","resolver_source":"raw_fallback","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"}}],"paper":{"arxiv_id":"2507.00771","last_updated":"2026-06-16T22:06:24Z","latest_version":2,"primary_category":"math.AG","snapshot_observed_at":"2026-08-09T18:45:45.697183Z","submitted_at":"2025-07-01T14:11:42Z","title":"Generic vanishing theory in positive characteristic"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":7,"verified_exact":4,"verified_fuzzy":1},"total_outbound_references":12},"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 12 of 12 outbound references and 1 inbound Pith citation observation for arXiv:2507.00771."}