{"as_of":"2026-08-22T21:56:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:f42c99587fbc6b92476b4b0d9cfa6e5085c4226c56f877a518e8bf5a002a60d9","coverage":[{"denominator":60,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":60,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T05:46:44.255260Z","state":"measured"},{"denominator":62,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":62,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+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":"2026-08-06T14:55:04.236786Z","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":"2026-05-19T03:52:01.463854Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"cited_work":{"arxiv_id":"2504.20312","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.20312","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Ascher, K","venue":null,"work_id":"23c2ea64-e72d-4fe3-8847-d3a1d528214c","year":null},"citing_paper":{"arxiv_id":"2507.12623","last_updated":"2026-04-16T13:31:11Z","snapshot_observed_at":"2026-07-06T21:58:24.684254Z","submitted_at":"2025-07-16T20:37:05Z","title":"Remarks on two problems by Hassett","version":2},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-05-19T03:51:19.419133Z"},"links":{"cited_paper":"/paper/2504.20312","citing_paper":"/paper/2507.12623"},"observation_digest":"sha256:cae01126e00f6f7d4d753a8816367a57f31027cefa96d45f3f55d8a83f5c4310","observation_id":"62ae2e11-2efc-4245-884b-0db2e86e21b8","resolution":{"observed_at":"2026-05-19T03:52:01.465683Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.20312","snapshot_observed_at":"2026-08-06T14:55:04.236786Z","title":"Ascher, K","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.17633","last_updated":"2025-07-23T16:01:04Z","snapshot_observed_at":"2026-08-21T08:54:27.003863Z","submitted_at":"2025-07-23T16:01:04Z","title":"Normal stable degenerations of Noether-Horikawa surfaces","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T14:55:04.236786Z"},"links":{"cited_paper":"/paper/2504.20312","citing_paper":"/paper/2507.17633"},"observation_digest":"sha256:75c65628b187a6d855ab8cec8c98c2f560fb014bbc0e96d08f24c609cb4b4427","observation_id":"c142957d-01b4-4bc2-9f72-5fb8e211b4ba","resolution":{"observed_at":"2026-08-06T14:55:04.236786Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2504.20312/citation-record","integrity":"/paper/2504.20312/integrity","json":"/paper/2504.20312/citation-record.json","paper":"/paper/2504.20312"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2307.06522","last_updated":"2023-07-13T01:52:24Z","snapshot_observed_at":"2026-08-21T08:53:41.523650Z","submitted_at":"2023-07-13T01:52:24Z","title":"Moduli of boundary polarized Calabi-Yau pairs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.06522","snapshot_observed_at":"2026-08-16T05:46:43.723579Z","title":"Moduli of boundary polarized Calabi-Yau pairs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.723579Z"},"links":{"cited_paper":"/paper/2307.06522","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:a60caa88894ef74b281ceeba32cebc59912e84e55f77893781b99b1bd2575862","observation_id":"a8fea70c-7044-4892-afc1-cc8aaa04a22a","resolution":{"observed_at":"2026-08-16T05:46:43.723579Z","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":"2026-08-16T05:46:43.733113Z","title":"Reductivity of the automorphism group of K -polystable F ano varieties","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.733113Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:6bfdf4b2e06914e695764afcbb0bf019080e32b8a786ac1e93afc4bb5c43dfc2","observation_id":"25e39db7-be7c-4ece-a332-0f34f398b68f","resolution":{"observed_at":"2026-08-16T05:46:43.733113Z","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":"2026-08-16T05:46:45.508639Z","title":"Wall crossing for moduli of stable log pairs","venue":null,"work_id":"5906d1eb-f822-4803-bb41-6e588a052ec2","year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.739623Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:bdb2b7cbc5fd1f32f6cfab3a87f52bd89112b70ac81de7b00a1f367926788e47","observation_id":"d434f520-72a9-4a33-a408-2189f95a706c","resolution":{"observed_at":"2026-08-16T05:46:45.515228Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.489229Z","title":"Mirror symmetry and the classification of orbifold del P ezzo surfaces","venue":null,"work_id":"d2df07a4-52e4-4ac7-a806-2062b8d6986f","year":2016},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.747030Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:184bc2f431d55c15ca39b7522995147b6ee2ab3efa5ef5f715857a107d61422b","observation_id":"a744ee73-8ce5-481b-9977-04734ebbd77f","resolution":{"observed_at":"2026-08-16T05:46:45.495015Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.461331Z","title":"Geometry of algebraic curves: volume II with a contribution by Joseph Daniel Harris","venue":null,"work_id":"a673c3a0-dc67-4db0-b5ea-2848c0a8a05c","year":2011},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.753273Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:3d314721c2b08b22ddd4fa2f81473535d6723217129427f78bb06cad877e65b9","observation_id":"c4893887-7b26-4119-8372-bce25e10b6c8","resolution":{"observed_at":"2026-08-16T05:46:45.468176Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.759022Z","title":"K-moduli of curves on a quadric surface and K 3 surfaces","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.759022Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:f8769d8dc50162c9c5e8550168439ec6d0e8c8b3d01744b0240f1b41135e5a00","observation_id":"405bbb16-304e-4e8d-aa9e-576ca123e4ae","resolution":{"observed_at":"2026-08-16T05:46:43.759022Z","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":"2026-08-16T05:46:43.766000Z","title":"Wall crossing for K -moduli spaces of plane curves","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.766000Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:d328552dca42ffee66ef5c1de9d286cfde70cec2c80c22e8c20c63047d920845","observation_id":"d56d8236-d766-4740-b59b-0807b6b342d4","resolution":{"observed_at":"2026-08-16T05:46:43.766000Z","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":"2026-08-16T05:46:45.409475Z","title":"Singularities with G _m -action and the log minimal model program for M _g","venue":null,"work_id":"40b05201-fd8c-46c9-ae9a-904ceb7fb574","year":2016},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.772073Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:911e4e0abd00ab066d28992c6002daaf1cf04d313eba7c167512033db32d1a72","observation_id":"06832c6c-d7d6-4d0a-9ff1-f0b2f7a70224","resolution":{"observed_at":"2026-08-16T05:46:45.415642Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.386348Z","title":"Second flip in the H assett- K eel program: existence of good moduli spaces","venue":null,"work_id":"9c565c93-3b4d-44f0-a47a-44912ba9ab78","year":2017},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.778809Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:5450ec1f5a2051ddb72275e72295e76c69d0fe0defdbba7e7f4dac9a6c7e8515","observation_id":"8c0694c9-1679-4347-8cba-44ce61e3364c","resolution":{"observed_at":"2026-08-16T05:46:45.392923Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.356673Z","title":"Second flip in the H assett- K eel program: projectivity","venue":null,"work_id":"e5bb9d42-cc6a-405b-aa97-7b350ba4f1a5","year":2017},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.785390Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:482ba54987f7ab59becebd7b9b0e962e787897037bbe1bec2f1156d521c52027","observation_id":"3c58f465-6744-45c1-a066-76d494f9d98f","resolution":{"observed_at":"2026-08-16T05:46:45.366480Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.333064Z","title":"Second flip in the H assett- K eel program: a local description","venue":null,"work_id":"8cfc5e6c-cafc-4519-9442-c9aaa6d4f311","year":2017},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.797162Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c92936adb46d09d2650f803723f94c9b73585fea80a4f2981d9d5644f666b535","observation_id":"ebab56db-d21e-49a9-8a4f-bf50e7c3ae81","resolution":{"observed_at":"2026-08-16T05:46:45.341117Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.803822Z","title":"Existence of moduli spaces for algebraic stacks","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.803822Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:45080b039c40b65b76a8b94fe05ed81e01808e2f5fcb2cb5b105d0bf928b4601","observation_id":"7d3bed80-9c26-4e4f-97cc-af46a405ce18","resolution":{"observed_at":"2026-08-16T05:46:43.803822Z","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":"2026-08-16T05:46:45.288697Z","title":"A L una \\' e tale slice theorem for algebraic stacks","venue":null,"work_id":"55ed7860-86cd-4fc2-91d8-629a3bf96668","year":2020},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.809601Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:ff02c40a452cee296a03cbda816a6f8e2e590498e360b49bdf4d344ae4667115","observation_id":"d2b237a5-6fa8-4cc2-839a-f6a217dd70c2","resolution":{"observed_at":"2026-08-16T05:46:45.294368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.815640Z","title":"Good moduli spaces for A rtin stacks","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.815640Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:f8e16ad910c6bf8874f2ebe85ec60a339fd6029534a96662edd7701fca509b0c","observation_id":"c1eb477f-fbfe-4a83-a8eb-eb1781a321cf","resolution":{"observed_at":"2026-08-16T05:46:43.815640Z","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":"2026-08-16T05:46:45.259317Z","title":"Stacks of cyclic covers of projective spaces","venue":null,"work_id":"8c7b903f-1ccc-408d-8e1f-7a2838fd15f3","year":2004},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.821784Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c4352cbc4415bf3c4ac7fac2d952052b44fbb781b8ac7e4005d75799aae9199a","observation_id":"0f06123d-6a7f-429e-915d-8504cc68434c","resolution":{"observed_at":"2026-08-16T05:46:45.265010Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.827789Z","title":"Hacon, and James McKernan","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.827789Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:1602bc0baf26b7bfbb1506340f23479de71b46f13b41fc666449137bc2346e17","observation_id":"ac40274a-0d1f-41c3-b93f-2889e67cf3a1","resolution":{"observed_at":"2026-08-16T05:46:43.827789Z","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":"2026-08-16T05:46:45.226344Z","title":"Ribbons and their canonical embeddings","venue":null,"work_id":"d964f918-7cec-48d0-81ce-15db8eed005c","year":1995},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.833880Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:b15082d231640ddedcff095637ede57639d749c3c2aa0f98c489203309f3628a","observation_id":"84b68e91-f11b-4ab0-80d3-adcb40903358","resolution":{"observed_at":"2026-08-16T05:46:45.232926Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2407.00850","last_updated":"2024-06-30T23:09:13Z","snapshot_observed_at":"2026-08-17T20:00:14.728246Z","submitted_at":"2024-06-30T23:09:13Z","title":"Good moduli spaces for boundary polarized Calabi-Yau surface pairs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.00850","snapshot_observed_at":"2026-08-16T05:46:43.839206Z","title":"Good moduli spaces for boundary polarized Calabi--Yau surface pairs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.839206Z"},"links":{"cited_paper":"/paper/2407.00850","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:7bc4502756a1da3c230e6771fc3165f98528930dd13c0971ddc6e5550c003969","observation_id":"fe7ab25f-7a17-4c58-ad0f-5dad0f7922c9","resolution":{"observed_at":"2026-08-16T05:46:43.839206Z","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":"2026-08-16T05:46:45.205812Z","title":"On C how stability for algebraic curves","venue":null,"work_id":"e7a93e7a-8336-4779-9d10-7bbc9504117f","year":2016},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.844767Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:59818e963093abc4263f504cbe0d376a8cfccc02378599a336ba3a889ba90767","observation_id":"fb3a611b-2f67-4295-801d-2aa256fa4ea1","resolution":{"observed_at":"2026-08-16T05:46:45.211601Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.182957Z","title":"Nagata compactification for algebraic spaces","venue":null,"work_id":"698d73e3-5d1f-40c9-a296-50754f0e4429","year":2012},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.850758Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:ceafadbf26e632ea7cc43b77e6921c4363841a46afea9e576f7d4d1190b36683","observation_id":"e0b31f1b-13f2-41c9-82ea-89a35711267f","resolution":{"observed_at":"2026-08-16T05:46:45.190497Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.157899Z","title":"The geometry of the ball quotient model of the moduli space of genus four curves","venue":null,"work_id":"3b8ae363-a91f-4d94-a8e0-5d23e60bdc79","year":2012},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.856193Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:1caa70ae9c49b46a6b3bc9ad3d7672206551edf68c2e1de721c280cdcea60be0","observation_id":"187b2b0e-b157-41dd-a695-c9f19c46540e","resolution":{"observed_at":"2026-08-16T05:46:45.168069Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.136114Z","title":"Log canonical models and variation of GIT for genus 4 canonical curves","venue":null,"work_id":"edb36734-034a-4630-9ea1-6a87ed4b85c4","year":2014},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.861134Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:13edb6d47b3f56611ee62cb930af159d0355b8d12a686b7c0d69f46d9d47f971","observation_id":"8851e2ee-5833-4036-9766-eecab0cb6396","resolution":{"observed_at":"2026-08-16T05:46:45.143970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.116540Z","title":"Dolgachev and Yi Hu","venue":null,"work_id":"bfe4a5c1-4ec6-4a68-8e53-702711ba0c52","year":1998},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.867186Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:cd1297f7a99af745a5b6953545668dbc0177493b8c5c5bac45ce82583aec1c9a","observation_id":"2e411e7e-48d3-47bc-90c3-181101f99656","resolution":{"observed_at":"2026-08-16T05:46:45.123123Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.095887Z","title":"Stable log surfaces, admissible covers, and canonical curves of genus 4","venue":null,"work_id":"7e15e583-da6b-4f7c-ada4-d7cb5eb2e60e","year":2021},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.873310Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:6f2bb3902e977560adb79a8288e4456b57ea6a4bf486731d2ec9deb739a496ec","observation_id":"2eed9404-242d-4324-84e9-d120f2158fc7","resolution":{"observed_at":"2026-08-16T05:46:45.102057Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.075337Z","title":null,"venue":null,"work_id":"0eaafd59-a6bf-4358-b444-ae16f2109ffe","year":2011},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":25,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.878779Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:859a675a00be512ebf34c36fa25166fb009172d9b85e5cdf3091fcae8bd765cf","observation_id":"112cce6d-1e7e-4c11-9b84-1a839c088a09","resolution":{"observed_at":"2026-08-16T05:46:45.080876Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.885081Z","title":"Deligne and D","venue":null,"work_id":null,"year":1969},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":26,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.885081Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:3b17378044578f344f38eabe1688b635ffee8e4d3aa94d41afc18676a45d4d5a","observation_id":"7fa25a7f-5f5c-4a93-9638-97de57dfade3","resolution":{"observed_at":"2026-08-16T05:46:43.885081Z","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":"2026-08-16T05:46:45.030327Z","title":"The final log canonical model of the moduli space of stable curves of genus 4","venue":null,"work_id":"76882754-ff16-4c9b-875d-2a96682d1f39","year":2012},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.890448Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:11118a85a382d693fe8eaf05c9639dc661387688b4ef28224e07b2673578ccc0","observation_id":"adac4a14-879d-4676-aecc-064916eaed28","resolution":{"observed_at":"2026-08-16T05:46:45.038330Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:45.009644Z","title":"Compact moduli of plane curves","venue":null,"work_id":"d5413f50-f6bc-4c53-af10-04de0d5a3ddf","year":2004},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":28,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.896174Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:2e100a4ae5e88316ff8f5fddb362225b773311cd65df67a9c25b3fc7ec53f527","observation_id":"3aa4c9fc-27d5-4ae9-8702-13023c2761f7","resolution":{"observed_at":"2026-08-16T05:46:45.016184Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.901478Z","title":"Algebraic geometry","venue":null,"work_id":null,"year":1977},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":29,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.901478Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:d49fd1eb4120daff093a79bae37e0cb090ddffbe22b4513eedd5b455d37f50c0","observation_id":"1ee31de2-8802-419f-b448-18ca866a9384","resolution":{"observed_at":"2026-08-16T05:46:43.901478Z","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":"2026-08-16T05:46:44.974335Z","title":"Classical and minimal models of the moduli space of curves of genus two","venue":null,"work_id":"6907528d-8a5e-4514-8fe1-3db63041fd8c","year":2005},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":30,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.907042Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:6b9816c0e653cd53223ef285a37712fde4cd187fdc4ab5eb86fb1315dd1ad4b3","observation_id":"cf0a27d1-22e8-4b4b-a3b1-b60f2629a422","resolution":{"observed_at":"2026-08-16T05:46:44.981366Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.956040Z","title":"Log canonical models for the moduli space of curves: the first divisorial contraction","venue":null,"work_id":"2361099c-0bcc-4d59-91b5-bf593db6ddf5","year":2009},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":31,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.912832Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:dfa035122ca2c657e21c37ebf23785fd9e09ec6ffd9ca540d971620b1e3203bb","observation_id":"2dbf600f-93b2-4163-b66b-6a1875e939e3","resolution":{"observed_at":"2026-08-16T05:46:44.961448Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.937668Z","title":"Log minimal model program for the moduli space of stable curves: the first flip","venue":null,"work_id":"320f8f19-fcba-43a1-b5ca-e684d5d59000","year":2013},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":32,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.919457Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c8a759294c0e9aa5d27b4bc231b3b23b91b19ce9deafeb34300210fd857837a4","observation_id":"e8eaf117-f788-430f-a25e-d4080cc32329","resolution":{"observed_at":"2026-08-16T05:46:44.943244Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.919358Z","title":"Stability of tri-canonical curves of genus two","venue":null,"work_id":"cdad1790-5a2c-41ec-882e-2f5d4dd9a9e4","year":2007},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":33,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.925148Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:3f06426c22caebbf0be5c1d61ecd27fdb32e9844f0a3baa443cb60308c0ce720","observation_id":"d90ba899-069c-4bcd-806b-c00506f8cb86","resolution":{"observed_at":"2026-08-16T05:46:44.925636Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.893770Z","title":"Log minimal model program for the moduli space of stable curves of genus three","venue":null,"work_id":"dd5f5f4e-082d-41a8-91a2-14234a6834c5","year":2010},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":34,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.932843Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c4ab772f171305bd4dddb012cf32929a1f95645a0ee0b889ce5cdb0f422010d3","observation_id":"299e3861-bfac-4037-b946-92c52d338e2c","resolution":{"observed_at":"2026-08-16T05:46:44.902180Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.870293Z","title":"A birational contraction of genus 2 tails in the moduli space of genus 4 curves I","venue":null,"work_id":"7855bdd9-ec73-47ae-ad32-f886117db984","year":2014},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":35,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.938740Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:6b21ca3f4f856a692ee822b512367f4914a3badf1624a4a6bf4578b761399617","observation_id":"fd6873fb-1c10-426e-b4fe-ea32ddda469e","resolution":{"observed_at":"2026-08-16T05:46:44.877078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2410.10753","last_updated":"2025-05-15T00:44:36Z","snapshot_observed_at":"2026-08-16T13:09:30.633108Z","submitted_at":"2024-10-14T17:25:58Z","title":"Projectivity of the moduli of equidimensional branchvarieties","version":2},"cited_work":{"arxiv_id":"2410.10753","doi":null,"metadata_source":"pith","pith_arxiv_id":"2410.10753","snapshot_observed_at":"2026-08-16T05:46:44.395080Z","title":"Projectivity of the moduli of equidimensional branchvarieties","venue":"math.AG","work_id":"b0b5ff0f-402a-411f-b085-6e348e84b0b9","year":2024},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":36,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.946329Z"},"links":{"cited_paper":"/paper/2410.10753","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:562158e2a37028c4e1c05d6529bdbbf8cef65a2de9e933dfcc7b77467a75e3f2","observation_id":"315cc7c5-fd30-4cd2-8990-931aec44957b","resolution":{"observed_at":"2026-08-16T05:46:44.402706Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.851934Z","title":"Moduli of curves , volume 187 of Graduate Texts in Mathematics","venue":null,"work_id":"b0707c27-2d3a-49f0-a2b7-cc939828d3d8","year":1998},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":37,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.953027Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:8b6f46eb55b13c42ba8e327ff4bcfaf86d58ac2c4fc0d5ed910460c5eb912ba8","observation_id":"affe9919-4c0e-4b87-8d38-d49267d192d7","resolution":{"observed_at":"2026-08-16T05:46:44.858271Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.832708Z","title":"Smoothable del P ezzo surfaces with quotient singularities","venue":null,"work_id":"dc621a36-d7ad-43c3-a527-6c428bd49c99","year":2010},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.958407Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:44619e4fec0e6b0a0498e99800e9e0893a98888202b20c46a456f522a3d862d0","observation_id":"9f503c11-97e3-4c54-954a-524030968f6a","resolution":{"observed_at":"2026-08-16T05:46:44.839231Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.811784Z","title":null,"venue":null,"work_id":"6ed0eb95-3bc0-48d0-89a5-cf7bf84140ba","year":1978},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":39,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.963865Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:0c947403e253e9477f10061ea2b3e50067ee63f50d77792f0a075fcaffe8a8af","observation_id":"ef31ab23-2f25-44cd-be50-7fc643122d5b","resolution":{"observed_at":"2026-08-16T05:46:44.818373Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.788690Z","title":"Classification of three-dimensional flips","venue":null,"work_id":"27349bce-38cb-40b0-924b-b3f049ae4d0b","year":1992},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":40,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.969223Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:47de059fe302ab7b621f6b6ed4bbc865758d6a7893c2560bc95fa520254873c1","observation_id":"a21530ab-d2f9-456b-8364-fc39c172d8d8","resolution":{"observed_at":"2026-08-16T05:46:44.794940Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:43.974234Z","title":"Birational geometry of algebraic varieties , volume 134 of Cambridge Tracts in Mathematics","venue":null,"work_id":null,"year":1998},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.974234Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:25088f922fc48e919dec9cff112d979f9915508a2266bc0959c094dbdac6243b","observation_id":"4c5a845d-fb9f-4863-8112-36858a0f4e27","resolution":{"observed_at":"2026-08-16T05:46:43.974234Z","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":"2026-08-16T05:46:43.979983Z","title":"Rational curves on algebraic varieties , volume 32 of Ergebnisse der Mathematik und ihrer Grenzgebiete","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":42,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.979983Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:b743a093fd50a20497f0018c8c93c8e9db63e3998d0ff5021bf9bfbff3588e14","observation_id":"bb218789-ddcf-4c6a-9584-aeb438035abf","resolution":{"observed_at":"2026-08-16T05:46:43.979983Z","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":"2026-08-16T05:46:44.736637Z","title":"Families of varieties of general type , volume 231 of Cambridge Tracts in Mathematics","venue":null,"work_id":"660b1aed-39b3-40da-9033-fcbfe9eb5566","year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":43,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:43.985930Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:3dd6c9007ccf056101cf1958f3e72f5b07560c1ac40ee3b2ada6e865260c1cdc","observation_id":"b0dcf5c6-5679-444d-8e39-0fa4744663d1","resolution":{"observed_at":"2026-08-16T05:46:44.743760Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.710240Z","title":"The moduli space of curves of genus 4 and Deligne - Mostow 's complex reflection groups","venue":null,"work_id":"38d4608d-9170-49a9-855f-194025b44429","year":2000},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":44,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.126290Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:022ce74460d717bc2724efe5847b48d62b691702503824b6399a45e13701d10e","observation_id":"ba4a4f8a-ca83-468b-bd3d-4ac902ca8a5f","resolution":{"observed_at":"2026-08-16T05:46:44.719455Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.132866Z","title":"Positivity in algebraic geometry","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":45,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.132866Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:08f64c177859a9356bf81df318234c55ca7eaba88321662a037a8bbf65da5049","observation_id":"1463e404-6ba4-43dd-9c9f-182d7693faf8","resolution":{"observed_at":"2026-08-16T05:46:44.132866Z","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":"2026-08-16T05:46:44.672874Z","title":"G IT versus B aily- B orel compactification for K3 's which are double covers of P^1 P^1","venue":null,"work_id":"ae3397b8-d0bd-4bbd-8d5c-501ed6a6f882","year":2021},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":46,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.142103Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c8097bf8b98b13e45b4322d62f0c7a42f7ab41fb2ef9b2c314073de9b1e7bdd9","observation_id":"724a1699-27da-48f4-8c2a-dd040adb90a8","resolution":{"observed_at":"2026-08-16T05:46:44.680389Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2403.16747","last_updated":"2025-02-13T16:27:41Z","snapshot_observed_at":"2026-08-16T14:06:41.595195Z","submitted_at":"2024-03-25T13:20:32Z","title":"K-moduli of Fano threefolds and genus four curves","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2403.16747","snapshot_observed_at":"2026-08-16T05:46:44.149528Z","title":"K-moduli of Fano threefolds and genus four curves","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":47,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.149528Z"},"links":{"cited_paper":"/paper/2403.16747","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:97292c42412b609452298b8a828c8d77aa77e7df11aef4109549898383410f4f","observation_id":"441bbe75-3103-4113-9a86-e12c9a3a5bdc","resolution":{"observed_at":"2026-08-16T05:46:44.149528Z","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":"2026-08-16T05:46:44.650094Z","title":"Mori theory of moduli spaces of stable curves","venue":null,"work_id":"f451cebe-1cb1-4f15-b097-0a2b4a317709","year":2010},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":48,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.155718Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:26d9883100622e0c80f009c7ca671d8ce87e3787cd67ad48b9280aa235b15795","observation_id":"3ddd0b09-9f6e-4a1a-a2bf-559791af3a38","resolution":{"observed_at":"2026-08-16T05:46:44.655874Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.627178Z","title":"Stability of projective varieties , volume No","venue":null,"work_id":"d5de917a-20a9-4359-9953-9e659aaf9d7d","year":1977},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":49,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.161692Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:f92a950c597d14df0ed1bca61b2cf14d8ba01b2158f0cd905d2ee910a4cdf0b4","observation_id":"327cc57f-8c3c-4695-bc02-aa1783defe22","resolution":{"observed_at":"2026-08-16T05:46:44.633380Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2311.01319","last_updated":"2023-11-02T15:33:17Z","snapshot_observed_at":"2026-08-19T17:00:49.202764Z","submitted_at":"2023-11-02T15:33:17Z","title":"MMP for locally stable families and wall crossing for moduli of stable pairs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.01319","snapshot_observed_at":"2026-08-16T05:46:44.168098Z","title":"MMP for locally stable families and wall crossing for moduli of stable pairs","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":50,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.168098Z"},"links":{"cited_paper":"/paper/2311.01319","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:7ffbfa3e8aaa861f502ddf9d7cf5b38ef6bcfb5ca13e6ca755af2185dc0a262f","observation_id":"f3b812b4-353f-4582-87cf-5810cea459d8","resolution":{"observed_at":"2026-08-16T05:46:44.168098Z","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":"2026-08-16T05:46:44.603680Z","title":"Le th\\' e or\\` e me de compactification de Nagata pour les espaces alg\\' e briques","venue":null,"work_id":"f4b76fc0-fcb5-4bbf-a2fa-c50dce4c12d8","year":1974},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":51,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.173884Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:58b2bcc91d9b981c6921f69fc070c8a3cf3620c53e230431ac3452b291c8ae2b","observation_id":"1a95f6f2-180c-4a03-9c3f-baed3a81fd89","resolution":{"observed_at":"2026-08-16T05:46:44.612465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.179470Z","title":"A new compactification of the moduli space of curves","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":52,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.179470Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:a5fc282a23a6432d40b9c1cbffc657ae0c98601dcf3b0e26fbdc93353fef6337","observation_id":"cb75b95e-fbef-4ce2-a1f5-e7bb2fad6727","resolution":{"observed_at":"2026-08-16T05:46:44.179470Z","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":"2026-08-16T05:46:44.185335Z","title":"Deformations of algebraic schemes , volume 334 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":53,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.185335Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:c8f4899df0e508f5001db6900ba99156107ab9a77439135fb3e6d55885305386","observation_id":"dc6d3584-f253-419e-b1b9-6939fd54a763","resolution":{"observed_at":"2026-08-16T05:46:44.185335Z","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":"2026-08-16T05:46:44.546883Z","title":"Towards a classification of modular compactifications of M _ g,n","venue":null,"work_id":"0dd2acfd-15ca-4161-899c-a32d5120c172","year":2013},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":54,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.192006Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:75f3ea743a7991153917c68bbb00e3945e5883d177752dd2284823f252ed3bdd","observation_id":"20a07888-6207-44c0-b5a2-054eb5ac39e1","resolution":{"observed_at":"2026-08-16T05:46:44.552841Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-16T05:46:44.218260Z","title":"Stacks Project","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":55,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.218260Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:22d637f6321314675c4fd5a30a9faeb27c9e342fe92eff4b6ad23af2f2a42005","observation_id":"a7fef9a5-3f5f-4ac5-a343-84bf43b739b3","resolution":{"observed_at":"2026-08-16T05:46:44.218260Z","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":"2026-08-16T05:46:44.227306Z","title":"Geometric invariant theory and flips","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":56,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.227306Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:08ade66d8b195c5aa2cbf8dcf9d35ea00f59e1b1b41aee48880d5e6888b4bea6","observation_id":"00862088-c4ce-4826-b541-34d9ce72415c","resolution":{"observed_at":"2026-08-16T05:46:44.227306Z","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":"2026-08-16T05:46:44.500072Z","title":"K-stability of F ano varieties , volume 50 of New Mathematical Monographs","venue":null,"work_id":"aa49dfd8-3695-4678-a3dc-c4f6751d3f55","year":2025},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":57,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.236416Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:307066c7fcf0312f4391dc5717c104351be6a1117b3e5dc837e735943a3d6f7b","observation_id":"99d0dce5-3da5-4ab5-88b7-834a5ef4e4d6","resolution":{"observed_at":"2026-08-16T05:46:44.507346Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2304.13259","last_updated":"2023-04-26T03:17:18Z","snapshot_observed_at":"2026-08-16T15:37:40.639593Z","submitted_at":"2023-04-26T03:17:18Z","title":"The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2304.13259","snapshot_observed_at":"2026-08-16T05:46:44.242033Z","title":"The Moduli Space of Genus Six Curves and K-stability: VGIT and the Hassett-Keel Program","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":58,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.242033Z"},"links":{"cited_paper":"/paper/2304.13259","citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:6f971ab9c4e328f7cf1c2157769089fcc67d0e5398a97092aa8c536143adc588","observation_id":"e95503f6-3762-4717-99c8-b7174055a872","resolution":{"observed_at":"2026-08-16T05:46:44.242033Z","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":"2026-08-16T05:46:44.248780Z","title":"Moduli of genus six curves and K -stability","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":59,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.248780Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:4a8a217c7fac6f54dd6ede5cdf7e7843459d652eb329048630a5527245846699","observation_id":"53554558-33bc-404b-b502-523b3851a5d9","resolution":{"observed_at":"2026-08-16T05:46:44.248780Z","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":"2026-08-16T05:46:44.255260Z","title":"On wall-crossing for K -stability","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four","version":1},"reference_index":60,"source":"arxiv_source","source_observed_at":"2026-08-16T05:46:44.255260Z"},"links":{"citing_paper":"/paper/2504.20312"},"observation_digest":"sha256:df354ecbf2f8967e0a81064f554cff3c47af1218bca6669447dcd4fad207f731","observation_id":"8de11497-05cc-427b-a8ce-2d3e0a87aaac","resolution":{"observed_at":"2026-08-16T05:46:44.255260Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2504.20312","last_updated":"2025-04-28T23:48:24Z","latest_version":1,"primary_category":"math.AG","snapshot_observed_at":"2026-08-21T08:53:53.316693Z","submitted_at":"2025-04-28T23:48:24Z","title":"Hassett--Keel Program in genus four"},"reference_resolution":{"displayed":60,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":24,"verified_exact":1,"verified_fuzzy":35},"total_outbound_references":60},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 60 of 60 outbound references and 2 inbound Pith citation observations for arXiv:2504.20312."}