{"as_of":"2026-08-16T06:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:869ed51a2b642c7d71ba098414f4596b3aaa4e19483b97574a9b5ea69b4d117c","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:52:23.585219Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+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":"2026-08-14T13:22:12.420634Z","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":"2026-08-14T13:22:12.484143Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"cited_work":{"arxiv_id":"1908.02744","doi":null,"metadata_source":"pith","pith_arxiv_id":"1908.02744","snapshot_observed_at":"2026-08-14T13:22:12.484143Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","venue":"math.AC","work_id":"0d16b860-d2dc-4053-9a27-edff94683616","year":2019},"citing_paper":{"arxiv_id":"1908.05678","last_updated":"2019-08-15T13:21:13Z","snapshot_observed_at":"2026-08-16T05:23:01.100645Z","submitted_at":"2019-08-15T13:21:13Z","title":"Edge rings of bipartite graphs with linear resolutions","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T13:22:12.420634Z"},"links":{"cited_paper":"/paper/1908.02744","citing_paper":"/paper/1908.05678"},"observation_digest":"sha256:cdddd4bd199b30ce2d2e285344af88f350a2e4641148240da036ebb952ac040b","observation_id":"dc6ed7b5-4885-4fcf-9990-01becc1eed2f","resolution":{"observed_at":"2026-08-14T13:22:12.489901Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1908.02744/citation-record","integrity":"/paper/1908.02744/integrity","json":"/paper/1908.02744/citation-record.json","paper":"/paper/1908.02744"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:52:23.953160Z","title":null,"venue":null,"work_id":"ee772871-4032-4ecc-a016-8253794a1550","year":1981},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.474764Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:41ba2fd170687526de94427a27ac062c9dd01dd55a8d1b14b2bfce82b1cd4f8f","observation_id":"6885aa09-34bc-4961-862f-f950d9b2ebe7","resolution":{"observed_at":"2026-08-14T14:52:23.956684Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.942586Z","title":"Avramov, A","venue":null,"work_id":"74537462-79e4-4b97-8f3a-2ae65091a1d0","year":2010},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.479457Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:862a9a4f3a29abbc26b1bf014f12f9e7db97870972f040e2f8a09171aef11226","observation_id":"7c45e337-1234-4b02-b658-0acbd39788f3","resolution":{"observed_at":"2026-08-14T14:52:23.946262Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.931769Z","title":"Biermann, A","venue":null,"work_id":"05095e86-2900-47df-9168-723c75da7038","year":2017},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.483078Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:34b3f76fc27db84200e7cf717e670eb3d69c6c08ee490112663c8aa3c8d916c4","observation_id":"ffca570e-5e86-4a57-a22a-8698acb11d18","resolution":{"observed_at":"2026-08-14T14:52:23.935708Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.921074Z","title":"Buchsbaum, D","venue":null,"work_id":"07a75d3b-05bc-492f-8dea-6cff521dd31c","year":1977},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.486878Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:3ae74b06b017e78fd77f6f46efc849e6a265171a24e1a8fd3694158611291e2e","observation_id":"7b3e9c62-91a0-4443-a4fb-5f3fc3031616","resolution":{"observed_at":"2026-08-14T14:52:23.924787Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.910150Z","title":"Conca, Koszul algebras and their syzygies","venue":null,"work_id":"8ccd37e3-0974-4b36-abaf-06fb3bd87e83","year":2014},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.490551Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:cfce6256f86a0378851e5f4dc8aa8660ab7517fcb3662f0fc28813a2e2a6941d","observation_id":"c9dfc263-78a7-4468-8d97-8ee2ff797654","resolution":{"observed_at":"2026-08-14T14:52:23.914133Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.899053Z","title":"Constantinescu, T","venue":null,"work_id":"396600e1-482d-4432-808d-99825d0ea17c","year":2019},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.494275Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:ceecb4de02a5ffa3a834bef6535ccb7ae8facf8b60717cd1c7308d5ca870fe80","observation_id":"b6c7e326-cf07-421a-ba2b-fcda5f9d8615","resolution":{"observed_at":"2026-08-14T14:52:23.902968Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.887751Z","title":null,"venue":null,"work_id":"67a19935-7b87-4a9d-9fb6-263ef6603b3b","year":2005},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.498131Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:836918fba2f1b9165a749d385161908cc966ba61dca686175d56df41ae4ed11b","observation_id":"9af674a8-db35-42a3-b094-6cb103d82dab","resolution":{"observed_at":"2026-08-14T14:52:23.891576Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.877919Z","title":null,"venue":null,"work_id":"d3444e44-2f89-4818-9d68-f34427a182cc","year":2013},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.501538Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:1c7cc04a6dfeac1a5f1472745756c9241b03ee9bfc0af83d5c4db26029526285","observation_id":"6e8ed11d-7143-4fc7-b255-51236a54b771","resolution":{"observed_at":"2026-08-14T14:52:23.881371Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.867490Z","title":"Eisenbud, M","venue":null,"work_id":"a4c329e3-5892-4dfc-a8fb-a64b42ac61fc","year":2005},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.505369Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:336cee4f5cb63b0cc2d4a097972a01816c3093e06ae4db17b9b71398aedf1766","observation_id":"178f8963-1839-4b13-b687-b0b2efee476f","resolution":{"observed_at":"2026-08-14T14:52:23.871016Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.857310Z","title":null,"venue":null,"work_id":"ebf248ca-2c22-4320-bf62-03e1d718891c","year":2015},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.508992Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:124ffdbdbbfabf9aae8553d3f4d31ddc44fefa4b5dc8004f42b8a79e87cabfe2","observation_id":"9ee8f63f-3e9d-4584-b79a-91820d7e64c7","resolution":{"observed_at":"2026-08-14T14:52:23.860948Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.847231Z","title":"Green and R","venue":null,"work_id":"09c9feb3-4e84-487a-8304-013718312642","year":1984},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.512663Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:61880170f9632a20671de17875a77ee49de28b9cdc491d753b9e08287189ee71","observation_id":"122b9245-4af4-4a6a-b3c3-f60a9ff87ffe","resolution":{"observed_at":"2026-08-14T14:52:23.850998Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.836870Z","title":"Green and R","venue":null,"work_id":"4c0e8202-fa9f-4e4e-a382-546b9d4b957a","year":1985},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.516176Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:fa493abb79faf35c067d05e743eaed87ad4891947c397575646ea05fa9bdc3b9","observation_id":"548b59c2-0e2a-4fd4-b7ae-35ee0ab96e14","resolution":{"observed_at":"2026-08-14T14:52:23.840537Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.826557Z","title":"Gulliksen, O","venue":null,"work_id":"c79863db-2d6b-4929-bce9-cede56449ecf","year":1972},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.519831Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:b9595f69c162475598e6375209578fcccf77a34785f21af751b24a89dccd1fc2","observation_id":"b87883cf-0571-4177-9716-489d4f498f68","resolution":{"observed_at":"2026-08-14T14:52:23.830142Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.815934Z","title":null,"venue":null,"work_id":"9af13b9f-9911-46c9-8512-e01752e5f05e","year":2019},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.523310Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:95591bfcae0b3384d5a6b8fde61203a1dc69a4c9e2ad8e9ceb439a18a24a1c01","observation_id":"0de4ae8a-fb35-4409-8345-40033fe1ec91","resolution":{"observed_at":"2026-08-14T14:52:23.819454Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.805701Z","title":"Hashimoto, Determinantal ideals without minimal fr ee resolutions, Nagoya Math","venue":null,"work_id":"7b86f4d7-48b8-40d2-86fe-581cb1b7e966","year":1990},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.526736Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:436a29bddce7af32d212d39d7ae7ae7fbd65d0db9883c7ef20434d7aa5282d51","observation_id":"c139625b-4ab5-4bd7-97fd-49e5440c87ab","resolution":{"observed_at":"2026-08-14T14:52:23.809452Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.793881Z","title":"Hashimoto and K","venue":null,"work_id":"f5392276-07df-473f-8f3d-3f818fb9ab2f","year":1992},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.529969Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:4a78806f19cee3aede78365f0a96a30755eb453ce770d42736e3dd82eb1423fd","observation_id":"8f0f40b3-22db-4fa9-93d1-a1f9d0ff4c71","resolution":{"observed_at":"2026-08-14T14:52:23.797773Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.781950Z","title":"Herzog, T","venue":null,"work_id":"e24a07e4-8294-4c19-b2b7-7eb42f27b30c","year":2018},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.533260Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:d48f26f320e286c670b2747c4195506f212ef3988e73b1966b20c0095009dc08","observation_id":"569ba52f-e2ed-458b-a1cf-6b8f67de3da0","resolution":{"observed_at":"2026-08-14T14:52:23.785777Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1090/proc/14382","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:52:23.613434Z","title":null,"venue":null,"work_id":"f34e7b1b-b331-4d43-90fb-acda35ba8b25","year":null},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.536858Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:b5c0f752c6c86f906f1de1c104a6817ebd2f26dd5f3d6a0a1425a23d29d263be","observation_id":"7eea8c85-8a13-43ed-b1f4-e1686e9af9f8","resolution":{"observed_at":"2026-08-14T14:52:23.618742Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.770997Z","title":null,"venue":null,"work_id":"12b9a9a0-f677-49fd-9450-6195bf7c1269","year":2005},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.540594Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:b21b9410f15ac147df243f1c711c61bd04dfb5cb6436e867128f12bbd1581c5f","observation_id":"46fff0f8-e5a3-4dc3-8345-77e758a70889","resolution":{"observed_at":"2026-08-14T14:52:23.775082Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.759869Z","title":"Lascoux, Syzygies des vari´ et´ es determinantales,Adv","venue":null,"work_id":"c69d3e40-2bf6-4e39-8ffc-fa1ef0be3d27","year":1978},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.543950Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:d0b6fb9a4a7599bbf5c92c71b159dd14abae362d8d82805ad8582a474e88a2db","observation_id":"85c18247-ecd8-4399-86f3-5c15b4a8e4f8","resolution":{"observed_at":"2026-08-14T14:52:23.763873Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.749223Z","title":"Mastroeni, Koszul almost complete intersections","venue":null,"work_id":"1f187b17-2edc-4ac5-b34b-9078f0336e02","year":2018},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.547660Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:e1118ddd8b30011b5c6f739ab861ec1024c65f1dca834ec62716afa84f2a947b","observation_id":"9e2af43f-d16a-4b19-830f-f49c836ad5a9","resolution":{"observed_at":"2026-08-14T14:52:23.753167Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.738486Z","title":"Grayson, and M","venue":null,"work_id":"473171b5-80d2-4a92-9cc4-78c0cb822be0","year":null},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.551009Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:ff3e60b7616087f5130db4d4bb8813828605bc5d7d173c978192a0885a9136c9","observation_id":"50f05cb1-b188-4661-9b78-20748bf87ab6","resolution":{"observed_at":"2026-08-14T14:52:23.742219Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.727270Z","title":"Matsuda, S","venue":null,"work_id":"d2410a86-91d2-49cb-8484-60966c534126","year":2013},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.554544Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:9fe78aa7c989afd1f8ad7dc5a9154bd3e960f4c0659528549489be4ac880a294","observation_id":"5d1883f1-211a-4d34-92db-32b31931ede8","resolution":{"observed_at":"2026-08-14T14:52:23.730932Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.716452Z","title":"Ohsugi, T","venue":null,"work_id":"a58329ab-b40e-40cd-9e00-89b5874bd252","year":1999},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.557908Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:790dd6bff68092186632d2f03967b2fd3d9db1dbfb16c1ef23b5cda8a5f6f95d","observation_id":"419020ef-f750-4c61-80db-4a435afc4709","resolution":{"observed_at":"2026-08-14T14:52:23.720206Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.705879Z","title":"Ohsugi, T","venue":null,"work_id":"44a56426-4935-4b39-9740-20cf2603b7d5","year":1999},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.561128Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:109ec6e853da305249bb3a0949933eee67742637dde9e299af30556b4a20e8f5","observation_id":"16152ccd-5cb4-4af5-8985-40feb09bd800","resolution":{"observed_at":"2026-08-14T14:52:23.709600Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.695262Z","title":"Ottaviani, R","venue":null,"work_id":"282a6f8f-00f9-4059-91b2-ba93ef4c0eec","year":2001},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.564395Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:93b0d1bd09f210c36d38643deed0d84c8cad0e79a630c7b3818086c7cbdb2a66","observation_id":"1d697559-acc8-4287-a033-9af092ebdf37","resolution":{"observed_at":"2026-08-14T14:52:23.699031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.684371Z","title":"Roberts, A minimal free complex associated to the min ors of a matrix","venue":null,"work_id":"fd73aad0-7043-4319-8105-dff737eba544","year":2018},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.567862Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:043a8e3c4e1d52bef66e3914d5f4908213079ed140f437930a4f635bd7dba7b1","observation_id":"0276108c-c81c-4c0c-a4d8-3fe1c720b835","resolution":{"observed_at":"2026-08-14T14:52:23.688387Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.672557Z","title":"Peeva, Graded syzygies","venue":null,"work_id":"86549357-3501-4aa8-be95-31b01d9d7a64","year":2011},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.571088Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:7451f83f027f90da840267ea0fb8ed8bcc962f8118ad1b2ac05408fd35e010d8","observation_id":"8ada5f6e-626e-4db4-be84-9b36c00a8ae6","resolution":{"observed_at":"2026-08-14T14:52:23.676498Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.661002Z","title":"Pragacz, J","venue":null,"work_id":"a4f8b522-59e4-458c-9fe5-f32062d7c01d","year":1985},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.574741Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:7312b4ce485c7ce3db32b9b05f1e09f43b55ac5adc119a658c678c9b1637ab44","observation_id":"dc8d4a7a-6785-4029-ac06-32b01dfd5756","resolution":{"observed_at":"2026-08-14T14:52:23.664746Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.650261Z","title":"Qureshi, Ideals generated by 2-minors, collections of cells and stack polyominoes, J.Algebra 357 (2012) 279–303","venue":null,"work_id":"49a6fdac-9df6-47f4-9a8e-4f50f6e75cff","year":2012},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.578325Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:5496d75149e369dff158906c4b0ed18eeea41122258f0e42c06afb823153d00f","observation_id":"a83c2b27-fe48-4e7b-a76b-fb69e13d3b7c","resolution":{"observed_at":"2026-08-14T14:52:23.653951Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.637733Z","title":"Rubei, Resolutions of Segre embeddings of projectiv e spaces of any dimension, J","venue":null,"work_id":"b5bd6064-e7c1-4e1c-95d3-a0e221f4a521","year":2007},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.581768Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:b4fc35543d24ce173a94ce970fe91ca8cb24468016679122938ab271b106d3f8","observation_id":"cb8cfa79-d40f-41af-b396-b5dd95b25949","resolution":{"observed_at":"2026-08-14T14:52:23.642202Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+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":"2026-08-14T14:52:23.626667Z","title":"Villarreal, Monomial algebras","venue":null,"work_id":"05831519-2539-4b8d-be9b-7b7341444e6d","year":2001},"citing_paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-14T14:52:23.585219Z"},"links":{"citing_paper":"/paper/1908.02744"},"observation_digest":"sha256:49da9d0f90377e7f5207f623425fedf24fa0118417250010912d9f5e4517259b","observation_id":"cade7551-ca92-481e-873a-f69ff4cd3663","resolution":{"observed_at":"2026-08-14T14:52:23.630517Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"1908.02744","last_updated":"2019-08-07T17:50:20Z","latest_version":1,"primary_category":"math.AC","snapshot_observed_at":"2026-08-16T04:38:17.408492Z","submitted_at":"2019-08-07T17:50:20Z","title":"Green-Lazarsfeld Condition for Toric Edge Ideals of Bipartite Graphs"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":6,"verified_exact":1,"verified_fuzzy":25},"total_outbound_references":32},"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":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:1908.02744."}