{"as_of":"2026-08-12T18:58:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:44dd6bd964a9e65a9bb53d1b6934903b84886c9408a2783ecc017559c1469c4b","coverage":[{"denominator":27,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":27,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T20:54:10.653651Z","state":"measured"},{"denominator":27,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":27,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-12T06:34:41.77262+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2412.05172/citation-record","integrity":"/paper/2412.05172/integrity","json":"/paper/2412.05172/citation-record.json","paper":"/paper/2412.05172"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"hep-th/0110071","last_updated":"2001-12-04T14:49:44Z","snapshot_observed_at":"2026-08-12T13:42:15.131479Z","submitted_at":"2001-10-08T15:34:13Z","title":"D-Brane Stability and Monodromy","version":2},"cited_work":{"arxiv_id":"hep-th/0110071","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0110071","snapshot_observed_at":"2026-08-11T20:54:11.061006Z","title":"D-Brane Stability and Monodromy","venue":"hep-th","work_id":"5025e7b6-f0ac-4444-a689-26b49c0200e4","year":2001},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.543055Z"},"links":{"cited_paper":"/paper/hep-th/0110071","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:68ba737e3e63e36414714f75672b1ec8ddfc6cdcd17229d568014304f7037c05","observation_id":"41975f0a-b2c8-4d27-adda-2f37a7f42192","resolution":{"observed_at":"2026-08-11T20:54:11.065545Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1311.2202","last_updated":"2014-04-04T15:19:46Z","snapshot_observed_at":"2026-07-06T03:27:46.306625Z","submitted_at":"2013-11-09T19:04:38Z","title":"Calabi's diastasis as interface entropy","version":2},"cited_work":{"arxiv_id":"1311.2202","doi":null,"metadata_source":"pith","pith_arxiv_id":"1311.2202","snapshot_observed_at":"2026-08-11T20:54:11.043664Z","title":"Calabi's diastasis as interface entropy","venue":"hep-th","work_id":"1e67187a-62a4-4a0a-ae23-059054b5e77d","year":2013},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.548223Z"},"links":{"cited_paper":"/paper/1311.2202","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:72cc7807de2edf6b3662ec523f47f4a564feb2e4631e474188e60d437bf058ac","observation_id":"d8df0ee6-adcf-4804-8860-2586a1fd807b","resolution":{"observed_at":"2026-08-11T20:54:11.047901Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0806.4734","last_updated":"2008-06-30T14:24:36Z","snapshot_observed_at":"2026-07-06T01:39:35.270236Z","submitted_at":"2008-06-30T14:24:36Z","title":"Defects and D-Brane Monodromies","version":1},"cited_work":{"arxiv_id":"0806.4734","doi":null,"metadata_source":"pith","pith_arxiv_id":"0806.4734","snapshot_observed_at":"2026-08-11T20:54:11.026393Z","title":"Defects and D-Brane Monodromies","venue":"hep-th","work_id":"87bb449a-d904-4763-9fb2-3d626ad44d1f","year":2008},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.552703Z"},"links":{"cited_paper":"/paper/0806.4734","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:3c96b004bc3cf4e5055878d23df917832401bb8645287444deec71bf7db13f4a","observation_id":"00ce5765-5b95-421a-a3b8-86eb59034546","resolution":{"observed_at":"2026-08-11T20:54:11.030761Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2101.12315","last_updated":"2021-01-28T23:04:03Z","snapshot_observed_at":"2026-07-06T10:36:37.920595Z","submitted_at":"2021-01-28T23:04:03Z","title":"Phase transitions in GLSMs and defects","version":1},"cited_work":{"arxiv_id":"2101.12315","doi":null,"metadata_source":"pith","pith_arxiv_id":"2101.12315","snapshot_observed_at":"2026-08-11T20:54:11.008331Z","title":"Phase transitions in GLSMs and defects","venue":"hep-th","work_id":"66fe4b21-93db-4031-9630-08f2710588a2","year":2021},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.557373Z"},"links":{"cited_paper":"/paper/2101.12315","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:eb84fe036dd75cf65b00d9b687e51241f2ece3c798899013b22bccc5b2e149f6","observation_id":"6975309d-8e3c-4ffd-8199-b0f91e20ace6","resolution":{"observed_at":"2026-08-11T20:54:11.012947Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2109.04124","last_updated":"2021-09-09T09:22:35Z","snapshot_observed_at":"2026-08-12T15:35:44.052373Z","submitted_at":"2021-09-09T09:22:35Z","title":"Defects and phase transitions to geometric phases of abelian GLSMs","version":1},"cited_work":{"arxiv_id":"2109.04124","doi":null,"metadata_source":"pith","pith_arxiv_id":"2109.04124","snapshot_observed_at":"2026-08-11T20:54:10.989304Z","title":"Defects and phase transitions to geometric phases of abelian GLSMs","venue":"hep-th","work_id":"7c185cdc-ec05-4273-957e-119d994cdf9e","year":2021},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.561769Z"},"links":{"cited_paper":"/paper/2109.04124","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:77637182aba356851138793ec3a475b7d0d4bcb64c76422d9f308041bc163dce","observation_id":"d325cbd8-8ff7-41dc-97d8-21c0342dcf20","resolution":{"observed_at":"2026-08-11T20:54:10.994062Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0707.0922","last_updated":"2007-07-06T08:26:30Z","snapshot_observed_at":"2026-07-06T01:28:33.457108Z","submitted_at":"2007-07-06T08:26:30Z","title":"B-type defects in Landau-Ginzburg models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0707.0922","snapshot_observed_at":"2026-08-11T20:54:10.565777Z","title":"B-type defects in Landa u-Ginzburg models","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.565777Z"},"links":{"cited_paper":"/paper/0707.0922","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:5e8524a4b8fda18c1dc1b97688e11c6e6cf1be36fdd011ac9ba1475f07ffa515","observation_id":"fb4443db-79a8-4892-973a-61fd28149b70","resolution":{"observed_at":"2026-08-11T20:54:10.565777Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0712.0188","last_updated":"2008-03-25T22:03:28Z","snapshot_observed_at":"2026-07-06T01:35:51.071281Z","submitted_at":"2007-12-02T21:16:54Z","title":"Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0712.0188","snapshot_observed_at":"2026-08-11T20:54:10.570647Z","title":"Defects and bulk pertur bations of boundary Landau- Ginzburg orbifolds","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.570647Z"},"links":{"cited_paper":"/paper/0712.0188","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:41502be60f356da4232ac4fb76cb9224e54c48bfaf0d6d000f302b00cbfbdbe5","observation_id":"e1acbbf0-3b81-417d-aa18-5d9733bbbeb1","resolution":{"observed_at":"2026-08-11T20:54:10.570647Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1508.04350","last_updated":"2016-03-20T11:52:22Z","snapshot_observed_at":"2026-07-06T04:27:00.684723Z","submitted_at":"2015-08-18T15:27:00Z","title":"Reflection and transmission of conformal perturbation defects","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1508.04350","snapshot_observed_at":"2026-08-11T20:54:10.574885Z","title":"Reflection and tran smission of conformal pertur- bation defects","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.574885Z"},"links":{"cited_paper":"/paper/1508.04350","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:ffd1c9a45fc074c4a6c4ebaac46c0c01d8efe4409a4e7d8d4ed3742845f00828","observation_id":"66ef5cf3-6416-451d-9c2c-9e549b57a342","resolution":{"observed_at":"2026-08-11T20:54:10.574885Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0305133","last_updated":"2003-06-06T21:48:05Z","snapshot_observed_at":"2026-08-05T11:54:54.336208Z","submitted_at":"2003-05-15T19:57:31Z","title":"Landau-Ginzburg Realization of Open String TFT","version":3},"cited_work":{"arxiv_id":"hep-th/0305133","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0305133","snapshot_observed_at":"2026-08-11T20:54:10.932974Z","title":"Landau-Ginzburg Realization of Open String TFT","venue":"hep-th","work_id":"387cfb73-8e18-4857-80c7-7ba2b93e3884","year":2003},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.578984Z"},"links":{"cited_paper":"/paper/hep-th/0305133","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:984a23f7af19d5ad169161bed03c2dc88d14eb3d76047fb06af144f4b510d0e7","observation_id":"17774fa9-d0dd-4fc5-82ed-4a0338d39cc8","resolution":{"observed_at":"2026-08-11T20:54:10.936917Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0902.3177","last_updated":"2009-02-18T16:04:01Z","snapshot_observed_at":"2026-08-12T15:21:24.496468Z","submitted_at":"2009-02-18T16:04:01Z","title":"Obstructions and lines of marginal stability from the world-sheet","version":1},"cited_work":{"arxiv_id":"0902.3177","doi":null,"metadata_source":"pith","pith_arxiv_id":"0902.3177","snapshot_observed_at":"2026-08-11T20:54:10.915502Z","title":"Obstructions and lines of marginal stability from the world-sheet","venue":"hep-th","work_id":"c8846910-2899-410a-9f36-9d28a3b5db3e","year":2009},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.583088Z"},"links":{"cited_paper":"/paper/0902.3177","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:4d56cb3fbd40b14e0b1cf2847e69b0919a1ad427ead9e870c3944fcbbd37e2a2","observation_id":"13c959a5-ad61-4ea3-aee5-c52df2c0cbd9","resolution":{"observed_at":"2026-08-11T20:54:10.919780Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1811.12385","last_updated":"2023-11-27T14:43:18Z","snapshot_observed_at":"2026-08-09T03:50:00.811566Z","submitted_at":"2018-11-29T18:52:16Z","title":"B-brane transport in anomalous (2,2) models and localization","version":2},"cited_work":{"arxiv_id":"1811.12385","doi":null,"metadata_source":"pith","pith_arxiv_id":"1811.12385","snapshot_observed_at":"2026-08-11T20:54:10.896165Z","title":"B-brane transport in anomalous (2,2) models and localization","venue":"hep-th","work_id":"b8d0b2e6-067c-4560-93dc-eeaf5e368484","year":2018},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.587289Z"},"links":{"cited_paper":"/paper/1811.12385","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:b3cd3b889cfacad763dc282431815fe1b2337f781ed184480676a7a74d15f564","observation_id":"765a483c-351f-4948-89ee-4494338d6a56","resolution":{"observed_at":"2026-08-11T20:54:10.900546Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1304.2913","last_updated":"2013-04-10T11:33:11Z","snapshot_observed_at":"2026-08-12T15:35:34.968604Z","submitted_at":"2013-04-10T11:33:11Z","title":"Grassmannian twists, derived equivalences and brane transport","version":1},"cited_work":{"arxiv_id":"1304.2913","doi":null,"metadata_source":"pith","pith_arxiv_id":"1304.2913","snapshot_observed_at":"2026-08-11T20:54:10.875322Z","title":"Grassmannian twists, derived equivalences and brane transport","venue":"math.AG","work_id":"309f48b4-6061-4421-a46e-00bc429a54b4","year":2013},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.591685Z"},"links":{"cited_paper":"/paper/1304.2913","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:f0709f534bae2d0b945760abe92d101b41563f8451ba44d290ac807e042bce96","observation_id":"a48114c0-f91a-4eb3-ac42-752d0d97a6e1","resolution":{"observed_at":"2026-08-11T20:54:10.880274Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1005.2779","last_updated":"2010-05-18T19:37:26Z","snapshot_observed_at":"2026-07-06T02:10:19.764387Z","submitted_at":"2010-05-16T22:03:13Z","title":"Spaces of Quantum Field Theories","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1005.2779","snapshot_observed_at":"2026-08-11T20:54:10.595812Z","title":"Spaces of Quantum Field Theories","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.595812Z"},"links":{"cited_paper":"/paper/1005.2779","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:fc86611b547ed5d599b83b7642756c8ed2cd73562305bda0de96e300938a88b1","observation_id":"61ea6350-8d1e-47af-8cce-34ab98438520","resolution":{"observed_at":"2026-08-11T20:54:10.595812Z","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":"2026-08-11T20:54:11.074757Z","title":"Homological algebra on a complete intersection , with an application to group representations","venue":null,"work_id":"6306c8f6-a360-48e1-b406-206b0d694cb6","year":1980},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.599922Z"},"links":{"citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:02f1d1a6d90b8e864b313098fb02f4789de933b99cf0f0499eb6843b34e2a8d3","observation_id":"024f12a9-a688-4fa7-9f73-6199dae05d7f","resolution":{"observed_at":"2026-08-11T20:54:11.079422Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1506.04087","last_updated":"2015-06-12T17:58:20Z","snapshot_observed_at":"2026-08-08T07:08:44.258698Z","submitted_at":"2015-06-12T17:58:20Z","title":"Algebra of the Infrared: String Field Theoretic Structures in Massive ${\\cal N}=(2,2)$ Field Theory In Two Dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1506.04087","snapshot_observed_at":"2026-08-11T20:54:10.603750Z","title":"Algebr a of the Infrared: String Field Theoretic Structures in Massive N = (2, 2) Field Theory In Two Dimensions","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.603750Z"},"links":{"cited_paper":"/paper/1506.04087","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:837668fb0ee1643159d6e90b9cfb10f2836edaf65998030a7261cef0ac9d59a9","observation_id":"1d90b908-aed2-4fcd-914a-d684b7c4520f","resolution":{"observed_at":"2026-08-11T20:54:10.603750Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.07602","last_updated":"2022-09-26T15:06:51Z","snapshot_observed_at":"2026-07-06T11:09:57.732606Z","submitted_at":"2021-05-17T04:14:15Z","title":"On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry","version":3},"cited_work":{"arxiv_id":"2105.07602","doi":null,"metadata_source":"pith","pith_arxiv_id":"2105.07602","snapshot_observed_at":"2026-08-11T20:54:10.826410Z","title":"On Supersymmetric Interface Defects, Brane Parallel Transport, Order-Disorder Transition and Homological Mirror Symmetry","venue":"hep-th","work_id":"7091ef3c-d6f2-49f6-b33e-15fd5a4cdeca","year":2021},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.607524Z"},"links":{"cited_paper":"/paper/2105.07602","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:caf5ca072b80ac1781f0365635fd0d298f879a279abe54f0a7f5bc1d20987517","observation_id":"ef02da93-06a3-416a-a177-982854e17eb0","resolution":{"observed_at":"2026-08-11T20:54:10.833057Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0803.2045","last_updated":"2008-03-14T18:30:28Z","snapshot_observed_at":"2026-07-06T01:35:44.689779Z","submitted_at":"2008-03-14T18:30:28Z","title":"Phases Of N=2 Theories In 1+1 Dimensions With Boundary","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0803.2045","snapshot_observed_at":"2026-08-11T20:54:10.611237Z","title":"Phases Of N=2 Theories In 1+1 Dimensions With Boundary","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.611237Z"},"links":{"cited_paper":"/paper/0803.2045","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:e0daf02630be623f53e423039f113aaaee4dead6aec401052145d4bb702b1608","observation_id":"8cdc670e-aecd-4c49-83ae-1c95d70fa0c5","resolution":{"observed_at":"2026-08-11T20:54:10.611237Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0005247","last_updated":"2000-05-28T23:31:20Z","snapshot_observed_at":"2026-07-07T04:36:49.685738Z","submitted_at":"2000-05-25T22:40:39Z","title":"D-Branes And Mirror Symmetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0005247","snapshot_observed_at":"2026-08-11T20:54:10.615021Z","title":"D-branes and mir ror symmetry","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.615021Z"},"links":{"cited_paper":"/paper/hep-th/0005247","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:9497776c8ac1be2161c401b8b0193abde8f954bbef003f879430d4ff31e4b51c","observation_id":"72f56be5-72e1-4951-b4ad-22c4db9a068b","resolution":{"observed_at":"2026-08-11T20:54:10.615021Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1308.2438","last_updated":"2013-08-11T23:58:35Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2013-08-11T23:58:35Z","title":"Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1308.2438","snapshot_observed_at":"2026-08-11T20:54:10.619318Z","title":"Exact Results In Two-Dimens ional (2,2) Supersymmetric Gauge Theories With Boundary","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.619318Z"},"links":{"cited_paper":"/paper/1308.2438","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:01da3653b6e6e0757d5d89aabaf19f73dc2d3782d92dd69b366ae2cbc6b4805c","observation_id":"39c6b626-b235-44b6-a396-c7deb33f7ca4","resolution":{"observed_at":"2026-08-11T20:54:10.619318Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0210296","last_updated":"2002-11-27T19:29:06Z","snapshot_observed_at":"2026-08-08T10:20:35.017455Z","submitted_at":"2002-10-30T22:56:00Z","title":"D-Branes in Landau-Ginzburg Models and Algebraic Geometry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0210296","snapshot_observed_at":"2026-08-11T20:54:10.623685Z","title":"D branes in Landau-Ginzburg models a nd algebraic geometry","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.623685Z"},"links":{"cited_paper":"/paper/hep-th/0210296","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:ac111470c79f5037136ced36edcbc6f85d749a13d17094e74448ca919a585055","observation_id":"70afb09d-f243-47cb-92b9-7855de3256b7","resolution":{"observed_at":"2026-08-11T20:54:10.623685Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.08961","last_updated":"2021-02-17T07:54:30Z","snapshot_observed_at":"2026-08-02T22:42:59.148477Z","submitted_at":"2020-06-16T07:33:48Z","title":"Complementary Projection Defects and Decompositions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.08961","snapshot_observed_at":"2026-08-11T20:54:10.628110Z","title":"Complementary projectio n defects and decomposition","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.628110Z"},"links":{"cited_paper":"/paper/2006.08961","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:3f500ba6126360c8268ea09fddacb954595fc85b014b5e5265c42acb97b3a2a5","observation_id":"5ffe43b7-0cdc-4240-a44c-49d8888bd620","resolution":{"observed_at":"2026-08-11T20:54:10.628110Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2312.07639","last_updated":"2024-11-04T21:05:39Z","snapshot_observed_at":"2026-07-06T17:00:45.756069Z","submitted_at":"2023-12-12T12:48:13Z","title":"Grade restriction and D-brane transport for a non-abelian GLSM of an elliptic curve","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.07639","snapshot_observed_at":"2026-08-11T20:54:10.632439Z","title":"Grade restriction and D-brane transport f or a non-abelian GLSM of an elliptic curve","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.632439Z"},"links":{"cited_paper":"/paper/2312.07639","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:ae94d03953990a7ec2f407c4c93c98e5a1297ea764a8d120c0a878b2293ccb63","observation_id":"07d40a58-e601-473d-89f1-b89863029a23","resolution":{"observed_at":"2026-08-11T20:54:10.632439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2404.14613","last_updated":"2024-06-18T06:23:18Z","snapshot_observed_at":"2026-08-08T13:25:05.896250Z","submitted_at":"2024-04-22T22:47:27Z","title":"B-type D-branes in hybrid models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2404.14613","snapshot_observed_at":"2026-08-11T20:54:10.636631Z","title":"B-type D-branes in hybrid models","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.636631Z"},"links":{"cited_paper":"/paper/2404.14613","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:d58d5b4169e26bf3170495f4bbb0b2f1cd8c45f0968c414593fc5b4f28998e18","observation_id":"a5e248c7-ef70-4960-9d79-b0037937a328","resolution":{"observed_at":"2026-08-11T20:54:10.636631Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.07109","last_updated":"2024-10-29T07:48:30Z","snapshot_observed_at":"2026-08-10T12:14:03.213842Z","submitted_at":"2024-02-11T05:39:32Z","title":"B-brane Transport and Grade Restriction Rule for Determinantal Varieties","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.07109","snapshot_observed_at":"2026-08-11T20:54:10.641002Z","title":"B-brane Transport and Grade Rest riction Rule for Determinantal Varieties","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.641002Z"},"links":{"cited_paper":"/paper/2402.07109","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:fb1b659d66c2f85d8ff25d18dffc0ef5b833f6b21a479608ba81339908403cd8","observation_id":"928cc990-8871-4e0e-b0ce-b3c4e107f016","resolution":{"observed_at":"2026-08-11T20:54:10.641002Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0105038","last_updated":"2001-05-03T18:46:30Z","snapshot_observed_at":"2026-07-07T04:39:55.331431Z","submitted_at":"2001-05-03T18:46:30Z","title":"Geometrical interpretation of D-branes in gauged WZW models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0105038","snapshot_observed_at":"2026-08-11T20:54:10.645348Z","title":"Geometrical interpretation of D-branes in gauged WZW models","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.645348Z"},"links":{"cited_paper":"/paper/hep-th/0105038","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:3b09937d222f2071bb1f99b614c820359e4724ba5b13b3a3934e0997c4b48011","observation_id":"a9cd2464-aa76-4fac-b7e4-725af8511a4e","resolution":{"observed_at":"2026-08-11T20:54:10.645348Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0910.5534","last_updated":"2010-11-24T16:44:23Z","snapshot_observed_at":"2026-07-06T01:59:38.529746Z","submitted_at":"2009-10-29T15:55:56Z","title":"Equivalences between GIT quotients of Landau-Ginzburg B-models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0910.5534","snapshot_observed_at":"2026-08-11T20:54:10.649405Z","title":"Equivalences between GIT quotients of Landau-Ginz burg B-models","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.649405Z"},"links":{"cited_paper":"/paper/0910.5534","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:fec3a39a24617a60782608eed77e28b65149f04f9aa3fd0250d89cf20149be00","observation_id":"78bff10c-490e-49a5-9871-64fc2359a90f","resolution":{"observed_at":"2026-08-11T20:54:10.649405Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9301042","last_updated":"1993-02-18T13:59:00Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"1993-01-12T15:11:00Z","title":"Phases of $N=2$ Theories In Two Dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9301042","snapshot_observed_at":"2026-08-11T20:54:10.653651Z","title":"Phases of N=2 theories in two-dimensions","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-11T20:54:10.653651Z"},"links":{"cited_paper":"/paper/hep-th/9301042","citing_paper":"/paper/2412.05172"},"observation_digest":"sha256:1ae52ed9aae02639366775ad8d384044c72c8b27f3ef581a6609c778594f995e","observation_id":"2b9f97a0-8c81-4c7b-8677-d91995834895","resolution":{"observed_at":"2026-08-11T20:54:10.653651Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2412.05172","last_updated":"2024-12-06T16:43:53Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-12T13:53:33.014195Z","submitted_at":"2024-12-06T16:43:53Z","title":"Defects and Phases of Higher Rank Abelian GLSMs"},"reference_resolution":{"displayed":27,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":16,"verified_exact":10,"verified_fuzzy":1},"total_outbound_references":27},"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":"2026-08-12T06:34:41.77262+00:00","source":"crossref"},{"observed_at":"2026-08-12T06:34:36.333875+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2412.05172."}