{"as_of":"2026-08-20T05:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:db29bf65cff8429261948d755e709eb477a73be0616541bbd0e87b6a31261ab0","coverage":[{"denominator":71,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":71,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T19:31:58.214872Z","state":"measured"},{"denominator":72,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":72,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+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":"2026-05-10T18:42:51.950485Z","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":"2026-05-11T00:05:49.618372Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"cited_work":{"arxiv_id":"2507.05645","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.05645","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Jeric, T","venue":null,"work_id":"608597b8-daf8-48ba-b578-e32db09d5e10","year":2025},"citing_paper":{"arxiv_id":"2604.06635","last_updated":"2026-04-08T03:20:37Z","snapshot_observed_at":"2026-08-15T03:12:40.830538Z","submitted_at":"2026-04-08T03:20:37Z","title":"Massive modes on magnetized blow-up manifold of $T^2/\\mathbb{Z}_N$","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-05-10T18:42:51.950485Z"},"links":{"cited_paper":"/paper/2507.05645","citing_paper":"/paper/2604.06635"},"observation_digest":"sha256:14ca87ab9689750f01f29bce652dcc297d188eed2335052fe4789b64077900a5","observation_id":"53ac104d-bd14-4cae-9ea0-c45ebdefc7f2","resolution":{"observed_at":"2026-05-11T00:05:49.621806Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.05645/citation-record","integrity":"/paper/2507.05645/integrity","json":"/paper/2507.05645/citation-record.json","paper":"/paper/2507.05645"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:58.811951Z","title":null,"venue":null,"work_id":"4fd75670-92ca-49a2-98ba-2d2e309a86fe","year":1985},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.054158Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:2256e5daa13758b142f1cbcc346e77ff2bdfd2f73292e329eb248762e1205ce3","observation_id":"5c37d299-6055-4657-afa8-c2744667e694","resolution":{"observed_at":"2026-08-06T19:31:58.814383Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.805035Z","title":null,"venue":null,"work_id":"769d156b-d15c-4bbe-8008-bacc0646ecbe","year":1986},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.057232Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:2f0e6344c16fb9b6b257169be65b1f767ea34f518d23483075fc73e251c0acf5","observation_id":"9fb8b4e9-c9a4-4956-8e75-55da90bd71a0","resolution":{"observed_at":"2026-08-06T19:31:58.807614Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.798393Z","title":"Witten, Phys","venue":null,"work_id":"78da7ab8-4f13-487b-b40a-2779921dee61","year":1984},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.059658Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:6808a393f9a3662fb01183fb48634eeae70fd02fa90c84393cd3c6b5127cfb46","observation_id":"e965ad45-2125-4926-8714-1df1872750ab","resolution":{"observed_at":"2026-08-06T19:31:58.800479Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9503030","last_updated":"1995-03-06T08:10:39Z","snapshot_observed_at":"2026-08-10T12:30:38.114208Z","submitted_at":"1995-03-06T08:10:39Z","title":"A WAY TO BREAK SUPERSYMMETRY","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9503030","snapshot_observed_at":"2026-08-06T19:31:58.061991Z","title":"Bachas, [arXiv:hep-th/9503030 [hep-th]]","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.061991Z"},"links":{"cited_paper":"/paper/hep-th/9503030","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:adf22c0c0350fa089219205da92114fd670f5d5556d9475a2e48faa18289dbf6","observation_id":"c7f8019f-a4b0-4ee0-895f-fd35a82893df","resolution":{"observed_at":"2026-08-06T19:31:58.061991Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9606139","last_updated":"1996-08-28T22:14:22Z","snapshot_observed_at":"2026-07-07T05:11:07.518713Z","submitted_at":"1996-06-24T02:13:47Z","title":"Branes Intersecting at Angles","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9606139","snapshot_observed_at":"2026-08-06T19:31:58.064960Z","title":"Berkooz, M","venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.064960Z"},"links":{"cited_paper":"/paper/hep-th/9606139","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:33f1f24c1db085992fc6447ef45fd58642dc3ce1b9a803d322d2c347228044aa","observation_id":"ee5dab87-52c9-4682-b7a9-181edf8947b1","resolution":{"observed_at":"2026-08-06T19:31:58.064960Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0007024","last_updated":"2000-07-04T12:36:25Z","snapshot_observed_at":"2026-08-14T10:00:46.195270Z","submitted_at":"2000-07-04T12:36:25Z","title":"Noncommutative Compactifications of Type I Strings on Tori with Magnetic Background Flux","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0007024","snapshot_observed_at":"2026-08-06T19:31:58.067396Z","title":"Blumenhagen, L","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.067396Z"},"links":{"cited_paper":"/paper/hep-th/0007024","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:9538d3ee95135e45765767114a062940aed7550f2b85fd91148a491fec3fbe8f","observation_id":"aa21022e-3f6e-4116-8b91-c8f707b87e4c","resolution":{"observed_at":"2026-08-06T19:31:58.067396Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0007090","last_updated":"2000-07-29T11:18:20Z","snapshot_observed_at":"2026-08-14T09:03:16.326200Z","submitted_at":"2000-07-11T23:01:51Z","title":"Type-I strings on magnetised orbifolds and brane transmutation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0007090","snapshot_observed_at":"2026-08-06T19:31:58.070515Z","title":"Angelantonj, I","venue":null,"work_id":null,"year":2000},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.070515Z"},"links":{"cited_paper":"/paper/hep-th/0007090","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:e2fab14f6565d16571a2a619aa8a806ec9881aadcd1567a9c1dabc7b6dcf9855","observation_id":"b6b04156-cb3c-4e16-a79c-67f01c4b1cc9","resolution":{"observed_at":"2026-08-06T19:31:58.070515Z","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":"th/0012156","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:58.689923Z","title":"Blumenhagen, B","venue":null,"work_id":"3295ed70-4afb-46da-9ec6-cf6ed720222c","year":2001},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.072940Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4b0efa171c42f3683c9642ec9803e55e076633e6366e077d450f4adb098d51cc","observation_id":"c72fd659-8058-4be4-90bc-3b83f2d5a3e6","resolution":{"observed_at":"2026-08-06T19:31:58.693588Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"th/0404229","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T19:31:58.622097Z","title":"Cremades, L","venue":null,"work_id":"ddbb7114-9fc1-4196-bce7-575a3b1b0832","year":2004},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.075441Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:80ebe63c7c2eb26c64773dac244709855402b4c71b9387f00f457815a8cbf8bb","observation_id":"4863869a-aac8-4b58-9e0c-7dd1a5fe748f","resolution":{"observed_at":"2026-08-06T19:31:58.625394Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0904.0910","last_updated":"2009-08-10T12:16:04Z","snapshot_observed_at":"2026-08-15T05:51:18.252119Z","submitted_at":"2009-04-06T12:29:21Z","title":"Fermion Wavefunctions in Magnetized branes: Theta identities and Yukawa couplings","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0904.0910","snapshot_observed_at":"2026-08-06T19:31:58.077434Z","title":"Antoniadis, A","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.077434Z"},"links":{"cited_paper":"/paper/0904.0910","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:8dde417993d2ec2fbec29b4df880c252ef1b3b591d81eb7aa3986b37604da756","observation_id":"5c54aa6e-e948-4b3e-b094-de6732a4222f","resolution":{"observed_at":"2026-08-06T19:31:58.077434Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1304.0978","last_updated":"2013-04-03T15:14:49Z","snapshot_observed_at":"2026-08-15T00:22:45.857334Z","submitted_at":"2013-04-03T15:14:49Z","title":"Magnetized Branes and the Six-Torus","version":1},"cited_work":{"arxiv_id":"1304.0978","doi":null,"metadata_source":"pith","pith_arxiv_id":"1304.0978","snapshot_observed_at":"2026-08-06T19:31:58.524397Z","title":"Magnetized Branes and the Six-Torus","venue":"hep-th","work_id":"2639e145-a102-4215-8c2a-5058c52da96a","year":2013},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.079759Z"},"links":{"cited_paper":"/paper/1304.0978","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:3824f87c6eeeea5c31cbe2db568d32ac085ce24380749e3b54906b48cb4fe501","observation_id":"65e5cc1c-3b3d-4e8c-977b-22bbbd78723f","resolution":{"observed_at":"2026-08-06T19:31:58.528402Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0903.3800","last_updated":"2009-09-25T07:12:59Z","snapshot_observed_at":"2026-08-15T05:52:24.611215Z","submitted_at":"2009-03-23T07:57:09Z","title":"Higher Order Couplings in Magnetized Brane Models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0903.3800","snapshot_observed_at":"2026-08-06T19:31:58.081994Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.081994Z"},"links":{"cited_paper":"/paper/0903.3800","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:af11c5f3a563f6150c1da129f5ab73467ad91e7c35d77541c435d37594e2b1de","observation_id":"2ad8b8f3-a3ca-45f1-a442-f4e9a5087486","resolution":{"observed_at":"2026-08-06T19:31:58.081994Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.09784","last_updated":"2017-09-28T02:18:18Z","snapshot_observed_at":"2026-08-14T20:28:55.570991Z","submitted_at":"2017-09-28T02:18:18Z","title":"Zero-modes on orbifolds : magnetized orbifold models by modular transformation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1709.09784","snapshot_observed_at":"2026-08-06T19:31:58.084089Z","title":"Kobayashi and S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.084089Z"},"links":{"cited_paper":"/paper/1709.09784","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:42b188c44c3da2f294235934c0192384263a42962ce24144b6b3e3f4b0a6987b","observation_id":"a628f61d-193c-4ce1-a512-1c71b8bcf280","resolution":{"observed_at":"2026-08-06T19:31:58.084089Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2101.00826","last_updated":"2021-11-29T02:54:49Z","snapshot_observed_at":"2026-08-16T18:54:29.447955Z","submitted_at":"2021-01-04T08:29:47Z","title":"Modular flavor symmetries of three-generation modes on magnetized toroidal orbifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2101.00826","snapshot_observed_at":"2026-08-06T19:31:58.086262Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.086262Z"},"links":{"cited_paper":"/paper/2101.00826","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:fa6a0cad2c56c6aa7ec8cca555e75986aa5a453f2d7107f3b5e04f08b9f00d02","observation_id":"c46224fb-866b-4f54-b939-2afb5de9f587","resolution":{"observed_at":"2026-08-06T19:31:58.086262Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1804.06644","last_updated":"2018-04-18T10:46:59Z","snapshot_observed_at":"2026-08-14T19:24:43.456048Z","submitted_at":"2018-04-18T10:46:59Z","title":"Modular symmetry and non-Abelian discrete flavor symmetries in string compactification","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1804.06644","snapshot_observed_at":"2026-08-06T19:31:58.088359Z","title":"Kobayashi, S","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.088359Z"},"links":{"cited_paper":"/paper/1804.06644","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:1d11b6366d23e0c070e1050aa384066bb54be044e2bf5bfa10d25d36bf7ddedb","observation_id":"96d83099-cdda-4226-9ad3-4b7be74ea701","resolution":{"observed_at":"2026-08-06T19:31:58.088359Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2005.12642","last_updated":"2020-11-07T04:41:22Z","snapshot_observed_at":"2026-08-16T12:07:19.382303Z","submitted_at":"2020-05-26T11:52:45Z","title":"Revisiting modular symmetry in magnetized torus and orbifold compactifications","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2005.12642","snapshot_observed_at":"2026-08-06T19:31:58.091050Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.091050Z"},"links":{"cited_paper":"/paper/2005.12642","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:e4fc374a44e017539434328104fa46f7e9238c2c67fb9d4b8e24517fb2eac082","observation_id":"50910aeb-563e-4e45-b446-c8e3647d1f60","resolution":{"observed_at":"2026-08-06T19:31:58.091050Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.11384","last_updated":"2018-11-28T04:43:41Z","snapshot_observed_at":"2026-08-16T10:38:17.093748Z","submitted_at":"2018-11-28T04:43:41Z","title":"Modular forms of finite modular subgroups from magnetized D-brane models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.11384","snapshot_observed_at":"2026-08-06T19:31:58.093210Z","title":"Kobayashi and S","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.093210Z"},"links":{"cited_paper":"/paper/1811.11384","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:f6a28787468e87729fb9c2b520bfdfe08fd75b548bd49de6ec7cc1d4f3ea0efc","observation_id":"bd35e923-54cf-439c-9a64-09b6dab656be","resolution":{"observed_at":"2026-08-06T19:31:58.093210Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2003.04174","last_updated":"2020-10-06T04:51:00Z","snapshot_observed_at":"2026-08-16T10:37:49.638926Z","submitted_at":"2020-03-09T14:32:20Z","title":"Modular Flavor Symmetry on Magnetized Torus","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2003.04174","snapshot_observed_at":"2026-08-06T19:31:58.095284Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.095284Z"},"links":{"cited_paper":"/paper/2003.04174","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:a6551fb128c641a1276a560841df8269ae8e765c99c0afc140a303972612ef0d","observation_id":"32efdfc6-66b6-4214-b6e1-4d863591bb21","resolution":{"observed_at":"2026-08-06T19:31:58.095284Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2007.06188","last_updated":"2020-07-13T04:55:20Z","snapshot_observed_at":"2026-08-16T10:49:31.184643Z","submitted_at":"2020-07-13T04:55:20Z","title":"Modular symmetry by orbifolding magnetized $T^2\\times T^2$: realization of double cover of $\\Gamma_N$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2007.06188","snapshot_observed_at":"2026-08-06T19:31:58.097413Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.097413Z"},"links":{"cited_paper":"/paper/2007.06188","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:d72fce7e56bc510f7d868eb644c9da37b6159487d2e1959f08277081ce757267","observation_id":"723b8a70-5e3c-4be5-8a8b-2757b7b6d264","resolution":{"observed_at":"2026-08-06T19:31:58.097413Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2102.11286","last_updated":"2021-02-22T19:00:02Z","snapshot_observed_at":"2026-08-17T21:57:18.986717Z","submitted_at":"2021-02-22T19:00:02Z","title":"Metaplectic Flavor Symmetries from Magnetized Tori","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2102.11286","snapshot_observed_at":"2026-08-06T19:31:58.099520Z","title":"Almumin, M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.099520Z"},"links":{"cited_paper":"/paper/2102.11286","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:7a36d7d05b605c29a0eba7b096b41a961fc505251556fe7932479985c414601c","observation_id":"a3c5e106-3593-4064-92d3-5c8054046f38","resolution":{"observed_at":"2026-08-06T19:31:58.099520Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2309.16447","last_updated":"2023-09-28T13:56:40Z","snapshot_observed_at":"2026-08-19T06:14:58.816936Z","submitted_at":"2023-09-28T13:56:40Z","title":"Modular symmetry in magnetized $T^{2g}$ torus and orbifold models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2309.16447","snapshot_observed_at":"2026-08-06T19:31:58.101554Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.101554Z"},"links":{"cited_paper":"/paper/2309.16447","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:151dcec3c11b1f8487fd4b38e5f7473df418e4474a24772f897a6624c9c892f9","observation_id":"ce2456a7-c517-4ace-8141-628fccf5fe84","resolution":{"observed_at":"2026-08-06T19:31:58.101554Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.02458","last_updated":"2024-09-04T05:48:27Z","snapshot_observed_at":"2026-08-16T13:21:31.868550Z","submitted_at":"2024-09-04T05:48:27Z","title":"Flavor symmetries from modular subgroups in magnetized compactifications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.02458","snapshot_observed_at":"2026-08-06T19:31:58.104095Z","title":"Kobayashi, K","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.104095Z"},"links":{"cited_paper":"/paper/2409.02458","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:413f482e44131eddc27a955806b64bf5f1672e4ed6f1da2a2a2c4d7cf9238b60","observation_id":"625944f8-fa40-4d7e-8131-9dc92a8a5a90","resolution":{"observed_at":"2026-08-06T19:31:58.104095Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0806.4748","last_updated":"2008-09-09T11:31:05Z","snapshot_observed_at":"2026-08-15T10:12:17.467235Z","submitted_at":"2008-06-29T11:31:25Z","title":"Magnetized orbifold models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0806.4748","snapshot_observed_at":"2026-08-06T19:31:58.106074Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.106074Z"},"links":{"cited_paper":"/paper/0806.4748","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:d220a4b173d1f14bb449d57cb809c84f415728d942e04bc4f86934a416f5dc0f","observation_id":"3d87446e-b082-45a3-acce-6349f61ba799","resolution":{"observed_at":"2026-08-06T19:31:58.106074Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1309.4925","last_updated":"2014-01-24T06:19:16Z","snapshot_observed_at":"2026-08-15T00:02:36.610193Z","submitted_at":"2013-09-19T10:49:54Z","title":"$Z_N$ twisted orbifold models with magnetic flux","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1309.4925","snapshot_observed_at":"2026-08-06T19:31:58.108302Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.108302Z"},"links":{"cited_paper":"/paper/1309.4925","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:bf000095404752451b07e13b51853cb8f1e32148c80c178d0f8938d51121c05f","observation_id":"8ec18892-05f5-4a75-97c9-47541ffc9ba7","resolution":{"observed_at":"2026-08-06T19:31:58.108302Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0812.3534","last_updated":"2008-12-18T13:34:38Z","snapshot_observed_at":"2026-08-15T05:58:59.139561Z","submitted_at":"2008-12-18T13:34:38Z","title":"Three generation magnetized orbifold models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0812.3534","snapshot_observed_at":"2026-08-06T19:31:58.110850Z","title":null,"venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.110850Z"},"links":{"cited_paper":"/paper/0812.3534","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:f068b0c07b2e6faaf38053e37201ad13aeb3eb69d53f351b157fae361ca6188c","observation_id":"1e1906ea-dd60-4cba-bec7-2a2c784118c5","resolution":{"observed_at":"2026-08-06T19:31:58.110850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1501.02787","last_updated":"2015-04-30T14:10:07Z","snapshot_observed_at":"2026-08-14T23:04:21.627945Z","submitted_at":"2015-01-12T20:14:27Z","title":"Classification of three-generation models on magnetized orbifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1501.02787","snapshot_observed_at":"2026-08-06T19:31:58.113012Z","title":null,"venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.113012Z"},"links":{"cited_paper":"/paper/1501.02787","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4c85ea69f32c1ab0981cef05887039e3f3733ce0668fd6b6fb6691eeb75ac46d","observation_id":"d4d91336-eae9-427e-978e-b38acbf16283","resolution":{"observed_at":"2026-08-06T19:31:58.113012Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1211.4317","last_updated":"2012-11-27T11:11:15Z","snapshot_observed_at":"2026-08-15T00:38:56.336377Z","submitted_at":"2012-11-19T07:09:22Z","title":"Phenomenological aspects of 10D SYM theory with magnetized extra dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1211.4317","snapshot_observed_at":"2026-08-06T19:31:58.115232Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.115232Z"},"links":{"cited_paper":"/paper/1211.4317","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:ebefd2c20b3dc618aa55586b882bcbc531d12957c4afc61b57ca335c15d1468f","observation_id":"41d017c4-a7a8-40e9-9bfd-0b289325a460","resolution":{"observed_at":"2026-08-06T19:31:58.115232Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1405.5012","last_updated":"2014-05-20T09:41:29Z","snapshot_observed_at":"2026-08-14T23:33:24.554222Z","submitted_at":"2014-05-20T09:41:29Z","title":"Gaussian Froggatt-Nielsen mechanism on magnetized orbifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1405.5012","snapshot_observed_at":"2026-08-06T19:31:58.117418Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.117418Z"},"links":{"cited_paper":"/paper/1405.5012","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:924ff1b374e3e229bbb3d4eba1f7705bff3e59b6b43fc0e6115c82aa65ca550e","observation_id":"20bccdfc-a5a2-4fa4-b432-86b0673bc9f4","resolution":{"observed_at":"2026-08-06T19:31:58.117418Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1605.00140","last_updated":"2016-09-01T12:06:43Z","snapshot_observed_at":"2026-08-14T21:59:22.675954Z","submitted_at":"2016-04-30T17:11:24Z","title":"Comprehensive Analysis of Yukawa Hierarchies on $T^2/Z_N$ with Magnetic Fluxes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1605.00140","snapshot_observed_at":"2026-08-06T19:31:58.119593Z","title":"Fujimoto, T","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.119593Z"},"links":{"cited_paper":"/paper/1605.00140","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:7b24d43b1a56a243476a0d881a0bf31e205ed8cf9aee29b1879633f08b2cc2f0","observation_id":"67918577-708d-416f-a6dc-18163f97f39a","resolution":{"observed_at":"2026-08-06T19:31:58.119593Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1701.06935","last_updated":"2017-01-24T15:38:48Z","snapshot_observed_at":"2026-08-14T21:19:43.940681Z","submitted_at":"2017-01-24T15:38:48Z","title":"Flavour mixings in flux compactifications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1701.06935","snapshot_observed_at":"2026-08-06T19:31:58.121654Z","title":"Buchmuller and J","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.121654Z"},"links":{"cited_paper":"/paper/1701.06935","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:f5e81659856846ae0a2054036e3115ba95a1ca890d9c84e60b6150bf900cc965","observation_id":"c142a3ca-16ab-4b9a-b5fc-787fa06bdbab","resolution":{"observed_at":"2026-08-06T19:31:58.121654Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1712.06862","last_updated":"2018-04-20T02:59:12Z","snapshot_observed_at":"2026-08-14T20:02:14.610085Z","submitted_at":"2017-12-19T10:53:03Z","title":"Flavour physics without flavour symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.06862","snapshot_observed_at":"2026-08-06T19:31:58.123867Z","title":"Buchmuller and K","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.123867Z"},"links":{"cited_paper":"/paper/1712.06862","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:41591ec3d60232f7f71661f437ab9cd0e2ad65c84022cd2640e1263a50f17876","observation_id":"fa284004-033d-456a-96aa-fbdaf9223bee","resolution":{"observed_at":"2026-08-06T19:31:58.123867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.07249","last_updated":"2022-09-15T12:34:57Z","snapshot_observed_at":"2026-08-16T16:32:18.150030Z","submitted_at":"2022-09-15T12:34:57Z","title":"Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.07249","snapshot_observed_at":"2026-08-06T19:31:58.126264Z","title":"Hoshiya, S","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.126264Z"},"links":{"cited_paper":"/paper/2209.07249","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:d8e319da0a35e56213ee7b7b6606727f40dcb5d3cf6c06829f1166a5791946b3","observation_id":"141d1657-ae54-4a6e-b490-673a5c5febf1","resolution":{"observed_at":"2026-08-06T19:31:58.126264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2203.01649","last_updated":"2022-08-29T03:27:26Z","snapshot_observed_at":"2026-08-16T17:17:15.697237Z","submitted_at":"2022-03-03T11:14:15Z","title":"Classifications of magnetized $T^4$ and $T^4/Z_2$ orbifold models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2203.01649","snapshot_observed_at":"2026-08-06T19:31:58.128797Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.128797Z"},"links":{"cited_paper":"/paper/2203.01649","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:5ba640b2ba1fc2844b3129f7d8510af14d566dc9b3fa67a0e0ee5495a8b6d723","observation_id":"8bab5eac-e060-4259-bbcf-5d4bb2c349ea","resolution":{"observed_at":"2026-08-06T19:31:58.128797Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.07813","last_updated":"2023-06-14T05:35:11Z","snapshot_observed_at":"2026-08-16T16:16:12.354701Z","submitted_at":"2022-11-15T00:35:39Z","title":"Number of zero-modes on magnetized $T^4/Z_N$ orbifolds analyzed by modular transformation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.07813","snapshot_observed_at":"2026-08-06T19:31:58.131498Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.131498Z"},"links":{"cited_paper":"/paper/2211.07813","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:ffb809653cd747fe3528c9de333cee521990c0c68af211d52a9024101b1f9974","observation_id":"cc6b0c67-99c8-49f5-b2e7-97711e449f2e","resolution":{"observed_at":"2026-08-06T19:31:58.131498Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.16709","last_updated":"2023-05-26T07:54:47Z","snapshot_observed_at":"2026-08-18T04:12:54.583691Z","submitted_at":"2023-05-26T07:54:47Z","title":"Zero-modes in magnetized $T^6/\\mathbb{Z}_N$ orbifold models through $Sp(6,\\mathbb{Z})$ modular symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.16709","snapshot_observed_at":"2026-08-06T19:31:58.134105Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.134105Z"},"links":{"cited_paper":"/paper/2305.16709","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:9b56048f61e8248591e260ddabb5174a63339a34db5f92a26efdd2b42cde6c72","observation_id":"684786f7-79c6-4e22-a702-c14e59c64cbc","resolution":{"observed_at":"2026-08-06T19:31:58.134105Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.14214","last_updated":"2020-10-27T11:43:13Z","snapshot_observed_at":"2026-08-16T19:10:18.250794Z","submitted_at":"2020-10-27T11:43:13Z","title":"Index theorem on $T^2/\\mathbb{Z}_N$ orbifolds","version":1},"cited_work":{"arxiv_id":"2010.14214","doi":null,"metadata_source":"pith","pith_arxiv_id":"2010.14214","snapshot_observed_at":"2026-08-06T19:31:58.377594Z","title":"Index theorem on $T^2/\\mathbb{Z}_N$ orbifolds","venue":"hep-th","work_id":"323593af-6c4e-4f1a-920a-a8343dbbc9ce","year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.136372Z"},"links":{"cited_paper":"/paper/2010.14214","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:bdaf6e529beb96712eee72593fa8b8a38b5cc850445d1bc87e3e0d9f91c9bc40","observation_id":"017150ac-3e2f-41d5-bf56-6048238defa9","resolution":{"observed_at":"2026-08-06T19:31:58.380043Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2211.04595","last_updated":"2022-11-08T22:34:25Z","snapshot_observed_at":"2026-08-16T16:17:38.231788Z","submitted_at":"2022-11-08T22:34:25Z","title":"Index theorem on magnetized blow-up manifold of $T^2/\\mathbb{Z}_N$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.04595","snapshot_observed_at":"2026-08-06T19:31:58.138993Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.138993Z"},"links":{"cited_paper":"/paper/2211.04595","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4b89b19b4b56c18cb374f74fd8834b2b4d607ad3803f362f356aced9211526fd","observation_id":"e749ab70-b6aa-4d30-8d04-98cd0fe68b77","resolution":{"observed_at":"2026-08-06T19:31:58.138993Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.09758","last_updated":"2024-08-19T07:37:09Z","snapshot_observed_at":"2026-08-16T13:25:37.274458Z","submitted_at":"2024-08-19T07:37:09Z","title":"Computation of the index on orbifold from the Atiyah-Segal-Singer fixed point theorem","version":1},"cited_work":{"arxiv_id":"2408.09758","doi":null,"metadata_source":"pith","pith_arxiv_id":"2408.09758","snapshot_observed_at":"2026-08-06T19:31:58.363103Z","title":"Computation of the index on orbifold from the Atiyah-Segal-Singer fixed point theorem","venue":"hep-th","work_id":"b4077618-12e7-43fd-9258-ea7530d53741","year":2024},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.141415Z"},"links":{"cited_paper":"/paper/2408.09758","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:ef87f181ff7e4326fe387a5883631c7fb103127c3e0f7f92fc9eb24fafdbba1b","observation_id":"d83ea7be-bc96-42cc-bf3c-52323a3755c8","resolution":{"observed_at":"2026-08-06T19:31:58.365729Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.792160Z","title":null,"venue":null,"work_id":"2fb1c72e-ee0c-4925-9211-b4e2f128bc61","year":1987},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.144043Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:595a7d2712effc32490a6ab671928d2d64308b4f3b0052f79f2bb901a2dfafce","observation_id":"64678fd8-98c7-45e0-a78a-6361f982696f","resolution":{"observed_at":"2026-08-06T19:31:58.794250Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.785512Z","title":null,"venue":null,"work_id":"f78d6232-62a3-463a-8dba-f183bf3f1198","year":1988},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.146063Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:e6ba043d66226f82b4187626a67ed2a7dfc21c6ec388d703a6df34565ac6736d","observation_id":"ebeacfd9-62ad-4d7c-9742-d6019854e9e4","resolution":{"observed_at":"2026-08-06T19:31:58.787744Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.779191Z","title":"Katsuki, Y","venue":null,"work_id":"b54e693c-465b-4fe4-a89b-21676553da81","year":1990},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.148464Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:b7ecdac152c9312a9327d2440e3b36e9efaaa0e9a460c55458d03db606eb7112","observation_id":"6a11b283-c34b-4bf7-938b-f30f160356f4","resolution":{"observed_at":"2026-08-06T19:31:58.781238Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.772974Z","title":"Kobayashi and N","venue":null,"work_id":"e7294ac7-e95e-4f73-8477-7932a2f6b583","year":1994},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.150648Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:16ce2bad0c189c6644556de3274db84e58cac1d2a8bf4691c78bd3ec659f38f0","observation_id":"cb53db59-0cef-4d7d-a5fd-368183c247c5","resolution":{"observed_at":"2026-08-06T19:31:58.774970Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0506090","last_updated":"2006-11-16T17:04:48Z","snapshot_observed_at":"2026-08-14T12:42:38.071238Z","submitted_at":"2005-06-13T19:43:31Z","title":"Moduli Stabilization in Type IIB Orientifolds (I)","version":2},"cited_work":{"arxiv_id":"hep-th/0506090","doi":null,"metadata_source":"pith","pith_arxiv_id":"hep-th/0506090","snapshot_observed_at":"2026-08-06T19:31:58.353009Z","title":"Moduli Stabilization in Type IIB Orientifolds (I)","venue":"hep-th","work_id":"b22bf912-b4e7-46b3-9fad-512a89b7c8b0","year":2005},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.152601Z"},"links":{"cited_paper":"/paper/hep-th/0506090","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:81e6b9ae16f257a005d85f88584066c33279d923f79d204da03844f996c4fe2f","observation_id":"48ec322f-8075-4832-a25c-fd68b0eadfa3","resolution":{"observed_at":"2026-08-06T19:31:58.356350Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1016/j.nuclphysb.2006.12.017","metadata_source":"openalex","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T05:30:23.456663Z","title":null,"venue":"Nuclear Physics B","work_id":"c948be84-840c-4025-a407-196631a6c539","year":2007},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.154785Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:84c21d9fbb360aab2c950a04cd0ff9f4b46f40984e864e80ce860bb4b22fa1ca","observation_id":"d485d16c-941a-423a-9f23-3a00869a38a0","resolution":{"observed_at":"2026-08-06T19:31:58.236222Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.766119Z","title":"Symplectic geometry","venue":null,"work_id":"e95b8fd8-3da3-47a7-9cb2-8b58287f9379","year":1943},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.156875Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:72f3e1b7b79a04a2c94a50568c8417ce8e9981154253f24f32a828f2722e17b7","observation_id":"ee0a2ce9-9594-4a23-b034-4adeb7788de2","resolution":{"observed_at":"2026-08-06T19:31:58.768554Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1204.5327","last_updated":"2012-04-24T10:36:43Z","snapshot_observed_at":"2026-08-15T04:12:07.067674Z","submitted_at":"2012-04-24T10:36:43Z","title":"Superfield description of 10D SYM theory with magnetized extra dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1204.5327","snapshot_observed_at":"2026-08-06T19:31:58.158906Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.158906Z"},"links":{"cited_paper":"/paper/1204.5327","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:1c529ac72485e67747ed1bc2a2af39e1016381f40f08944ec031a3b5bf343894","observation_id":"1e0ee134-fa86-4968-aa81-f0a990d43957","resolution":{"observed_at":"2026-08-06T19:31:58.158906Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07952","last_updated":"2020-10-15T18:00:07Z","snapshot_observed_at":"2026-08-16T19:13:10.159392Z","submitted_at":"2020-10-15T18:00:07Z","title":"Automorphic Forms and Fermion Masses","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07952","snapshot_observed_at":"2026-08-06T19:31:58.161088Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.161088Z"},"links":{"cited_paper":"/paper/2010.07952","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4198a92584da04497b27a466c030555335fab9cb52a59b2bb7061f9ede44d66b","observation_id":"fca030fd-2d9a-4419-a10f-44689c639b72","resolution":{"observed_at":"2026-08-06T19:31:58.161088Z","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":"2026-08-06T19:31:58.760172Z","title":"Theta Functions","venue":null,"work_id":"e390ded4-bb97-4a88-a829-972bc8b1ecec","year":1972},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.163115Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:c6c9a1675c6e104a9cdce7efc83602fefb4c53b95d11d106eaaa7de027c7d0f0","observation_id":"90c329cb-9210-4fb7-8a78-728b9d3db383","resolution":{"observed_at":"2026-08-06T19:31:58.762305Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.753600Z","title":"Siegelsche Modulformen","venue":null,"work_id":"5c202712-19c2-4ee7-8b5c-0df48a54f7d8","year":1983},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.165202Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:96339da8be5cd3f45be0c81c596974707e53ef332674dd607ba138cdb82eeeaf","observation_id":"a50e4db2-f4c4-488a-924e-c69d3fa5c428","resolution":{"observed_at":"2026-08-06T19:31:58.756012Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.746915Z","title":"Singular Modular Forms and Theta Relations","venue":null,"work_id":"d632f3ee-f150-4ad6-bc9c-44d02815cb41","year":1991},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.167279Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:a18bbbd4f499ee8e8d99d014efc066b9103d692ab4c5989f0c5e1b1d96268ff9","observation_id":"0a467504-111a-4bc1-962e-b121bfbada76","resolution":{"observed_at":"2026-08-06T19:31:58.749139Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.740578Z","title":"Introductory lecture on siegel modular forms","venue":null,"work_id":"d9015a69-7b26-43a7-8ce2-78817309f9df","year":1990},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.169087Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:2b10a285dd213821a063be8542590e83e769068c85df443d3fa6978f5e578434","observation_id":"fe9d236f-203d-49d4-bb7e-6c02e38fc673","resolution":{"observed_at":"2026-08-06T19:31:58.742894Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.733808Z","title":"The 1-2-3 of Modular Forms","venue":null,"work_id":"81035d34-bc80-4e2d-868c-10c8f97cd705","year":2008},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.170996Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4980b5652deb665c086241974f7ba88d8f712076f3d49cd2a4988be2b5573296","observation_id":"3cb288b5-56d6-40af-bf21-5ac5327fea22","resolution":{"observed_at":"2026-08-06T19:31:58.736534Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.727186Z","title":"Theta functions on Riemann surfaces","venue":null,"work_id":"cd6202ff-2d35-45e2-90bc-cabfe177c9e5","year":1973},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.172873Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:f80f1278066187e012f39914d4cfbbd9f280867d24bd0cf6862e1a6e932f1c88","observation_id":"5f27efef-19b9-457c-8ee3-4a6ea84476e6","resolution":{"observed_at":"2026-08-06T19:31:58.729621Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+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":"2026-08-06T19:31:58.720844Z","title":"Tata Lecture on Theta I","venue":null,"work_id":"88100243-063a-49a3-a3b4-98efff602680","year":1984},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.174652Z"},"links":{"citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:623dee0b289fea7e623fc038650a1fd81b51eedacec30b3fe6784fceb65387c5","observation_id":"4844576b-8e33-4829-b150-bbc71c50f5c1","resolution":{"observed_at":"2026-08-06T19:31:58.723002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1706.08749","last_updated":"2017-09-29T15:31:15Z","snapshot_observed_at":"2026-08-14T20:51:24.559802Z","submitted_at":"2017-06-27T09:26:24Z","title":"Are neutrino masses modular forms?","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1706.08749","snapshot_observed_at":"2026-08-06T19:31:58.176541Z","title":"Feruglio, in From My Vast Repertoire ...: Guido Altarelli’s Legacy, A","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.176541Z"},"links":{"cited_paper":"/paper/1706.08749","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:386d4eb54e3ed39a85841954407e68551e228a8733a1c378517ee055a3180b7e","observation_id":"ac5c5bd7-fa6a-4bd7-998e-db5ec69c4dd3","resolution":{"observed_at":"2026-08-06T19:31:58.176541Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1803.10391","last_updated":"2018-07-10T08:17:32Z","snapshot_observed_at":"2026-08-16T00:16:28.049438Z","submitted_at":"2018-03-28T02:37:18Z","title":"Neutrino mixing from finite modular groups","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1803.10391","snapshot_observed_at":"2026-08-06T19:31:58.178815Z","title":"Kobayashi, K","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.178815Z"},"links":{"cited_paper":"/paper/1803.10391","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:7c26e87162a909dccc41a585e3243b22746dc0572d053d3d97cdf7d63275b6e2","observation_id":"cdd05c0b-a0ff-4f77-b979-78d8b428c291","resolution":{"observed_at":"2026-08-06T19:31:58.178815Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.11040","last_updated":"2018-07-17T15:52:30Z","snapshot_observed_at":"2026-08-16T00:16:27.036628Z","submitted_at":"2018-06-28T15:45:34Z","title":"Lepton Masses and Mixing from Modular $S_4$ Symmetry","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.11040","snapshot_observed_at":"2026-08-06T19:31:58.181403Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.181403Z"},"links":{"cited_paper":"/paper/1806.11040","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:a18a0b9c0e737921dad143810fed9d61977a163eb3939ff0cb13c85e43f2093d","observation_id":"4e8c197b-c3ec-4bff-bffd-42ce7fa67e49","resolution":{"observed_at":"2026-08-06T19:31:58.181403Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1807.01125","last_updated":"2018-09-25T12:57:47Z","snapshot_observed_at":"2026-08-14T18:56:12.744181Z","submitted_at":"2018-07-03T12:44:03Z","title":"Modular Invariance Faces Precision Neutrino Data","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1807.01125","snapshot_observed_at":"2026-08-06T19:31:58.183416Z","title":null,"venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.183416Z"},"links":{"cited_paper":"/paper/1807.01125","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:a7cd5736e7f8a7682feee5aa91af62facb3474f8d01e8590c6ca8aa8c4988020","observation_id":"a49c2929-ad1e-4bb3-b241-d608d5569fd2","resolution":{"observed_at":"2026-08-06T19:31:58.183416Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1808.03012","last_updated":"2018-10-18T08:58:58Z","snapshot_observed_at":"2026-08-17T23:15:28.439251Z","submitted_at":"2018-08-09T03:57:54Z","title":"Modular $A_4$ invariance and neutrino mixing","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1808.03012","snapshot_observed_at":"2026-08-06T19:31:58.185743Z","title":"Kobayashi, N","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.185743Z"},"links":{"cited_paper":"/paper/1808.03012","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:4ba22df840614362c826cf130158a5f028bf477235280e32ff51efc9e5ca6218","observation_id":"fab270b7-429e-4d9a-acf5-185d633133ec","resolution":{"observed_at":"2026-08-06T19:31:58.185743Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1811.04933","last_updated":"2019-04-12T18:11:33Z","snapshot_observed_at":"2026-08-14T18:00:26.053617Z","submitted_at":"2018-11-12T19:00:01Z","title":"Modular $S_4$ Models of Lepton Masses and Mixing","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1811.04933","snapshot_observed_at":"2026-08-06T19:31:58.187915Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.187915Z"},"links":{"cited_paper":"/paper/1811.04933","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:b56ea2cbad08ab03f1e72670c94b3819d3d680784f4159e05b6f5c56b8779fe2","observation_id":"c102a7a8-5cbb-4988-b129-92f8458e35f0","resolution":{"observed_at":"2026-08-06T19:31:58.187915Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.02158","last_updated":"2019-04-29T17:50:15Z","snapshot_observed_at":"2026-08-16T00:16:26.469595Z","submitted_at":"2018-12-05T18:51:00Z","title":"Modular $A_5$ Symmetry for Flavour Model Building","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.02158","snapshot_observed_at":"2026-08-06T19:31:58.190377Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.190377Z"},"links":{"cited_paper":"/paper/1812.02158","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:07eda37c7dafe72f02f9696eb7df311a0f38a5eb16210a509d798840f711f60c","observation_id":"2e3aa503-b17c-47bf-8bbf-ff304b4c1091","resolution":{"observed_at":"2026-08-06T19:31:58.190377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.05620","last_updated":"2020-01-31T21:59:58Z","snapshot_observed_at":"2026-08-17T21:49:14.999307Z","submitted_at":"2018-12-13T19:00:02Z","title":"$SU(5)$ Grand Unified Theory with $A_4$ Modular Symmetry","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.05620","snapshot_observed_at":"2026-08-06T19:31:58.193385Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.193385Z"},"links":{"cited_paper":"/paper/1812.05620","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:bdf0dc911bbb3acd42b25584712a392c403e17d65854866051734ee1432e82c8","observation_id":"4b5536da-f706-4ccc-a861-85b137609023","resolution":{"observed_at":"2026-08-06T19:31:58.193385Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.09677","last_updated":"2019-02-19T05:41:23Z","snapshot_observed_at":"2026-08-14T17:39:11.884735Z","submitted_at":"2018-12-23T09:43:56Z","title":"CP violation of quarks in $A_4$ modular invariance","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.09677","snapshot_observed_at":"2026-08-06T19:31:58.195847Z","title":"Okada and M","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.195847Z"},"links":{"cited_paper":"/paper/1812.09677","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:23cdfedd4993bac8546aa84572371878896d97e0e28a804a66df683990cf03a5","observation_id":"e5b1c1ca-e3a2-40ec-8ed3-f71663f1f092","resolution":{"observed_at":"2026-08-06T19:31:58.195847Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.11072","last_updated":"2019-06-19T07:12:50Z","snapshot_observed_at":"2026-08-14T17:39:12.526860Z","submitted_at":"2018-12-23T08:38:32Z","title":"Finite modular subgroups for fermion mass matrices and baryon/lepton number violation","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.11072","snapshot_observed_at":"2026-08-06T19:31:58.198126Z","title":"Kobayashi, Y","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.198126Z"},"links":{"cited_paper":"/paper/1812.11072","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:6553dd90801b24440e903d1349e4f26c5605212a7fa6f3e674caf7535996f66d","observation_id":"eee9a0b1-e585-4fed-9df0-6ad7e22d741d","resolution":{"observed_at":"2026-08-06T19:31:58.198126Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1812.11289","last_updated":"2019-04-19T00:14:40Z","snapshot_observed_at":"2026-08-14T17:37:17.979538Z","submitted_at":"2018-12-29T05:35:47Z","title":"Trimaximal Neutrino Mixing from Modular A4 Invariance with Residual Symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1812.11289","snapshot_observed_at":"2026-08-06T19:31:58.200451Z","title":null,"venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.200451Z"},"links":{"cited_paper":"/paper/1812.11289","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:95ff7cc36eb34f540d4aeeb6beaa67f9f2a1bb46e2f086e0db2e302f4c5af419","observation_id":"05d1ea14-b142-403e-b606-dfe79dae4a62","resolution":{"observed_at":"2026-08-06T19:31:58.200451Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2307.03384","last_updated":"2023-07-18T01:35:11Z","snapshot_observed_at":"2026-08-16T15:18:04.164102Z","submitted_at":"2023-07-07T04:46:12Z","title":"Modular flavor symmetric models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2307.03384","snapshot_observed_at":"2026-08-06T19:31:58.202648Z","title":"Kobayashi and M","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.202648Z"},"links":{"cited_paper":"/paper/2307.03384","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:1c41e8a41d87dc04cbae1722854286dd5fe09709a8f64f6a9ddef6ef212a3bf1","observation_id":"7e44ddf3-f7eb-48be-8996-897a93625f26","resolution":{"observed_at":"2026-08-06T19:31:58.202648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2311.09282","last_updated":"2023-11-15T19:00:00Z","snapshot_observed_at":"2026-08-19T18:03:02.964353Z","submitted_at":"2023-11-15T19:00:00Z","title":"Neutrino Mass and Mixing with Modular Symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2311.09282","snapshot_observed_at":"2026-08-06T19:31:58.205152Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.205152Z"},"links":{"cited_paper":"/paper/2311.09282","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:8f86c1c06f0e3483ed866b5ce791f37beb152479826ecf0c7b8b4b6510bf0fe8","observation_id":"11cd6161-4cbd-4817-89ee-9962c9e14da2","resolution":{"observed_at":"2026-08-06T19:31:58.205152Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.17978","last_updated":"2023-10-27T08:48:51Z","snapshot_observed_at":"2026-08-16T14:48:21.282821Z","submitted_at":"2023-10-27T08:48:51Z","title":"$Sp(6,Z)$ modular symmetry in flavor structures: quark flavor models and Siegel modular forms for $\\widetilde{\\Delta}(96)$","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.17978","snapshot_observed_at":"2026-08-06T19:31:58.207948Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.207948Z"},"links":{"cited_paper":"/paper/2310.17978","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:7257604cbb9bb7c5d8dbdcb4aaba39f839292b994dd49e7bb6dccdbc164155fb","observation_id":"e2ff8682-f83a-4a6f-9ff2-9738e61ad76c","resolution":{"observed_at":"2026-08-06T19:31:58.207948Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.02867","last_updated":"2019-08-09T04:17:27Z","snapshot_observed_at":"2026-08-14T16:51:23.038073Z","submitted_at":"2019-04-05T04:49:17Z","title":"Wavefunctions and Yukawa Couplings on Resolutions of $T^2/\\mathbb{Z}_N$ Orbifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.02867","snapshot_observed_at":"2026-08-06T19:31:58.210331Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.210331Z"},"links":{"cited_paper":"/paper/1904.02867","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:7fe92e0cd0a45e872353264e4bed7cfff79e892344c7936852b6fa20b13ccb19","observation_id":"6c9f6116-3e1d-4251-96e0-7eed6e191e1d","resolution":{"observed_at":"2026-08-06T19:31:58.210331Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1911.01930","last_updated":"2020-03-31T08:52:05Z","snapshot_observed_at":"2026-08-13T08:25:12.806360Z","submitted_at":"2019-11-05T16:46:41Z","title":"Flavor structure of magnetized $T^2/\\mathbb{Z}_2$ blow-up models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1911.01930","snapshot_observed_at":"2026-08-06T19:31:58.212648Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.212648Z"},"links":{"cited_paper":"/paper/1911.01930","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:962420b28ceaa1a4a3bf3ec1edf047ca64c5649356cef1be918e1b3962008b97","observation_id":"00153d2b-9509-4c7d-b1a4-6ad0f52c2ed0","resolution":{"observed_at":"2026-08-06T19:31:58.212648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2301.10356","last_updated":"2023-04-04T00:46:33Z","snapshot_observed_at":"2026-08-16T16:00:21.291744Z","submitted_at":"2023-01-24T23:58:51Z","title":"Remark on modular weights in low-energy effective field theory from type II string theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2301.10356","snapshot_observed_at":"2026-08-06T19:31:58.214872Z","title":"Kikuchi, T","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T19:31:58.214872Z"},"links":{"cited_paper":"/paper/2301.10356","citing_paper":"/paper/2507.05645"},"observation_digest":"sha256:24afc555adfdb25330328580ba3669bd766fd42940407d0306e630c56061e691","observation_id":"d1b462ad-3154-4219-bc59-bb359d4fefa7","resolution":{"observed_at":"2026-08-06T19:31:58.214872Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.05645","last_updated":"2025-07-08T03:54:06Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-17T16:14:08.153794Z","submitted_at":"2025-07-08T03:54:06Z","title":"Generation structures and Yukawa couplings in magnetized $T^{2g}/\\mathbb{Z}_N$ models"},"reference_resolution":{"displayed":71,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":53,"verified_exact":7,"verified_fuzzy":11},"total_outbound_references":71},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 71 of 71 outbound references and 1 inbound Pith citation observation for arXiv:2507.05645."}