{"as_of":"2026-08-19T13:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:aa49531711d8d6ef6260a1daa3831fc54798d356e5390aea1fbcc1f6a9b181dc","coverage":[{"denominator":80,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":80,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T10:04:14.180606Z","state":"measured"},{"denominator":80,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":80,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2607.20622/citation-record","integrity":"/paper/2607.20622/integrity","json":"/paper/2607.20622/citation-record.json","paper":"/paper/2607.20622"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"hep-th/0307041","last_updated":"2003-08-01T21:35:30Z","snapshot_observed_at":"2026-07-07T04:47:34.491860Z","submitted_at":"2003-07-03T19:15:48Z","title":"SL(2,Z) Action On Three-Dimensional Conformal Field Theories With Abelian Symmetry","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0307041","snapshot_observed_at":"2026-08-01T10:04:07.481247Z","title":null,"venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.481247Z"},"links":{"cited_paper":"/paper/hep-th/0307041","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:82792dabf84f91eabe4f3b86682ce686e453c5cc75d0ee0324795c619cd819a0","observation_id":"9f1fdb1c-b59d-475b-ad6f-1dd84f966d4c","resolution":{"observed_at":"2026-08-01T10:04:07.481247Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1606.01989","last_updated":"2016-07-27T00:17:38Z","snapshot_observed_at":"2026-08-18T11:31:16.153210Z","submitted_at":"2016-06-07T01:13:26Z","title":"A Duality Web in 2+1 Dimensions and Condensed Matter Physics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1606.01989","snapshot_observed_at":"2026-08-01T10:04:07.533515Z","title":"Seiberg, T","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.533515Z"},"links":{"cited_paper":"/paper/1606.01989","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:1fc46b8972fe8bc24d7b72c2cca7c09fd7318c55718e30fe7d9585e9ec2e4dd2","observation_id":"42901e6a-bc34-4e0d-bec4-c3a508123040","resolution":{"observed_at":"2026-08-01T10:04:07.533515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1606.01893","last_updated":"2016-06-19T15:42:38Z","snapshot_observed_at":"2026-08-14T21:53:58.363409Z","submitted_at":"2016-06-06T20:00:00Z","title":"Particle-Vortex Duality from 3d Bosonization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1606.01893","snapshot_observed_at":"2026-08-01T10:04:07.633122Z","title":"Karch and D","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.633122Z"},"links":{"cited_paper":"/paper/1606.01893","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:1a313de65886c13c39ceb07336452ee0ee034c7092c16ff18753c9cbc7eda4e7","observation_id":"e2f8f21c-9575-44cf-8162-5c6c3d76fdf6","resolution":{"observed_at":"2026-08-01T10:04:07.633122Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1703.02426","last_updated":"2017-12-26T03:19:55Z","snapshot_observed_at":"2026-08-18T03:24:26.200301Z","submitted_at":"2017-03-07T15:12:59Z","title":"Deconfined quantum critical points: symmetries and dualities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1703.02426","snapshot_observed_at":"2026-08-01T10:04:07.655443Z","title":null,"venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.655443Z"},"links":{"cited_paper":"/paper/1703.02426","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:441e2260ce0ce0f4420e0643b1b7c55cf7b887e7ac24ecbd60d5cd503b0c35e7","observation_id":"c9c367b4-0582-4b12-952d-2a9c5eba0e0d","resolution":{"observed_at":"2026-08-01T10:04:07.655443Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:07.769907Z","title":"Gaillard and B","venue":null,"work_id":null,"year":1981},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.769907Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:b9cfefadb09e3a13d05315f9c55c8cbc7d4880b56b1f13f70a954a5b7ecd3ce5","observation_id":"818b1c8f-06bd-4891-8dc9-95a16224b9ba","resolution":{"observed_at":"2026-08-01T10:04:07.769907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1108.4389","last_updated":"2011-08-22T17:51:48Z","snapshot_observed_at":"2026-08-15T04:37:37.636546Z","submitted_at":"2011-08-22T17:51:48Z","title":"Gauge Theories Labelled by Three-Manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1108.4389","snapshot_observed_at":"2026-08-01T10:04:07.861537Z","title":"Dimofte, D","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.861537Z"},"links":{"cited_paper":"/paper/1108.4389","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:9c7d740e183a2525ad2df1bf71f0aedaef6379b25fa82c3dbac6d5ba5232de49","observation_id":"cb7b2486-4ec8-4eb7-b189-7fdd6faae394","resolution":{"observed_at":"2026-08-01T10:04:07.861537Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0904.0840","last_updated":"2009-04-06T04:19:05Z","snapshot_observed_at":"2026-08-18T00:58:48.634419Z","submitted_at":"2009-04-06T04:19:05Z","title":"Abelian duality, walls and boundary conditions in diverse dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0904.0840","snapshot_observed_at":"2026-08-01T10:04:07.949892Z","title":"Kapustin and M","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:07.949892Z"},"links":{"cited_paper":"/paper/0904.0840","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e368a5e595cc728bee3ccf33802eecf1054400115e3ab80e6bf6146b17b0f36a","observation_id":"82f493db-be29-414b-afe8-438b0ec1fdc6","resolution":{"observed_at":"2026-08-01T10:04:07.949892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:08.027357Z","title":"Hua and I","venue":null,"work_id":null,"year":1949},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.027357Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:493af69dc80a09c65a8ec38f528a895bf40c59b7fdec791c4914c54c4ff2a053","observation_id":"585662d0-0288-437b-a4ba-399bc5f8e59e","resolution":{"observed_at":"2026-08-01T10:04:08.027357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1803.07366","last_updated":"2018-04-18T13:49:27Z","snapshot_observed_at":"2026-08-17T18:02:13.395449Z","submitted_at":"2018-03-20T11:11:22Z","title":"Anomalies of Duality Groups and Extended Conformal Manifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1803.07366","snapshot_observed_at":"2026-08-01T10:04:08.129246Z","title":"Seiberg, Y","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.129246Z"},"links":{"cited_paper":"/paper/1803.07366","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f6d7fa65668004ff641a367e4940b6e1de99d41a34d024e8891c02e9d8438f72","observation_id":"e3057ca0-5899-4851-ad81-580de7a40f36","resolution":{"observed_at":"2026-08-01T10:04:08.129246Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:08.218864Z","title":"Korkmaz and A.I","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.218864Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:ec01d3ab29aecf0f1ce21752dfa161b3c65c919761a74f5146735d4c2ed75008","observation_id":"ce4b8f30-918a-497b-be8c-97604f44be48","resolution":{"observed_at":"2026-08-01T10:04:08.218864Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:08.283821Z","title":"Harer,The second homology group of the mapping class group of an orientable surface, Invent","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.283821Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f5316b5675ef6ea2976c2e90d6cb2bc5e3e607097a3fcbcca30920845f849585","observation_id":"5ef4e7c3-2121-40be-b119-2cfc98680674","resolution":{"observed_at":"2026-08-01T10:04:08.283821Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2502.14032","last_updated":"2025-06-05T02:57:54Z","snapshot_observed_at":"2026-08-18T04:58:05.793016Z","submitted_at":"2025-02-19T19:00:01Z","title":"Critical theories connecting gapped phases with $\\mathbb{Z}_2\\times\\mathbb{Z}_2$ symmetry from the duality web","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2502.14032","snapshot_observed_at":"2026-08-01T10:04:08.334518Z","title":"Karch and R.C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.334518Z"},"links":{"cited_paper":"/paper/2502.14032","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f3b91290309a9859f8aa8efc3394c9a6dd1f99b392440e6df4325ffe56d8dc7e","observation_id":"9d140728-7825-4573-8969-7f14680f0055","resolution":{"observed_at":"2026-08-01T10:04:08.334518Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1904.00569","last_updated":"2019-11-19T07:22:27Z","snapshot_observed_at":"2026-08-15T09:01:53.653257Z","submitted_at":"2019-04-01T05:47:45Z","title":"Counting Rules of Nambu-Goldstone Modes","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1904.00569","snapshot_observed_at":"2026-08-01T10:04:08.430527Z","title":"Watanabe,Counting rules of nambu–goldstone modes,Annu","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.430527Z"},"links":{"cited_paper":"/paper/1904.00569","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:bae6ec0dbe790fb69ee836b201839bfa0752e253fef4916b57ebfebc876d7061","observation_id":"fd843a34-ed42-4786-8303-2143af30d655","resolution":{"observed_at":"2026-08-01T10:04:08.430527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1205.3156","last_updated":"2014-05-13T23:34:41Z","snapshot_observed_at":"2026-08-15T04:09:54.303076Z","submitted_at":"2012-05-14T19:59:51Z","title":"Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1205.3156","snapshot_observed_at":"2026-08-01T10:04:08.487134Z","title":"Lu and A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.487134Z"},"links":{"cited_paper":"/paper/1205.3156","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:1bd2e345a1a7f145539acc107b47daa228f26bd90c458ebbcfe57460121407b6","observation_id":"4b7a6487-8c94-44e8-93b4-d20083cfd1ad","resolution":{"observed_at":"2026-08-01T10:04:08.487134Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1302.2634","last_updated":"2016-04-13T01:59:26Z","snapshot_observed_at":"2026-08-18T01:41:11.268596Z","submitted_at":"2013-02-11T21:01:05Z","title":"Classification and Properties of Symmetry Enriched Topological Phases: A Chern-Simons approach with applications to Z2 spin liquids","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1302.2634","snapshot_observed_at":"2026-08-01T10:04:08.568841Z","title":"Lu and A","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.568841Z"},"links":{"cited_paper":"/paper/1302.2634","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e6830e927dcb7eb9e2e23c53a69e280279b5465d8c4a4cfa277366fbc84d5a1d","observation_id":"ba61344a-6c91-415f-a90e-2396d9a8ba28","resolution":{"observed_at":"2026-08-01T10:04:08.568841Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1410.4540","last_updated":"2019-10-15T16:12:53Z","snapshot_observed_at":"2026-08-14T23:15:23.982033Z","submitted_at":"2014-10-16T19:21:13Z","title":"Symmetry Fractionalization, Defects, and Gauging of Topological Phases","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1410.4540","snapshot_observed_at":"2026-08-01T10:04:08.623650Z","title":"Barkeshli, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.623650Z"},"links":{"cited_paper":"/paper/1410.4540","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f8ee9e8f139cb8468d15af8d39385c2fbcd13e6bb7d252410d40faa4570b8bb6","observation_id":"5b4ca874-8a9c-4f79-a9b1-44433b3a356c","resolution":{"observed_at":"2026-08-01T10:04:08.623650Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/9506066","last_updated":"1995-10-31T18:03:51Z","snapshot_observed_at":"2026-07-07T02:43:50.384486Z","submitted_at":"1995-06-15T08:09:04Z","title":"Topological orders and Edge excitations in FQH states","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/9506066","snapshot_observed_at":"2026-08-01T10:04:08.728408Z","title":"Wen,Topological orders and edge excitations in fractional quantum hall states,Adv","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.728408Z"},"links":{"cited_paper":"/paper/cond-mat/9506066","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:0e468ea4591c00c111af204ea21c53b71bda2c3329082165426e0d338161de1d","observation_id":"4e03d38e-ff75-463e-92e3-78db2c7004f1","resolution":{"observed_at":"2026-08-01T10:04:08.728408Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2201.07239","last_updated":"2022-06-01T02:31:24Z","snapshot_observed_at":"2026-08-16T17:27:31.449131Z","submitted_at":"2022-01-18T19:00:01Z","title":"Gauging U(1) symmetry in (2+1)d topological phases","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2201.07239","snapshot_observed_at":"2026-08-01T10:04:08.796187Z","title":"Cheng and C.-M","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.796187Z"},"links":{"cited_paper":"/paper/2201.07239","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:58b766b4c9d0702ae0a81d4c978f6ebfef5d9593ac1085c53e16f93c4093f2f2","observation_id":"2d707c65-5f9b-400e-b7b1-5ed373433be6","resolution":{"observed_at":"2026-08-01T10:04:08.796187Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.15347","last_updated":"2022-11-30T17:54:54Z","snapshot_observed_at":"2026-08-17T23:26:37.169730Z","submitted_at":"2022-05-30T18:00:27Z","title":"Gauging Lie group symmetry in (2+1)d topological phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.15347","snapshot_observed_at":"2026-08-01T10:04:08.846297Z","title":"Cheng, P.-S","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.846297Z"},"links":{"cited_paper":"/paper/2205.15347","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:0754a7ba9db63ac767cc7621130c6f5f211f2f392658c46d19b80567b14712df","observation_id":"fd5b5fd9-9218-466e-bfb9-b22cd1ea2daa","resolution":{"observed_at":"2026-08-01T10:04:08.846297Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/0010246","last_updated":"2000-10-26T18:53:41Z","snapshot_observed_at":"2026-08-19T11:18:00.094664Z","submitted_at":"2000-10-26T18:53:41Z","title":"Particle-Vortex Duality and the Modular Group: Applications to the Quantum Hall Effect and Other 2-D Systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/0010246","snapshot_observed_at":"2026-08-01T10:04:08.921362Z","title":"Burgess and B.P","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.921362Z"},"links":{"cited_paper":"/paper/hep-th/0010246","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e5a360908484df4b413365d10d3a6928dd4f546a5f5467e92d6a01559b05d680","observation_id":"3b213ae4-601b-422e-b625-6af763d25bac","resolution":{"observed_at":"2026-08-01T10:04:08.921362Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0105621","last_updated":"2001-05-31T14:34:48Z","snapshot_observed_at":"2026-08-15T17:37:21.007515Z","submitted_at":"2001-05-31T14:34:48Z","title":"Duality and Non-linear Response for Quantum Hall Systems","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0105621","snapshot_observed_at":"2026-08-01T10:04:08.993993Z","title":"Burgess and B.P","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:08.993993Z"},"links":{"cited_paper":"/paper/cond-mat/0105621","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:d9ce2b92a4b571dd8438e12a1f5559881b96794e909ad6c304d480037bfd8013","observation_id":"bc8c046c-3ad3-40f2-a843-f98e2256df5c","resolution":{"observed_at":"2026-08-01T10:04:08.993993Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0701535","last_updated":"2007-11-07T15:00:47Z","snapshot_observed_at":"2026-07-07T02:38:16.856165Z","submitted_at":"2007-01-23T14:22:32Z","title":"Duality, the Semi-Circle Law and Quantum Hall Bilayers","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0701535","snapshot_observed_at":"2026-08-01T10:04:09.083663Z","title":"Burgess and B.P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.083663Z"},"links":{"cited_paper":"/paper/cond-mat/0701535","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:3a6e279a6f1fbc6811c640b3cccb5be418af7e8d2fcd0fd35ed9dfabc15611e7","observation_id":"220b0ba3-6018-4317-a4e9-801b327d7a8f","resolution":{"observed_at":"2026-08-01T10:04:09.083663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1008.5257","last_updated":"2010-09-14T10:45:13Z","snapshot_observed_at":"2026-08-15T05:10:02.974640Z","submitted_at":"2010-08-31T08:58:16Z","title":"Experimental probes of emergent symmetries in the quantum Hall system","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1008.5257","snapshot_observed_at":"2026-08-01T10:04:09.187484Z","title":"L¨ utken and G.G","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.187484Z"},"links":{"cited_paper":"/paper/1008.5257","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:0be8007b9d7a223738b3144d0bd8a7f4d9fa758b81eecc022423f1fa7768a51f","observation_id":"77f1cdc1-ee16-4635-a393-f6977c0cda55","resolution":{"observed_at":"2026-08-01T10:04:09.187484Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1111.4902","last_updated":"2012-03-23T13:58:53Z","snapshot_observed_at":"2026-08-15T04:28:17.235626Z","submitted_at":"2011-11-21T15:41:16Z","title":"An RG potential for the quantum Hall effects","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1111.4902","snapshot_observed_at":"2026-08-01T10:04:09.250101Z","title":"Nissinen and C.A","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.250101Z"},"links":{"cited_paper":"/paper/1111.4902","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:2c0d1786707575169176263f7f0d71e038f39f964a927cee0025e33d8f42db49","observation_id":"daf2f728-b896-4e8b-a5a8-0f9fcd4d5d8d","resolution":{"observed_at":"2026-08-01T10:04:09.250101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1302.1436","last_updated":"2013-05-01T03:38:20Z","snapshot_observed_at":"2026-08-15T00:29:40.645549Z","submitted_at":"2013-02-06T16:55:35Z","title":"Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1302.1436","snapshot_observed_at":"2026-08-01T10:04:09.323587Z","title":"Geraedts and O.I","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.323587Z"},"links":{"cited_paper":"/paper/1302.1436","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:a7917cd4c0fd1b698de6d6ff27f525cb8e11f02df8bdce95414731bee2070305","observation_id":"b0de0fbe-3fc6-4a5d-b93e-233aba3186ab","resolution":{"observed_at":"2026-08-01T10:04:09.323587Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1502.03446","last_updated":"2015-09-02T20:10:38Z","snapshot_observed_at":"2026-08-19T03:00:59.004855Z","submitted_at":"2015-02-11T21:00:13Z","title":"Is the Composite Fermion a Dirac Particle?","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1502.03446","snapshot_observed_at":"2026-08-01T10:04:09.409504Z","title":"Son,Is the Composite Fermion a Dirac Particle?,Phys","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.409504Z"},"links":{"cited_paper":"/paper/1502.03446","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:7e802b03fef53b15b0debfa12bfed388179c05fd208853cfe43ee06ae53b6ebc","observation_id":"9d4b0132-c079-485e-8046-afe41ebc7714","resolution":{"observed_at":"2026-08-01T10:04:09.409504Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1801.04936","last_updated":"2018-05-14T20:14:48Z","snapshot_observed_at":"2026-08-14T19:54:58.196139Z","submitted_at":"2018-01-15T19:00:04Z","title":"Loop Models, Modular Invariance, and Three Dimensional Bosonization","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1801.04936","snapshot_observed_at":"2026-08-01T10:04:09.481032Z","title":"Goldman and E","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.481032Z"},"links":{"cited_paper":"/paper/1801.04936","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:c07c466b392a9ecce158fb563969e066d9d106fbc104938c493ab8a61e87b948","observation_id":"2db4af13-afb9-492f-b30e-c23c80df25a4","resolution":{"observed_at":"2026-08-01T10:04:09.481032Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.565245Z","title":"Haldane,Fractional quantization of the hall effect: A hierarchy of incompressible quantum fluid states,Phys","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.565245Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:1670f5080340983744f37a9d92384e5fc53e6338783681f41759ca20a8f21664","observation_id":"4e797382-e3b5-4ea5-86b3-f05b9d3528f7","resolution":{"observed_at":"2026-08-01T10:04:09.565245Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.645632Z","title":"Halperin,Statistics of quasiparticles and the hierarchy of fractional quantized hall states, Phys","venue":null,"work_id":null,"year":1984},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.645632Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:5ac568004753a2c412636aa366107eee567b2765d38a92dc92ef94b46339af6c","observation_id":"d5570e78-3299-48b7-b29f-7eb86935d4fb","resolution":{"observed_at":"2026-08-01T10:04:09.645632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.720014Z","title":"Halperin,Theory of the quantized hall conductance,Helv","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.720014Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:3f27fd995152da64d077564c3cae82e0113a9aa65a81d269db73bb8b9632782e","observation_id":"cda09b97-b92e-4c01-aa43-e0418f9b1c2f","resolution":{"observed_at":"2026-08-01T10:04:09.720014Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.799926Z","title":"Nguyen, N.J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.799926Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:aae434be8e53b33ac8be94f424176b3eace63f2f3a65b931928fca2b6c0874bf","observation_id":"35b417b4-f2f6-4220-84a4-70a069d80333","resolution":{"observed_at":"2026-08-01T10:04:09.799926Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.858564Z","title":"Jain,Composite-fermion approach for the fractional quantum hall effect,Phys","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.858564Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:07bf7c06ee66b6af82e219f3b2980f4a5351ac70fa084bd9d02959430e142d99","observation_id":"e3de2483-d433-482b-9aae-ccbc6ce40a40","resolution":{"observed_at":"2026-08-01T10:04:09.858564Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:09.925105Z","title":"Scarola and J","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:09.925105Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:3bee286fa4010d17037cf9559261ddb19df8c3bad01acd60d230ef37882faab6","observation_id":"b7c02bf2-62b7-4c7c-81e6-99fc1404c178","resolution":{"observed_at":"2026-08-01T10:04:09.925105Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.06128","last_updated":"2024-11-05T16:38:22Z","snapshot_observed_at":"2026-08-16T14:28:07.296858Z","submitted_at":"2024-01-11T18:59:28Z","title":"A SymTFT for Continuous Symmetries","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.06128","snapshot_observed_at":"2026-08-01T10:04:10.012693Z","title":"Brennan and Z","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.012693Z"},"links":{"cited_paper":"/paper/2401.06128","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:ead5f4023bb781032d78e3c2fca9fa680129a9aeb8a725e4d5793d095086fe17","observation_id":"c2f3d6c4-1bfc-4bbf-93cf-09ab511cb4f6","resolution":{"observed_at":"2026-08-01T10:04:10.012693Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.10165","last_updated":"2025-02-28T16:16:40Z","snapshot_observed_at":"2026-08-16T14:26:22.494737Z","submitted_at":"2024-01-18T17:49:32Z","title":"Anomalies and gauging of U(1) symmetries","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.10165","snapshot_observed_at":"2026-08-01T10:04:10.104077Z","title":"Antinucci and F","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.104077Z"},"links":{"cited_paper":"/paper/2401.10165","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:ce91d1778ea449c20e09e07364f597e909a0772ca74b39fe58768e14f7efa1ae","observation_id":"9d0c712f-e537-4429-bbf2-ea81c23cc7a0","resolution":{"observed_at":"2026-08-01T10:04:10.104077Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:10.194264Z","title":"Apruzzi, F","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.194264Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:35d54e35ab15b0e6c1e6cbaeb94eb05ac648f3064e975ea23514d310502f604e","observation_id":"6652f170-cb17-4bf3-8d37-7dec058a015f","resolution":{"observed_at":"2026-08-01T10:04:10.194264Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:10.261279Z","title":"Jia and Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.261279Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:580b1262edb40a7132929f11753267e879d8670b705e58f0ddd74397f549c901","observation_id":"32535ebf-a51c-4f2b-a6db-1684b6f4d412","resolution":{"observed_at":"2026-08-01T10:04:10.261279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2009.10099","last_updated":"2020-10-12T09:00:03Z","snapshot_observed_at":"2026-08-15T08:17:35.655537Z","submitted_at":"2020-09-21T18:00:32Z","title":"$SL(2,\\mathbb{Z})$ action on QFTs with $\\mathbb{Z}_2$ symmetry and the Brown-Kervaire invariants","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2009.10099","snapshot_observed_at":"2026-08-01T10:04:10.350060Z","title":"Bhardwaj, Y","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.350060Z"},"links":{"cited_paper":"/paper/2009.10099","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e8a750ac0dacfc6c29d75aebb5e57dd1d5d31549a77ffdf09d2ba68e08b4ebea","observation_id":"73b0d8a9-ebcd-4bd7-8090-9384075e75ac","resolution":{"observed_at":"2026-08-01T10:04:10.350060Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.09567","last_updated":"2019-06-02T04:59:46Z","snapshot_observed_at":"2026-08-14T17:11:29.139542Z","submitted_at":"2019-02-25T19:07:57Z","title":"3d Abelian Gauge Theories at the Boundary","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.09567","snapshot_observed_at":"2026-08-01T10:04:10.423538Z","title":"Di Pietro, D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.423538Z"},"links":{"cited_paper":"/paper/1902.09567","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:be6d01f63ec6a19f0efbd3c6eb61aa9bae0727f7e130850602679db2093025e9","observation_id":"dcb248d6-77df-4d03-b2a7-d51503acd2a0","resolution":{"observed_at":"2026-08-01T10:04:10.423538Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:10.492925Z","title":"B¨ urgisser,Elements of finite order in symplectic groups,Archiv der Mathematik39(1982) 501","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.492925Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:981570762e923a82048df5538d0490d73701146f5dce24fc9279baa1777d267a","observation_id":"88f038c8-33af-4b5c-9c17-0ea885b10335","resolution":{"observed_at":"2026-08-01T10:04:10.492925Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1710.04851","last_updated":"2018-12-13T09:07:12Z","snapshot_observed_at":"2026-08-14T20:24:09.161461Z","submitted_at":"2017-10-13T09:27:49Z","title":"Cohomology of symplectic groups and Meyer's signature theorem","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1710.04851","snapshot_observed_at":"2026-08-01T10:04:10.551610Z","title":"Benson, C","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.551610Z"},"links":{"cited_paper":"/paper/1710.04851","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:96e1c08a8afeab16557abd6e9904caa54b07c400104ea4685baafd0c0bf95169","observation_id":"9ae15bff-c3b3-4868-af22-4205a1e1c02c","resolution":{"observed_at":"2026-08-01T10:04:10.551610Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:10.630826Z","title":"Barkeshli, P","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.630826Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:cc69b00a740c6f6c9685cc499056de3c260c2494ba6fa10569e590d599211c05","observation_id":"2dd2b7fc-3d12-48f7-8437-64decf847c0b","resolution":{"observed_at":"2026-08-01T10:04:10.630826Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2004.12048","last_updated":"2020-10-21T02:23:51Z","snapshot_observed_at":"2026-08-13T22:54:42.294749Z","submitted_at":"2020-04-25T03:39:43Z","title":"In and around Abelian anyon models","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.12048","snapshot_observed_at":"2026-08-01T10:04:10.686080Z","title":"Wang and Z","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.686080Z"},"links":{"cited_paper":"/paper/2004.12048","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e00968a55058985a37dd2ce9d757a6827e02c7b6c72f310eec2f63f204eb3ce8","observation_id":"f9069d8b-c264-4145-99cb-27b531d5bec2","resolution":{"observed_at":"2026-08-01T10:04:10.686080Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0506438","last_updated":"2008-01-01T04:29:56Z","snapshot_observed_at":"2026-08-05T12:27:26.288818Z","submitted_at":"2005-06-17T12:42:36Z","title":"Anyons in an exactly solved model and beyond","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0506438","snapshot_observed_at":"2026-08-01T10:04:10.806250Z","title":"Kitaev,Anyons in an exactly solved model and beyond,Annals Phys.321(2006) 2 [cond-mat/0506438]","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.806250Z"},"links":{"cited_paper":"/paper/cond-mat/0506438","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:8bd910319308812d649e04c0834648b829e5783e6edb21612f82530b11b7bfd3","observation_id":"550c82dd-56eb-4e49-b016-daf2ae3fea69","resolution":{"observed_at":"2026-08-01T10:04:10.806250Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1302.2951","last_updated":"2013-02-12T23:30:07Z","snapshot_observed_at":"2026-08-15T00:29:01.280281Z","submitted_at":"2013-02-12T23:30:07Z","title":"A K matrix Construction of Symmetry Enriched Phases of Matter","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1302.2951","snapshot_observed_at":"2026-08-01T10:04:10.937128Z","title":"Hung and Y","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:10.937128Z"},"links":{"cited_paper":"/paper/1302.2951","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:eff52fbe136a46f0e0e683a636d4a3bd427c214d2bfa8c6708f18bbdef143901","observation_id":"07d4a73a-c901-48a9-ad6d-bfff00408c6b","resolution":{"observed_at":"2026-08-01T10:04:10.937128Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1905.12656","last_updated":"2019-05-29T18:07:11Z","snapshot_observed_at":"2026-08-14T16:24:14.717621Z","submitted_at":"2019-05-29T18:07:11Z","title":"Lectures on Dualities in 2+1 Dimensions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1905.12656","snapshot_observed_at":"2026-08-01T10:04:11.044104Z","title":"Turner,Dualities in 2+1 Dimensions,PoSModave2018(2019) 001 [1905.12656]","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.044104Z"},"links":{"cited_paper":"/paper/1905.12656","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:cbf5c751d9305446dd0e8ff3f75d3118c8bda73549acbb5ea2c7a1f20140e609","observation_id":"04676a1d-ce20-4c42-b5ee-86b54e161e66","resolution":{"observed_at":"2026-08-01T10:04:11.044104Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2207.10712","last_updated":"2025-06-28T22:17:14Z","snapshot_observed_at":"2026-08-19T09:44:49.959986Z","submitted_at":"2022-07-21T19:01:09Z","title":"Topological Holography: Towards a Unification of Landau and Beyond-Landau Physics","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2207.10712","snapshot_observed_at":"2026-08-01T10:04:11.145820Z","title":"Moradi, S.F","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.145820Z"},"links":{"cited_paper":"/paper/2207.10712","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:d06817630267f42edf0eab06995515161a9463e561fb13ea2bff8e65fc00ec11","observation_id":"b2161dbd-7c27-4795-96bd-1bb92b88d74c","resolution":{"observed_at":"2026-08-01T10:04:11.145820Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2310.16878","last_updated":"2025-06-01T13:14:20Z","snapshot_observed_at":"2026-08-19T12:08:50.932966Z","submitted_at":"2023-10-25T18:00:01Z","title":"Topological holography, quantum criticality, and boundary states","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2310.16878","snapshot_observed_at":"2026-08-01T10:04:11.207161Z","title":"Huang and M","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.207161Z"},"links":{"cited_paper":"/paper/2310.16878","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:4c473782bfec3a432933d6bed7121b51d7dbf32ebc1b60dfab811f52437351e0","observation_id":"efc74334-903f-4ba7-b15c-129f1e81088a","resolution":{"observed_at":"2026-08-01T10:04:11.207161Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.280418Z","title":"Spieler,Exploring two dimensionalZ 2 invariant phases with time reversal symmetry and their transitions with topological operations,JHEP10(2025) 069 [2504.20021]","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.280418Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:867bf80840b2daa5a7d675073b45f39000ebf9569160000248f9fa6a090ac309","observation_id":"744cf792-c40f-4bf4-956d-ec829b3a36ce","resolution":{"observed_at":"2026-08-01T10:04:11.280418Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.391252Z","title":"Blok and X.G","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.391252Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f5c3cd4904794c11ac4f328c4cea529dc148d11a1fc8b6b8dbe977e09941b88a","observation_id":"344040aa-fce9-4684-9130-475fb3f1c5e2","resolution":{"observed_at":"2026-08-01T10:04:11.391252Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.492734Z","title":"Read,Excitation structure of the hierarchy scheme in the fractional quantum hall effect, Phys","venue":null,"work_id":null,"year":1990},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.492734Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:4e9fb8c5135f3f2f5a7eb11b6e58599db1305a281a88f30f16e368ed66142e7a","observation_id":"77c9bd0d-ba8e-43bd-80dc-13791e083f72","resolution":{"observed_at":"2026-08-01T10:04:11.492734Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.573279Z","title":"Wen and A","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.573279Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:75789143f9c1a60ec7775d5594b723642fc53a670746c137a68a19f9c5fca0eb","observation_id":"af875036-a172-4d38-ad45-f5267c50491b","resolution":{"observed_at":"2026-08-01T10:04:11.573279Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.588765Z","title":"Tong,Lectures on the Quantum Hall Effect, 6, 2016","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.588765Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e04700c54105b18ce1fd59d8345beff5379d0eef36ac024723eb6f0b75c7f836","observation_id":"c529936d-345e-43fd-852f-9d50d2dc0645","resolution":{"observed_at":"2026-08-01T10:04:11.588765Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:11.591891Z","title":"Kohn,Cyclotron resonance and de haas-van alphen oscillations of an interacting electron gas,Phys","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.591891Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:85834f1d2d1810b64349b89b0c403ab32e58c92d61211b7f15074b480e27975a","observation_id":"52223e0e-5ef4-4c32-9afb-e51a47a6aaa1","resolution":{"observed_at":"2026-08-01T10:04:11.591891Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1109.2651","last_updated":"2011-09-13T00:08:34Z","snapshot_observed_at":"2026-08-15T04:35:27.485113Z","submitted_at":"2011-09-13T00:08:34Z","title":"Hall Viscosity and Electromagnetic Response","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1109.2651","snapshot_observed_at":"2026-08-01T10:04:11.710805Z","title":"Hoyos and D.T","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.710805Z"},"links":{"cited_paper":"/paper/1109.2651","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:ffabf843a494d576c7092fd99679f3e9c1733c790800fe6905d54b984be25da3","observation_id":"8ed33bb2-66db-486b-b01a-d863af9f250d","resolution":{"observed_at":"2026-08-01T10:04:11.710805Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2406.12068","last_updated":"2025-03-18T03:34:13Z","snapshot_observed_at":"2026-08-19T02:41:11.027710Z","submitted_at":"2024-06-17T20:12:30Z","title":"Hierarchy construction for non-abelian fractional quantum Hall states via anyon condensation","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2406.12068","snapshot_observed_at":"2026-08-01T10:04:11.883485Z","title":"Zhang, A","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:11.883485Z"},"links":{"cited_paper":"/paper/2406.12068","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:f0b98bea1598d77b4bb0928a3866c99e15ed4a96aed025610ac68822ccc2a52b","observation_id":"ab812ae0-56a9-425f-99dd-d516d9dec617","resolution":{"observed_at":"2026-08-01T10:04:11.883485Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:12.117973Z","title":"Balatsky and E","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:12.117973Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:b5dac3ed3d638e8c8261f9ae1ebd1e2d49829e20539256cfe29b9bc62c599fa0","observation_id":"28eb2daa-234a-4ad9-a5a1-301c7626921e","resolution":{"observed_at":"2026-08-01T10:04:12.117973Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:12.369679Z","title":"Milovanovi´ c and N","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:12.369679Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:954273b7bdcfbc3744f23535105009d25b9cd4d4e4d72c08a900a480e36ce651","observation_id":"bbb527ed-6b50-4ab6-a912-34b3a8110043","resolution":{"observed_at":"2026-08-01T10:04:12.369679Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1605.07324","last_updated":"2017-03-03T09:32:50Z","snapshot_observed_at":"2026-08-14T21:56:03.128880Z","submitted_at":"2016-05-24T07:36:28Z","title":"The enigma of the $\\nu=2+\\frac{3}{8}$ fractional quantum Hall effect","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1605.07324","snapshot_observed_at":"2026-08-01T10:04:12.549735Z","title":"Hutasoit, A.C","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:12.549735Z"},"links":{"cited_paper":"/paper/1605.07324","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:fb8a946043eaa18507e8f01c6f1a777105fd50abec1fff779b3c50e3beed4980","observation_id":"af75f1dc-a864-408d-bd06-9ca2cb318645","resolution":{"observed_at":"2026-08-01T10:04:12.549735Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1602.04251","last_updated":"2016-05-05T18:50:08Z","snapshot_observed_at":"2026-08-14T22:10:30.957277Z","submitted_at":"2016-02-12T22:24:38Z","title":"Gapped Boundary Phases of Topological Insulators via Weak Coupling","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1602.04251","snapshot_observed_at":"2026-08-01T10:04:12.784826Z","title":"Seiberg and E","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:12.784826Z"},"links":{"cited_paper":"/paper/1602.04251","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:934b0193e3040bca79523ef8a0a81aa49a0aa2564dbf49de58614d05cc0c57f4","observation_id":"05652a0a-b83c-4e94-9c6b-60da04368406","resolution":{"observed_at":"2026-08-01T10:04:12.784826Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:12.941721Z","title":"Moore and N","venue":null,"work_id":null,"year":1991},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:12.941721Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:d4948b3139b2440b3982d7d3129b40073d6775917fd899567ffb7accff29d59d","observation_id":"3ccfac28-6160-44c3-875f-f3a31b033bfb","resolution":{"observed_at":"2026-08-01T10:04:12.941721Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/9809384","last_updated":"1998-10-06T23:33:45Z","snapshot_observed_at":"2026-08-17T13:05:54.263247Z","submitted_at":"1998-09-29T21:39:26Z","title":"Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/9809384","snapshot_observed_at":"2026-08-01T10:04:13.080632Z","title":"Read and E","venue":null,"work_id":null,"year":1999},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.080632Z"},"links":{"cited_paper":"/paper/cond-mat/9809384","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:816e00a21a9816d1df83d7be40c9caef9a290054fc811e7e6397b4482d02df97","observation_id":"cc4b12ed-78a2-444d-99ec-b294e992ebd2","resolution":{"observed_at":"2026-08-01T10:04:13.080632Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1307.8244","last_updated":"2021-11-09T17:26:26Z","snapshot_observed_at":"2026-08-18T20:48:47.890960Z","submitted_at":"2013-07-31T08:04:28Z","title":"Anyon condensation and tensor categories","version":7},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1307.8244","snapshot_observed_at":"2026-08-01T10:04:13.248381Z","title":"Kong,Anyon condensation and tensor categories,Nucl","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.248381Z"},"links":{"cited_paper":"/paper/1307.8244","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:49fc8e2a43be3f445e5d580bf87614e0b0c0860e8de063bf7d184a443bea4790","observation_id":"b93991f4-4023-4a98-a6b0-36a460b4d4f2","resolution":{"observed_at":"2026-08-01T10:04:13.248381Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0711.3204","last_updated":"2008-09-18T20:51:17Z","snapshot_observed_at":"2026-08-19T10:03:26.343725Z","submitted_at":"2007-11-20T20:40:12Z","title":"Fractional Quantum Hall Hierarchy and the Second Landau Level","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0711.3204","snapshot_observed_at":"2026-08-01T10:04:13.332935Z","title":"Bonderson and J.K","venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.332935Z"},"links":{"cited_paper":"/paper/0711.3204","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e14f775471ea749166353526db188d98c15d4d0b2525be44118096c395483c85","observation_id":"43669b56-a04b-42e8-97e5-5a5f1aec5773","resolution":{"observed_at":"2026-08-01T10:04:13.332935Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1010.4270","last_updated":"2010-10-20T18:27:46Z","snapshot_observed_at":"2026-08-15T05:05:17.825676Z","submitted_at":"2010-10-20T18:27:46Z","title":"Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1010.4270","snapshot_observed_at":"2026-08-01T10:04:13.387244Z","title":"Barkeshli and X.-G","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.387244Z"},"links":{"cited_paper":"/paper/1010.4270","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:98aebc2b8eea379b6d29d78cd00cd4b0ee5e0fed628caa880ebaa5ad048b8b0f","observation_id":"93f6f655-6eb1-4ab1-a4ed-ad2914e2d2f5","resolution":{"observed_at":"2026-08-01T10:04:13.387244Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0906.0356","last_updated":"2009-06-01T18:48:11Z","snapshot_observed_at":"2026-08-15T05:47:10.811903Z","submitted_at":"2009-06-01T18:48:11Z","title":"Non-Abelian Two-component Fractional Quantum Hall States","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0906.0356","snapshot_observed_at":"2026-08-01T10:04:13.440656Z","title":"Barkeshli and X.-G","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.440656Z"},"links":{"cited_paper":"/paper/0906.0356","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:df05e5a4c57e1e042a5ab78a2466aec445483f1a7757d8b2c8e73dad420e1302","observation_id":"85b403c0-517d-491e-b6e6-13670ca1d867","resolution":{"observed_at":"2026-08-01T10:04:13.440656Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1810.05174","last_updated":"2018-10-11T18:00:05Z","snapshot_observed_at":"2026-08-18T20:57:02.682416Z","submitted_at":"2018-10-11T18:00:05Z","title":"Duality between $(2+1)d$ Quantum Critical Points","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1810.05174","snapshot_observed_at":"2026-08-01T10:04:13.480144Z","title":"Senthil, D.T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.480144Z"},"links":{"cited_paper":"/paper/1810.05174","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:90fce69a676376fa440c19a128057c79614f8bad09ba339a53175adac35dec64","observation_id":"28884187-45b0-4301-9f62-2df890e720cc","resolution":{"observed_at":"2026-08-01T10:04:13.480144Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1510.06032","last_updated":"2016-01-19T18:52:59Z","snapshot_observed_at":"2026-08-14T22:27:00.792486Z","submitted_at":"2015-10-20T20:05:20Z","title":"Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1510.06032","snapshot_observed_at":"2026-08-01T10:04:13.530204Z","title":"Xu and Y.-Z","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.530204Z"},"links":{"cited_paper":"/paper/1510.06032","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e1c09584c2a7fe24356980fa46b614878ecb63b108d6b33edcc1b0f5b5bbd590","observation_id":"a2d30ae9-47b2-4375-9fec-b1d79cad82db","resolution":{"observed_at":"2026-08-01T10:04:13.530204Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1609.02560","last_updated":"2016-09-08T20:00:03Z","snapshot_observed_at":"2026-08-14T21:40:41.589899Z","submitted_at":"2016-09-08T20:00:03Z","title":"A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1609.02560","snapshot_observed_at":"2026-08-01T10:04:13.568963Z","title":"Cheng and C","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.568963Z"},"links":{"cited_paper":"/paper/1609.02560","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:407a72bdd3be6de913e520e0bb27e673223100c7a0318793f072e5b49cb4b2b6","observation_id":"7b740e62-ffff-4ba2-a2de-0e0ed8421f30","resolution":{"observed_at":"2026-08-01T10:04:13.568963Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1708.03050","last_updated":"2017-08-10T02:03:28Z","snapshot_observed_at":"2026-08-14T20:42:13.308636Z","submitted_at":"2017-08-10T02:03:28Z","title":"Emergent Symmetry and Tricritical Points near the deconfined Quantum Critical Point","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1708.03050","snapshot_observed_at":"2026-08-01T10:04:13.610379Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.610379Z"},"links":{"cited_paper":"/paper/1708.03050","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:1059c78e54f58840586947f454df0a51f8b1162b01f31d533592ad054b9bcde7","observation_id":"c954ba4d-339e-490d-9a76-56021f748297","resolution":{"observed_at":"2026-08-01T10:04:13.610379Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.05147","last_updated":"2021-11-29T19:29:24Z","snapshot_observed_at":"2026-08-16T18:32:23.370637Z","submitted_at":"2021-04-12T00:54:03Z","title":"Self-duality protected multi-criticality in deconfined quantum phase transitions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.05147","snapshot_observed_at":"2026-08-01T10:04:13.674020Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.674020Z"},"links":{"cited_paper":"/paper/2104.05147","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:19e1df604d00babdeb5109e30fd48351d2f3bba8fceb87cfb17edec3ab5d710f","observation_id":"00f40802-d9d3-431e-b1ce-3d195bbd4cc0","resolution":{"observed_at":"2026-08-01T10:04:13.674020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:13.737951Z","title":"Dumitrescu, P","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.737951Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:aa121a53e5141bc4d818fa0d43a42130c909fa0b2a75c26e43df4f794f2ed60e","observation_id":"3e3f11a1-d233-4c32-9e22-0a93a394839f","resolution":{"observed_at":"2026-08-01T10:04:13.737951Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:13.787556Z","title":"Behr,Eine endliche pr¨ asentation der symplektischen gruppe sp4 (z).,Mathematische Zeitschrift141(1975) 47","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.787556Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:099f3aa0d6f2d56d1c82228afb1483e76a1e30202eec24b2c3e36668261892ca","observation_id":"dddcf0b5-e063-472b-9d34-c6dbc527d48c","resolution":{"observed_at":"2026-08-01T10:04:13.787556Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T10:04:13.820899Z","title":"Farb and D","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":74,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.820899Z"},"links":{"citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:c7d955d83ed13ac1e61f89e7f73feac48087aa48243003ab1f1203390287743e","observation_id":"a39a0cc3-8d94-4fdc-818f-0fd4bfe0f03f","resolution":{"observed_at":"2026-08-01T10:04:13.820899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.05550","last_updated":"2019-10-05T09:44:25Z","snapshot_observed_at":"2026-08-14T17:16:13.002490Z","submitted_at":"2019-02-14T18:59:55Z","title":"A Web of 2d Dualities: ${\\bf Z}_2$ Gauge Fields and Arf Invariants","version":5},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.05550","snapshot_observed_at":"2026-08-01T10:04:13.881527Z","title":"Karch, D","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.881527Z"},"links":{"cited_paper":"/paper/1902.05550","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:6cbdf5719ebbad6d015df0ef15718e90df9b6ab6e75ea970fff8917e42f52e80","observation_id":"d188fea8-4819-4aa6-8b4f-17bb9fc73f8f","resolution":{"observed_at":"2026-08-01T10:04:13.881527Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2008.05960","last_updated":"2020-08-13T15:09:01Z","snapshot_observed_at":"2026-08-16T00:52:09.217114Z","submitted_at":"2020-08-13T15:09:01Z","title":"Orbifold groupoids","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2008.05960","snapshot_observed_at":"2026-08-01T10:04:13.941590Z","title":"Gaiotto and J","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":76,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.941590Z"},"links":{"cited_paper":"/paper/2008.05960","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:787aa73004952edc67c32d08cc6ea6179bd187b30de4f8c6db8a6323438c1ddb","observation_id":"6114fab7-4207-43bd-83b1-9b0df1ed9158","resolution":{"observed_at":"2026-08-01T10:04:13.941590Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.14939","last_updated":"2024-06-25T19:33:28Z","snapshot_observed_at":"2026-08-19T02:01:56.879602Z","submitted_at":"2024-05-23T18:00:02Z","title":"Realizing triality and $p$-ality by lattice twisted gauging in (1+1)d quantum spin systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.14939","snapshot_observed_at":"2026-08-01T10:04:13.990984Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":77,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:13.990984Z"},"links":{"cited_paper":"/paper/2405.14939","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e37e9c6e6b6fb01645fc6e7b20850fea3f1ff953d211a9c9aea2975416c8bf55","observation_id":"b1c10aa0-b5e7-4784-8edb-932aeb77b1de","resolution":{"observed_at":"2026-08-01T10:04:13.990984Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.09611","last_updated":"2024-06-18T12:43:53Z","snapshot_observed_at":"2026-08-18T21:50:01.505763Z","submitted_at":"2024-05-15T18:00:01Z","title":"Fermionic quantum criticality through the lens of topological holography","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.09611","snapshot_observed_at":"2026-08-01T10:04:14.060675Z","title":"Huang,Fermionic quantum criticality through the lens of topological holography,Phys","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":78,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:14.060675Z"},"links":{"cited_paper":"/paper/2405.09611","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:6265b454b1740a7e1b8a6b55b60994ee043eb3fe0f4d0d6e731657752d9db81d","observation_id":"1187a645-f413-4c40-9be9-c211e4b37cd4","resolution":{"observed_at":"2026-08-01T10:04:14.060675Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0904.2197","last_updated":"2009-04-29T23:53:30Z","snapshot_observed_at":"2026-08-15T05:50:33.105315Z","submitted_at":"2009-04-14T20:20:26Z","title":"The effects of interactions on the topological classification of free fermion systems","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0904.2197","snapshot_observed_at":"2026-08-01T10:04:14.124873Z","title":"Fidkowski and A","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":79,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:14.124873Z"},"links":{"cited_paper":"/paper/0904.2197","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:e2011f99faa68d168138ede198ee07d20ccaf9e946525fbdc1dcf559c999d53e","observation_id":"50ebe113-b329-4fdb-ac54-89c6532bbf18","resolution":{"observed_at":"2026-08-01T10:04:14.124873Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.7329","last_updated":"2015-08-18T02:35:01Z","snapshot_observed_at":"2026-08-18T20:30:31.081725Z","submitted_at":"2014-06-27T22:30:39Z","title":"Fermionic Symmetry Protected Topological Phases and Cobordisms","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.7329","snapshot_observed_at":"2026-08-01T10:04:14.180606Z","title":"Kapustin, R","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies","version":1},"reference_index":80,"source":"pdf_text","source_observed_at":"2026-08-01T10:04:14.180606Z"},"links":{"cited_paper":"/paper/1406.7329","citing_paper":"/paper/2607.20622"},"observation_digest":"sha256:93cf43ccb125fd01ef66c1ac22c5b1c67378718883fecc03d56a1a8770215cbb","observation_id":"51c02fb9-133d-4f58-9ff6-2c0344f86a12","resolution":{"observed_at":"2026-08-01T10:04:14.180606Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.20622","last_updated":"2026-07-22T18:00:03Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-16T18:19:36.259520Z","submitted_at":"2026-07-22T18:00:03Z","title":"Sp(4,Z) actions on 3d U(1)^2 symmetric theories: Order-five duality and bilayer quantum Hall hierarchies"},"reference_resolution":{"displayed":80,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":80,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":80},"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 19 August 2026, this Paper Citation Record lists 80 of 80 outbound references and 0 inbound Pith citation observations for arXiv:2607.20622."}