{"as_of":"2026-08-14T16:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d5fc185f298392bb68d6f7482689dd10372f0e4ee4cca8ad8ed57c4f56e6e24a","coverage":[{"denominator":24,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":24,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T10:37:41.830260Z","state":"measured"},{"denominator":25,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":25,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-03T15:13:22.275045Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.05131","snapshot_observed_at":"2026-08-03T15:13:22.275045Z","title":"Freed, Michael J","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2512.18277","last_updated":"2026-06-08T12:14:08Z","snapshot_observed_at":"2026-08-08T07:33:00.785405Z","submitted_at":"2025-12-20T08:49:51Z","title":"Cobordism of nested manifolds","version":2},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-03T15:13:22.275045Z"},"links":{"cited_paper":"/paper/2506.05131","citing_paper":"/paper/2512.18277"},"observation_digest":"sha256:fb6d4b0bbc1d84ede46e497bbc465534d53edd9448cdfa405d0b241b27bae26a","observation_id":"bcff32ab-a7e4-4d15-b59f-b1f3aa6c538b","resolution":{"observed_at":"2026-08-03T15:13:22.275045Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2506.05131/citation-record","integrity":"/paper/2506.05131/integrity","json":"/paper/2506.05131/citation-record.json","paper":"/paper/2506.05131"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.785179Z","title":null,"venue":null,"work_id":"6e4dd9b7-ea05-4db5-b259-af9e746f5aa5","year":1990},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":1,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.159649Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:fd2818ce2c6045cfdc68253929e48a3a2d1bbaa7aa22fa5e61b6f3ada44e47ab","observation_id":"6892e22f-1caa-45ac-9b81-1008da43b778","resolution":{"observed_at":"2026-08-07T10:37:42.798346Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1601.07185","last_updated":"2016-01-26T21:00:09Z","snapshot_observed_at":"2026-08-14T01:33:00.904416Z","submitted_at":"2016-01-26T21:00:09Z","title":"Topological Defects on the Lattice I: The Ising model","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1601.07185","snapshot_observed_at":"2026-08-07T10:37:40.229594Z","title":null,"venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":2,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.229594Z"},"links":{"cited_paper":"/paper/1601.07185","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:95a3f3d9207f3ac1c050f3d3fde141e7284383c0d59b9354df7d8e0257bd56eb","observation_id":"15eeecc3-3e52-47d7-bf21-66376bb56ec6","resolution":{"observed_at":"2026-08-07T10:37:40.229594Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.737900Z","title":"Blanchet, N","venue":null,"work_id":"b8c0731b-9cea-4b2d-ad01-347b46d19817","year":1995},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.374650Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:008f2d6ba3d0bd9de4166ee89eb36f9f306f5d5b2828e789d1b3285c2f52895b","observation_id":"4cf5c7b9-7ff1-4ad5-be75-3393b5fc68cc","resolution":{"observed_at":"2026-08-07T10:37:42.753429Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.699096Z","title":"5, Cambridge University Press, Cambridge, 1996","venue":null,"work_id":"f4507f34-e753-47d5-a704-ef55b35a1406","year":1996},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.446074Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:5dcc2ecca624913fcb31011b8abb07774d0bb738a9929a188e74535ed5777846","observation_id":"45d871b0-3b24-48ba-bb18-7b44babf39a8","resolution":{"observed_at":"2026-08-07T10:37:42.709360Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.01139","last_updated":"2022-05-04T18:41:17Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2021-11-01T18:00:00Z","title":"Non-Invertible Duality Defects in 3+1 Dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.01139","snapshot_observed_at":"2026-08-07T10:37:40.516884Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":5,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.516884Z"},"links":{"cited_paper":"/paper/2111.01139","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:6a3b708007dc80c954316aa01fb50d361e4c4a5852a099a669a96b0eb359f338","observation_id":"d393564b-c0e3-4f7c-bfd5-77b44a2cf9b0","resolution":{"observed_at":"2026-08-07T10:37:40.516884Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.664508Z","title":"thesis, University of Texas at Austin, 2011","venue":null,"work_id":"cc8dcd1f-5f49-4312-8cb6-7604c758656c","year":2011},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.639857Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:78ac0d6c4a78aa9ea917cb7731af5b3fedef22918b41bd6185747706ed31ab95","observation_id":"961948b6-56e8-49b1-a617-c56792feaa59","resolution":{"observed_at":"2026-08-07T10:37:42.674085Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/0203060","last_updated":"2017-04-28T10:07:43Z","snapshot_observed_at":"2026-08-13T05:19:24.465910Z","submitted_at":"2002-03-07T03:01:37Z","title":"On fusion categories","version":11},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0203060","snapshot_observed_at":"2026-08-07T10:37:40.741472Z","title":null,"venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":7,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.741472Z"},"links":{"cited_paper":"/paper/math/0203060","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:a3621b7705425748070fa048df58e7222a84cf16e4d9c81ffb5e199c124b5e75","observation_id":"9e3ed305-5d73-4f56-902b-075c235405ea","resolution":{"observed_at":"2026-08-07T10:37:40.741472Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.629773Z","title":"Freed, Quantum theory from a geometric viewpoint","venue":null,"work_id":"2fcb036e-3519-4cbf-affa-a91cd719d477","year":null},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":8,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.834703Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:93754b4f14d31a3a558bd4e987d6ff52e75331b822d77ab420ef4d6e1121471f","observation_id":"bbbd1f02-f68f-4da3-8d7d-5f4a3789bad5","resolution":{"observed_at":"2026-08-07T10:37:42.638646Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0404051","last_updated":"2004-10-20T08:12:27Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2004-04-02T15:21:09Z","title":"Kramers-Wannier duality from conformal defects","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0404051","snapshot_observed_at":"2026-08-07T10:37:40.937274Z","title":"u rg Fr\\","venue":null,"work_id":null,"year":2004},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":9,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:40.937274Z"},"links":{"cited_paper":"/paper/cond-mat/0404051","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:bc975bbb2c13973d7039f89884141e24a31ff2941632e141bef97621c289b5bd","observation_id":"dbae4055-f58a-41f0-b7aa-f23e9d7f3144","resolution":{"observed_at":"2026-08-07T10:37:40.937274Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2209.07471","last_updated":"2024-07-31T17:27:01Z","snapshot_observed_at":"2026-08-08T06:31:17.264290Z","submitted_at":"2022-09-15T17:10:11Z","title":"Topological symmetry in quantum field theory","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2209.07471","snapshot_observed_at":"2026-08-07T10:37:41.164561Z","title":"Freed, Gregory W","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":10,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.164561Z"},"links":{"cited_paper":"/paper/2209.07471","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:8f21aeb32bcf9b8ed08f221c8864dca1deb2c1444b039ee68bfc8f73e56603c8","observation_id":"f0d17adf-c167-41a2-a621-d1dcc0f591b0","resolution":{"observed_at":"2026-08-07T10:37:41.164561Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1806.00008","last_updated":"2021-02-16T20:57:23Z","snapshot_observed_at":"2026-07-06T06:42:20.997236Z","submitted_at":"2018-05-31T14:46:21Z","title":"Topological dualities in the Ising model","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1806.00008","snapshot_observed_at":"2026-08-07T10:37:41.336377Z","title":"Freed and Constantin Teleman, Topological dualities in the I sing model , Geom","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.336377Z"},"links":{"cited_paper":"/paper/1806.00008","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:0e4b04408e8159aacfb50ed53878358d5160f5d4db4bf1ad9b47bf5245335852","observation_id":"357c9c2c-291b-45a6-aa48-88def6327e9d","resolution":{"observed_at":"2026-08-07T10:37:41.336377Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2006.10200","last_updated":"2021-08-09T23:24:16Z","snapshot_observed_at":"2026-08-10T18:38:20.099181Z","submitted_at":"2020-06-17T23:40:17Z","title":"Gapped boundary theories in three dimensions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2006.10200","snapshot_observed_at":"2026-08-07T10:37:41.447063Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":12,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.447063Z"},"links":{"cited_paper":"/paper/2006.10200","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:1a1aac0339272e0d8bc86be11d62d5669e9762fe30f9049c23a0232f2264dfb8","observation_id":"43aae690-f9ae-4b45-8dd4-b927ae355733","resolution":{"observed_at":"2026-08-07T10:37:41.447063Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.597889Z","title":null,"venue":null,"work_id":"c6dfce14-8eca-4271-820b-ff707d101a7d","year":1989},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":13,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.543957Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:667c07e988b91ae948c49246f63842734a54dcecb936ea82aa5729655940a1f8","observation_id":"ad463acf-6baf-4388-9739-455e2d1b33bb","resolution":{"observed_at":"2026-08-07T10:37:42.604650Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"quant-ph/9707021","last_updated":"1997-07-09T18:28:27Z","snapshot_observed_at":"2026-07-07T07:27:02.186468Z","submitted_at":"1997-07-09T18:28:27Z","title":"Fault-tolerant quantum computation by anyons","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"quant-ph/9707021","snapshot_observed_at":"2026-08-07T10:37:41.688900Z","title":"1, 2--30, http://arxiv.org/abs/arXiv:quant-ph/9707021 arXiv:quant-ph/9707021","venue":null,"work_id":null,"year":2003},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":14,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.688900Z"},"links":{"cited_paper":"/paper/quant-ph/9707021","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:5ce20d2df21f95300a49af7df41232d7cd54a408dea354ffc1f7d60beae6188a","observation_id":"f85656c5-1f67-46d6-b161-fe10c3072079","resolution":{"observed_at":"2026-08-07T10:37:41.688900Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1104.5047","last_updated":"2012-09-28T17:40:20Z","snapshot_observed_at":"2026-07-06T02:26:52.901468Z","submitted_at":"2011-04-26T23:13:57Z","title":"Models for gapped boundaries and domain walls","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1104.5047","snapshot_observed_at":"2026-08-07T10:37:41.746230Z","title":null,"venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":15,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.746230Z"},"links":{"cited_paper":"/paper/1104.5047","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:e9efb71ccc0a7ab3020fe5758c0f66ed2c18641648b06563286e9aa8b7727682","observation_id":"a02918e1-2b44-446b-ae6e-2fca89bb9f1f","resolution":{"observed_at":"2026-08-07T10:37:41.746230Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2111.01141","last_updated":"2022-04-17T04:03:18Z","snapshot_observed_at":"2026-08-13T17:42:05.405049Z","submitted_at":"2021-11-01T18:00:00Z","title":"Kramers-Wannier-like duality defects in (3+1)d gauge theories","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2111.01141","snapshot_observed_at":"2026-08-07T10:37:41.757326Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":16,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.757326Z"},"links":{"cited_paper":"/paper/2111.01141","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:a7784a0ec1b686623247371b70aad8df11fe03e5f786d6116f31b10951d5012b","observation_id":"42b3c5df-0bd1-4cc9-930a-c53da6989ec8","resolution":{"observed_at":"2026-08-07T10:37:41.757326Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.10161","last_updated":"2021-05-21T06:56:10Z","snapshot_observed_at":"2026-08-13T19:18:56.431241Z","submitted_at":"2021-05-21T06:56:10Z","title":"Wick rotation and the positivity of energy in quantum field theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.10161","snapshot_observed_at":"2026-08-07T10:37:41.775639Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":17,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.775639Z"},"links":{"cited_paper":"/paper/2105.10161","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:586abab7a69075ecbbd95e09c35797586f44501feca06f0e9abf5172866a62c6","observation_id":"9bd90c4b-04da-459e-9f20-f61fdbf69d22","resolution":{"observed_at":"2026-08-07T10:37:41.775639Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0404617","last_updated":"2004-04-27T13:24:42Z","snapshot_observed_at":"2026-08-04T19:23:46.056516Z","submitted_at":"2004-04-26T15:50:47Z","title":"String-net condensation: A physical mechanism for topological phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0404617","snapshot_observed_at":"2026-08-07T10:37:41.785171Z","title":"Levin and Xiao-Gang Wen, String net condensation: A Physical mechanism for topological phases , Phys","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":18,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.785171Z"},"links":{"cited_paper":"/paper/cond-mat/0404617","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:e97945ff0677264f420ed0837fb8707123362a92f45d6888b36dc4ecf1227234","observation_id":"2f892909-1701-4f31-bcdd-878ba870b13c","resolution":{"observed_at":"2026-08-07T10:37:41.785171Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.563218Z","title":null,"venue":null,"work_id":"a97e419d-dcdf-4ee8-9ca3-6d08929a382d","year":1990},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":19,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.796339Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:b0e3f647571ca3a8319c5a1d2868845eaee53ecf8b93ccb1e68b79ba0eb6f747","observation_id":"7f09e81a-6357-44f8-9b4e-419826dc5af5","resolution":{"observed_at":"2026-08-07T10:37:42.570530Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.527632Z","title":"Reshetikhin and V","venue":null,"work_id":"0271966e-0dde-4cfc-adf2-6e95c2a4bf0a","year":1991},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":20,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.803573Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:3d4441d2237008fa05f07e42c97ea2619c1df757344c9faaf422e44b895ed678","observation_id":"7cb162ee-f6b4-42bc-8ee6-40c9dd9d4cce","resolution":{"observed_at":"2026-08-07T10:37:42.537547Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:42.480146Z","title":"https://online.kitp.ucsb.edu/online/strings05/segal/rm/jwvideo.html","venue":null,"work_id":"6a31b401-23e0-4c28-8aab-b3bb91cf0cd5","year":null},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":21,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.809192Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:19cd31ac0fc327aa2d7bb25dc0d115b3498ffd7324115974d3ee580af033aeba","observation_id":"1894d92f-8e9e-4863-8fa8-e0e83eacb2c0","resolution":{"observed_at":"2026-08-07T10:37:42.488465Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-07T10:37:41.816042Z","title":null,"venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":22,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.816042Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:3377e248565d0375177ff2af79cb8dec56e46df9577b9ff3f7aa1b2c59e8d099","observation_id":"17523d8b-9468-42f5-8302-7d149eed36e8","resolution":{"observed_at":"2026-08-07T10:37:41.816042Z","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":"2026-08-07T10:37:41.824745Z","title":null,"venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":23,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.824745Z"},"links":{"citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:975c28b89020b9239dd6949e41b0b13fdcff5178168ebb22f1a822ce4a1fd971","observation_id":"6735dda3-089d-4570-aac5-f7d616add5b2","resolution":{"observed_at":"2026-08-07T10:37:41.824745Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.06691","last_updated":"2024-02-08T19:56:45Z","snapshot_observed_at":"2026-08-13T04:23:02.175430Z","submitted_at":"2024-02-08T19:56:45Z","title":"Volume-Dependent Field Theories","version":1},"cited_work":{"arxiv_id":"2402.06691","doi":null,"metadata_source":"pith","pith_arxiv_id":"2402.06691","snapshot_observed_at":"2026-08-07T10:37:41.942425Z","title":"Volume-Dependent Field Theories","venue":"math-ph","work_id":"c767c064-91a7-4a79-83ee-8c60b686e143","year":2024},"citing_paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory","version":1},"reference_index":24,"source":"arxiv_source","source_observed_at":"2026-08-07T10:37:41.830260Z"},"links":{"cited_paper":"/paper/2402.06691","citing_paper":"/paper/2506.05131"},"observation_digest":"sha256:184eefc2f5c0962804eee02dbcf12d4f6945035cd7b5753105b43a8cd5f09988","observation_id":"35eac7ad-5823-43e2-96ab-e1c275b94bf6","resolution":{"observed_at":"2026-08-07T10:37:41.960152Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2506.05131","last_updated":"2025-06-05T15:17:26Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-10T12:18:45.382581Z","submitted_at":"2025-06-05T15:17:26Z","title":"Discrete quantum systems from topological field theory"},"reference_resolution":{"displayed":24,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":17,"verified_exact":1,"verified_fuzzy":6},"total_outbound_references":24},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2506.05131."}