{"as_of":"2026-08-16T19:13:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:b8dff2f925f75d41a34ae54ddc524799a25c79e466152ef7638fb44f80a3c2f1","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":7,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":7,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-16T10:20:21.621788Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-16T07:50:05.495013Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":"2010.07950","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fusion 2-categories With no Line Operators are Grouplike","venue":null,"work_id":"d742fd44-2aa8-4607-a770-a4ec367ed900","year":2021},"citing_paper":{"arxiv_id":"2305.18296","last_updated":"2023-06-07T01:44:22Z","snapshot_observed_at":"2026-08-10T21:00:13.538331Z","submitted_at":"2023-05-29T17:59:50Z","title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","version":2},"reference_index":103,"source":"pdf_text","source_observed_at":"2026-05-16T07:50:05.029267Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2305.18296"},"observation_digest":"sha256:5d0e98eb11e48018f5716c61ae9f207340417ac571fe860d84a4dcb7dfebf84a","observation_id":"8caef244-2325-4978-8a22-b3181029ad59","resolution":{"observed_at":"2026-05-16T07:50:05.497076Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-08-11T11:48:24.689695Z","title":"Fusion 2-categories with no line operators are grouplike","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.15019","last_updated":"2025-05-05T14:35:54Z","snapshot_observed_at":"2026-08-14T17:56:38.673992Z","submitted_at":"2024-12-19T16:31:06Z","title":"Compact Semisimple Tensor 2-Categories are Morita Connected","version":2},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-11T11:48:24.689695Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2412.15019"},"observation_digest":"sha256:64357f0ee7c98c5f647e3abe5943fb17ed1e4bbbe007d1c7df53cbd052a0f68b","observation_id":"8f515e24-a0f5-48e5-95e5-51424b7f6c11","resolution":{"observed_at":"2026-08-11T11:48:24.689695Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-08-11T10:27:54.753331Z","title":"Fusion 2-categories With no Line Operators are Grouplike,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-11T15:37:17.654956Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T10:27:54.753331Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2412.16681"},"observation_digest":"sha256:98ea1d90230d785de2ec62922a99ea8115d2edf4532f0e42d2a2a5a555a47926","observation_id":"f5160751-ff44-4984-bfb6-8b9fcde531f5","resolution":{"observed_at":"2026-08-11T10:27:54.753331Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-08-16T10:20:21.621788Z","title":"Fusion 2-categories With no Line Operators are Grouplike,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2504.18501","last_updated":"2025-04-28T11:33:23Z","snapshot_observed_at":"2026-08-16T18:49:55.730596Z","submitted_at":"2025-04-25T17:14:44Z","title":"SymTFT, Protected Gaplessness, and Spontaneous Breaking of Non-invertible Symmetries","version":2},"reference_index":114,"source":"pdf_text","source_observed_at":"2026-08-16T10:20:21.621788Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2504.18501"},"observation_digest":"sha256:2be840e4fca370384d422b5fe5fe30e403dc959984fe4b646863ccefeec14857","observation_id":"73d4e738-3fdd-4ee2-ad34-cd454144bcba","resolution":{"observed_at":"2026-08-16T10:20:21.621788Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-08-15T16:09:45.958571Z","title":"Fusion 2-categories with no line operators are grouplike","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2509.10603","last_updated":"2026-07-10T10:20:42Z","snapshot_observed_at":"2026-08-16T00:52:43.197425Z","submitted_at":"2025-09-12T18:00:01Z","title":"The Classification of 3+1d Symmetry Enriched Topological Order","version":3},"reference_index":61,"source":"arxiv_source","source_observed_at":"2026-08-15T16:09:45.958571Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2509.10603"},"observation_digest":"sha256:a9109ad3b082efd94481d3bde308ca3ebd0bcb639fbc07d627051c531407520f","observation_id":"ee104b3d-2744-498f-b24e-dcbcadb9ab17","resolution":{"observed_at":"2026-08-15T16:09:45.958571Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":"2010.07950","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Fusion 2-categories With no Line Operators are Grouplike","venue":null,"work_id":"d742fd44-2aa8-4607-a770-a4ec367ed900","year":2021},"citing_paper":{"arxiv_id":"2604.24847","last_updated":"2026-04-27T18:00:01Z","snapshot_observed_at":"2026-07-06T23:10:47.277692Z","submitted_at":"2026-04-27T18:00:01Z","title":"The Classification of Pauli Stabilizer Codes: A Lattice and Continuum Treatise","version":1},"reference_index":41,"source":"arxiv_source","source_observed_at":"2026-05-08T01:19:18.233755Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2604.24847"},"observation_digest":"sha256:bb021efd9d131cec05ba213bc913887d802897f9da5c89a33690ab69a8413109","observation_id":"b439780d-c6ad-414f-810f-b422a90f665e","resolution":{"observed_at":"2026-05-11T23:11:16.045480Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2010.07950","snapshot_observed_at":"2026-08-14T04:36:06.630757Z","title":"Johnson-Freyd and M","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2608.08766","last_updated":"2026-08-11T17:59:19Z","snapshot_observed_at":"2026-08-14T23:11:58.273304Z","submitted_at":"2026-08-09T15:28:28Z","title":"Understanding Non-Split 2-Group Symmetry: (3+1)D SymTFT, Anomaly and Bordism","version":2},"reference_index":187,"source":"pdf_text","source_observed_at":"2026-08-14T04:36:06.630757Z"},"links":{"cited_paper":"/paper/2010.07950","citing_paper":"/paper/2608.08766"},"observation_digest":"sha256:8f1c94b66dd3866587f61afdd5ed159fda4ad901e4d51c715ddb93bebae2459b","observation_id":"fbb4e5c4-d058-447c-bdf1-2eb26bc505e5","resolution":{"observed_at":"2026-08-14T04:36:06.630757Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2010.07950/citation-record","integrity":"/paper/2010.07950/integrity","json":"/paper/2010.07950/citation-record.json","paper":"/paper/2010.07950"},"outbound":[],"paper":{"arxiv_id":"2010.07950","last_updated":"2020-10-15T18:00:03Z","latest_version":1,"primary_category":"math.QA","snapshot_observed_at":"2026-08-16T19:13:09.957476Z","submitted_at":"2020-10-15T18:00:03Z","title":"Fusion 2-categories with no line operators are grouplike"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 7 inbound Pith citation observations for arXiv:2010.07950."}