{"as_of":"2026-08-07T22:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:40afb2f7676a9d576c7cc82deab0c07bbaf7e71b7b53b799bb40f173b4ed5e73","coverage":[{"denominator":65,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":65,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T13:17:31.486685Z","state":"measured"},{"denominator":78,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":78,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":13,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":13,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-05T10:58:32.870611Z","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":"2026-07-03T12:58:08.420669Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-08-05T10:58:32.870611Z","title":"Shirley, C","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2509.03600","last_updated":"2025-09-03T18:01:22Z","snapshot_observed_at":"2026-08-05T10:58:30.301563Z","submitted_at":"2025-09-03T18:01:22Z","title":"Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-05T10:58:32.870611Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2509.03600"},"observation_digest":"sha256:992432e6ad41c54d9871ebf0837ebfb89da67a6463a3f454c06ba0ecaa800f5e","observation_id":"f9da1cd4-2d67-45ca-b9b9-9fa0abbafffc","resolution":{"observed_at":"2026-08-05T10:58:32.870611Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2510.23701","last_updated":"2025-10-27T18:00:00Z","snapshot_observed_at":"2026-07-09T23:18:06.399917Z","submitted_at":"2025-10-27T18:00:00Z","title":"Onsiteability of Higher-Form Symmetries","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-18T03:18:47.456335Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2510.23701"},"observation_digest":"sha256:4d1302e2a690e59a6c20576aa2eaa4e037102e2a12ee7e3939f841565ba0551e","observation_id":"3c6419bd-42dd-4092-bfc4-9d5ea30a15bb","resolution":{"observed_at":"2026-05-18T03:20:48.931335Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-08-03T09:26:55.802636Z","title":"Shirley, C","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2601.14359","last_updated":"2026-07-10T13:08:13Z","snapshot_observed_at":"2026-08-04T02:51:04.909134Z","submitted_at":"2026-01-20T19:00:00Z","title":"Exactly Solvable 1+1d Chiral Lattice Gauge Theories","version":2},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-03T09:26:55.802636Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2601.14359"},"observation_digest":"sha256:da0212cd28d39bf1ae937438ecda6bc8224c3b91e28730900a094f93f8286b51","observation_id":"6d8fb1ae-529e-4991-a534-6518a9270fe4","resolution":{"observed_at":"2026-08-03T09:26:55.802636Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2602.11696","last_updated":"2026-04-07T06:24:20Z","snapshot_observed_at":"2026-08-02T06:40:28.269146Z","submitted_at":"2026-02-12T08:22:02Z","title":"Symmetry Spans and Enforced Gaplessness","version":2},"reference_index":136,"source":"pdf_text","source_observed_at":"2026-05-16T03:25:08.257953Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2602.11696"},"observation_digest":"sha256:a830e34610aef63bbed55d95b199b8425c39a839d9cbd50e46985c9fedc5fcef","observation_id":"b3515e76-5184-4324-85b4-f1150d38a617","resolution":{"observed_at":"2026-05-16T03:27:13.256091Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2604.00347","last_updated":"2026-04-29T13:00:48Z","snapshot_observed_at":"2026-08-02T09:30:53.262883Z","submitted_at":"2026-04-01T00:53:03Z","title":"Lieb-Schultz-Mattis Anomalies and Anomaly Matching","version":2},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-05-13T22:38:46.850119Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2604.00347"},"observation_digest":"sha256:d10c4b4ff1890470691e2e4325088108553e9902968c228a80a0f98da615ccd5","observation_id":"ad01ae2d-8afc-4ae7-a77c-c67daa4dd14e","resolution":{"observed_at":"2026-05-13T22:43:23.451539Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2604.27363","last_updated":"2026-04-30T03:19:28Z","snapshot_observed_at":"2026-07-06T23:12:52.141592Z","submitted_at":"2026-04-30T03:19:28Z","title":"Constructing Bulk Topological Orders via Layered Gauging","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-05-07T10:16:03.883006Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2604.27363"},"observation_digest":"sha256:5066dd431fce5491b5195726ad94e9e22a0a195ab25376d44505d833f6044948","observation_id":"0ae5b8b0-c30e-4dfa-b521-e08f56bc9102","resolution":{"observed_at":"2026-05-12T09:36:26.766525Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2605.03891","last_updated":"2026-05-05T15:48:37Z","snapshot_observed_at":"2026-07-06T23:16:44.876986Z","submitted_at":"2026-05-05T15:48:37Z","title":"Parameterized Families of Toric Code Phase: $em$-duality family and higher-order anyon pumping","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-05-07T04:07:13.027020Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2605.03891"},"observation_digest":"sha256:7dec176d347132c98a3db3c61429b074734ff8ee5e60700b480099da4371f85c","observation_id":"7c1c0ce7-da2f-4d19-972d-f7b482e9a30b","resolution":{"observed_at":"2026-05-12T10:41:31.158882Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2605.04159","last_updated":"2026-05-31T09:23:57Z","snapshot_observed_at":"2026-08-03T04:48:13.385469Z","submitted_at":"2026-05-05T18:00:32Z","title":"Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-05-08T18:06:58.176527Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2605.04159"},"observation_digest":"sha256:967350bc6dd6cf7ef308c06b4f92dbc529e39d2d40f724aba128b5d34c18f6f9","observation_id":"bb19cd06-2069-4b43-8164-57041396961a","resolution":{"observed_at":"2026-05-09T06:45:44.616229Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2605.04159","last_updated":"2026-05-31T09:23:57Z","snapshot_observed_at":"2026-08-03T04:48:13.385469Z","submitted_at":"2026-05-05T18:00:32Z","title":"Establishing Mixed-State Phase Equivalence beyond Renormalization Fixed Points","version":2},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-06-30T23:51:01.473850Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2605.04159"},"observation_digest":"sha256:ce0489a763121d9ba47ef1d0d846d00a8888cca382105b9460a768f00c8f2ead","observation_id":"2425fc54-4dab-4d68-80c6-3b09011777cf","resolution":{"observed_at":"2026-07-01T13:15:45.554055Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2605.16482","last_updated":"2026-05-24T14:27:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-05-15T18:00:00Z","title":"When Symmetries Twist: Anomaly Inflow on Monodromy Defects","version":1},"reference_index":111,"source":"pdf_text","source_observed_at":"2026-05-20T16:34:21.544962Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2605.16482"},"observation_digest":"sha256:65105dd6fe9ea1c0f9681b62f7a6618b4b0dfaf70617e9cedd47d9f74b587856","observation_id":"462bd595-a348-464e-ae47-a529af119e78","resolution":{"observed_at":"2026-05-20T16:38:39.686497Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2605.16482","last_updated":"2026-05-24T14:27:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-05-15T18:00:00Z","title":"When Symmetries Twist: Anomaly Inflow on Monodromy Defects","version":2},"reference_index":111,"source":"pdf_text","source_observed_at":"2026-06-30T19:16:14.613475Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2605.16482"},"observation_digest":"sha256:8bc034a69cf93e3c9bc9e5a6ea0acfb6bb1494e0914f3cc0be139796ac9daf50","observation_id":"d089202a-9928-4141-8c88-c8e4942a40f9","resolution":{"observed_at":"2026-07-01T14:55:47.799583Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2606.11527","last_updated":"2026-06-10T00:11:44Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-06-10T00:11:44Z","title":"Invariants of Sequential Circuits and Generalized Non-Abelian Statistics","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-06-27T08:37:53.035253Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2606.11527"},"observation_digest":"sha256:440606c13771a995bfcde1ce8ae30e00253a016e4a43d8e9f502a0bbe3896ffd","observation_id":"c19b971a-a4b5-4105-87ac-62fec946242a","resolution":{"observed_at":"2026-07-03T12:58:08.422211Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"cited_work":{"arxiv_id":"2507.21267","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.21267","snapshot_observed_at":"2026-07-03T12:58:08.420669Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":"43e58d57-374c-4eea-aba1-58fc997149d5","year":2025},"citing_paper":{"arxiv_id":"2606.12510","last_updated":"2026-06-10T18:00:00Z","snapshot_observed_at":"2026-08-02T01:02:16.372751Z","submitted_at":"2026-06-10T18:00:00Z","title":"Infinite-Order Lattice Chiral Anomalies and CPT","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-06-27T09:09:32.548222Z"},"links":{"cited_paper":"/paper/2507.21267","citing_paper":"/paper/2606.12510"},"observation_digest":"sha256:bdc362af32d1fe0a1890e99cdc85ded769e5da889e405585d00bca3eb7e23aca","observation_id":"66b0eebb-e760-458e-b59c-64d96b57bd80","resolution":{"observed_at":"2026-07-03T11:58:07.151223Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.21267/citation-record","integrity":"/paper/2507.21267/integrity","json":"/paper/2507.21267/citation-record.json","paper":"/paper/2507.21267"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T13:17:31.890431Z","title":"First we choose a re- striction Ug,A of the symmetry operator Ug to a disk A: Ug,A = ˆS[{˜σz p}] ∏ p∈A σx p ˜σz p = { σz p, if p ∈ A 1, otherwise","venue":null,"work_id":"af7b4314-ef95-412a-81f3-6a97aa81a529","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.342838Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:0bea0308d73af8123a8f95dba099450138c09d852fc2f90fb7780598cee5ed98","observation_id":"721c9a77-5fe5-4b04-b017-4e6ff3463c98","resolution":{"observed_at":"2026-08-06T13:17:31.893009Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.883706Z","title":"dynamical gaugeability","venue":null,"work_id":"70a04da8-b17a-46e9-acaf-9146c077e55e","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.345351Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:d4302abb11b4fecdaa284f43d6ad9a408f8eaf77d8c5912664d4066821d08ae7","observation_id":"dd4aba30-f74f-422a-beb5-87ed2aa17ee7","resolution":{"observed_at":"2026-08-06T13:17:31.886002Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.864641Z","title":"Here, we use ‘ ∝’ to denote equality up to a phase","venue":null,"work_id":"6da6bcd1-4cf9-4f4f-80e6-c0f0834cea7f","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.352209Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:466aae455f36d82b5a182c537f0f8f24818a414c452f67dedff186e56b693bbc","observation_id":"a2409c5f-ce55-4b4b-90c6-b456389efce0","resolution":{"observed_at":"2026-08-06T13:17:31.866853Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.897023Z","title":"We conclude that the equivalence class [ω] ∈ H 2(G, Q+) is a well-defined quantity insensitive to the particular choice of restriction","venue":null,"work_id":"c93072cf-d4b3-4bbd-8510-d90da7ed93b6","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.340046Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:dbf52159e64b71553fce5ac15eec025eb0cdc41012eb2f44c9417f27d1029d21","observation_id":"fe297e4d-93c1-472c-887e-9e25c8e9419a","resolution":{"observed_at":"2026-08-06T13:17:31.899368Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.877534Z","title":null,"venue":null,"work_id":"685e7883-5185-49a3-9171-a4877bb112c6","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.347765Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:6f4b19977d1929adb643c9a167f74071c89f94f3ac591218159b703ca7c7ba34","observation_id":"b8f6afb5-7e3b-496e-96ae-3da4f8f82fe4","resolution":{"observed_at":"2026-08-06T13:17:31.879624Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.871227Z","title":null,"venue":null,"work_id":"3506a1af-00a7-4e0b-9d6a-bb9025711bf2","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.349885Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:ad41b2077c41a24694dccf8833d4f5edfe1e72afb9498e2ccb3009e30a6724ec","observation_id":"63dd5851-1f7c-4b52-934f-db696f227abf","resolution":{"observed_at":"2026-08-06T13:17:31.873281Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.857870Z","title":"Let {gij} be a background gauge field – that is, an as- signment of group elements to links ⟨ij⟩ with the identifica- tion gij = g−1 ji","venue":null,"work_id":"0f0646e2-36cd-48b5-9568-01ca36ef0762","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.354439Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:0cb6442712880aef289a480cc53a4bee709c86f740a7566cf9e9d0c5686cff9d","observation_id":"c2003229-530d-4122-809a-fd2001348d2b","resolution":{"observed_at":"2026-08-06T13:17:31.860516Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.851718Z","title":"Generalized Symmetries in Quantum Field Theory","venue":null,"work_id":"695346a3-20ce-4866-a7ed-af337445489e","year":2025},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.356452Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:ec5d49464df4cd6806ebd5f8877ef95de2e91ce7580f1da6775064e7a4fcb063","observation_id":"f87bb469-9887-4de7-a72b-de936438477d","resolution":{"observed_at":"2026-08-06T13:17:31.853908Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.844956Z","title":"Gross, V","venue":null,"work_id":"446ddf5a-84f3-48e3-9ede-404d9f23963d","year":2012},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.358848Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:9a3eca0887b7915cc4e7ef2f5a04f9a9f645612459ac65baf360ad3b3a94bd42","observation_id":"6a745e0a-ec82-49a1-b5e1-7d2e4d05a1c0","resolution":{"observed_at":"2026-08-06T13:17:31.847353Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.838518Z","title":null,"venue":null,"work_id":"57e5e9b8-ba65-444b-a7af-bc55b6885afa","year":1985},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.360883Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:c04e1b7486482bac6f55f779ad0889e986d89a8583b8b31ee1119eef44986409","observation_id":"bafe340f-8deb-4b9e-8077-1c0b94dd08eb","resolution":{"observed_at":"2026-08-06T13:17:31.840788Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.831802Z","title":"Chen, Z.-X","venue":null,"work_id":"ab3c92fa-d394-4ad5-8bd1-0e148eefb684","year":2011},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.363158Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:c22a14a6251d708f587b0692435b73ef809d8e3185fab5bc8ba72e4d9e9d2631","observation_id":"d41b8472-7a2f-4123-bab4-35a8565de6db","resolution":{"observed_at":"2026-08-06T13:17:31.834352Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.818126Z","title":"Chen, Z.-C","venue":null,"work_id":"ad3f6a89-8dac-4d40-bb4d-3a14fc8bb298","year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.367235Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:c28c2261ed26f7ec985fdf742c2fd19bebe44fc298177b9a7907bd7c54336199","observation_id":"37111b11-fce3-4b6e-ba4e-7cfd09a5bf1d","resolution":{"observed_at":"2026-08-06T13:17:31.820779Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.810922Z","title":"Vishwanath and T","venue":null,"work_id":"3949875c-78c5-43ff-99c0-801599ddf498","year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.369567Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:d525f92e520e5dba47f3c488a7dff3f7c6b9005b4bdcb4a853cdaaca76b081e9","observation_id":"347a9512-9ecb-4a9b-b2ca-a5ba2daf1422","resolution":{"observed_at":"2026-08-06T13:17:31.814118Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1409.5436","last_updated":"2015-01-09T22:46:06Z","snapshot_observed_at":"2026-07-06T03:54:57.456461Z","submitted_at":"2014-09-18T20:00:07Z","title":"Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1409.5436","snapshot_observed_at":"2026-08-06T13:17:31.371479Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.371479Z"},"links":{"cited_paper":"/paper/1409.5436","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:faa85df840f761b82173742d1b1f102de01fe4d6d0616bf3723dab3ca75aaf14","observation_id":"1b91b0f6-9145-436f-a4b6-65e07680018a","resolution":{"observed_at":"2026-08-06T13:17:31.371479Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2401.02533","last_updated":"2024-01-04T20:48:51Z","snapshot_observed_at":"2026-07-06T17:11:50.961895Z","submitted_at":"2024-01-04T20:48:51Z","title":"Anomalous symmetries of quantum spin chains and a generalization of the Lieb-Schultz-Mattis theorem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2401.02533","snapshot_observed_at":"2026-08-06T13:17:31.373858Z","title":"Kapustin and N","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.373858Z"},"links":{"cited_paper":"/paper/2401.02533","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:ed5d6609505d4258398ce36fa436bc89e524ed4426b3eac980e8f42375324ca0","observation_id":"79556746-e239-4cf5-ba3d-5d8b406dee5c","resolution":{"observed_at":"2026-08-06T13:17:31.373858Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.05004","last_updated":"2026-05-27T13:27:50Z","snapshot_observed_at":"2026-07-06T19:46:54.707852Z","submitted_at":"2024-11-07T18:59:51Z","title":"Non-onsite symmetry breaking: topological phase coexistence and criticality","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.05004","snapshot_observed_at":"2026-08-06T13:17:31.376204Z","title":"Zhang, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.376204Z"},"links":{"cited_paper":"/paper/2411.05004","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:a53254eb58b0db97e7bb3f88cfb48f2ff45eba48d69890952e4fecd05addf801","observation_id":"ff416092-fde7-42d1-afdc-3644d4f326e5","resolution":{"observed_at":"2026-08-06T13:17:31.376204Z","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":"2026-08-06T13:17:31.381470Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.381470Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:e9037eb9eda32abcd52cd1b71e95438c79a0de4266674cd5afcc0016533def19","observation_id":"e6858274-3546-4b15-bb0d-59d9655ed8b0","resolution":{"observed_at":"2026-08-06T13:17:31.381470Z","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":"2026-08-06T13:17:31.801487Z","title":"’t Hooft, NA TO Sci","venue":null,"work_id":"4205420e-9484-4b05-ac1b-e31eee70e0cb","year":1980},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.383370Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:a6f163244a076a79b09473a9c8c52f602f7fd6f7044b9626b42adf94d09f364d","observation_id":"e4ba789b-66fd-49c6-a891-c15f381b5c23","resolution":{"observed_at":"2026-08-06T13:17:31.803423Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1303.1803","last_updated":"2013-07-30T14:52:26Z","snapshot_observed_at":"2026-08-05T08:21:49.252003Z","submitted_at":"2013-03-07T20:38:08Z","title":"Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders","version":4},"cited_work":{"arxiv_id":"1303.1803","doi":null,"metadata_source":"pith","pith_arxiv_id":"1303.1803","snapshot_observed_at":"2026-08-06T13:17:31.564691Z","title":"Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders","venue":"hep-th","work_id":"addc1c89-e8e5-44f8-b4ec-9e61300b6087","year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.385225Z"},"links":{"cited_paper":"/paper/1303.1803","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:db92d518fafc44a25649bd0767729da02b2584c5b8cf76b376899f1bc2cecda9","observation_id":"540652f7-24d0-49ec-aa59-e5ce2593faf2","resolution":{"observed_at":"2026-08-06T13:17:31.569026Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1403.0617","last_updated":"2014-03-03T22:17:54Z","snapshot_observed_at":"2026-08-02T18:44:13.799283Z","submitted_at":"2014-03-03T22:17:54Z","title":"Anomalies of discrete symmetries in three dimensions and group cohomology","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1403.0617","snapshot_observed_at":"2026-08-06T13:17:31.387519Z","title":"Kapustin and R","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.387519Z"},"links":{"cited_paper":"/paper/1403.0617","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:862f0e0536385ac61e6ed1da1f05576524427393bd73f62f5446298eed4894ce","observation_id":"26cb25ac-cb79-4c95-8438-4f982714e4ce","resolution":{"observed_at":"2026-08-06T13:17:31.387519Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1404.3230","last_updated":"2014-04-16T20:51:39Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2014-04-11T21:36:51Z","title":"Anomalies of discrete symmetries in various dimensions and group cohomology","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1404.3230","snapshot_observed_at":"2026-08-06T13:17:31.389739Z","title":"Kapustin and R","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.389739Z"},"links":{"cited_paper":"/paper/1404.3230","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:9698a7e446d4ebb07e1811d4dfa6e9d51df858ccb6659814fbe4080b5748f884","observation_id":"11e0ba79-315b-44cc-898d-661a44af4cd3","resolution":{"observed_at":"2026-08-06T13:17:31.389739Z","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":"2026-08-06T13:17:31.795767Z","title":"Seifnashri, SciPost Physics 16, 098 (2024)","venue":null,"work_id":"451434e2-e327-40fe-a115-3bb91cf7e646","year":2024},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.391956Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:28f9acee7dc1b2562c692d9996240b98ab6671cb74157d09aecc12930ea3dea9","observation_id":"1c4b50c9-8fcb-44d9-aa5c-1feb993961d0","resolution":{"observed_at":"2026-08-06T13:17:31.797768Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1902.10285","last_updated":"2022-09-19T16:00:46Z","snapshot_observed_at":"2026-08-07T12:15:13.063714Z","submitted_at":"2019-02-27T00:54:07Z","title":"Classification of Quantum Cellular Automata","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.10285","snapshot_observed_at":"2026-08-06T13:17:31.393865Z","title":"Freedman and M","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.393865Z"},"links":{"cited_paper":"/paper/1902.10285","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:5cea4e2218acff36f5dccf28599aede54f639bd6b0cd9f6c62ff22526f284b9d","observation_id":"d3981db6-2554-4017-9e47-72599b853753","resolution":{"observed_at":"2026-08-06T13:17:31.393865Z","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":"2026-08-06T13:17:31.790098Z","title":null,"venue":null,"work_id":"afb4558d-9825-4a78-914f-d8f417a09d5c","year":2017},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.396773Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:28eaff1ecdac6c3dec8c0a91742e6e7233a2a3272d2c14be612158519b1da3b7","observation_id":"3451901c-bd81-4cf9-a03a-b3ca2be73217","resolution":{"observed_at":"2026-08-06T13:17:31.792027Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.771487Z","title":null,"venue":null,"work_id":"fc06b002-5244-4224-af3f-406422570b48","year":2025},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.405195Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:9ec40489c5c5883f8308817cebd90c60bb4248cc847010fa83282226a34513d9","observation_id":"baaeb405-f7d8-4cc5-89b1-1497458b1e30","resolution":{"observed_at":"2026-08-06T13:17:31.773621Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2505.04719","last_updated":"2025-09-05T00:14:16Z","snapshot_observed_at":"2026-08-07T15:49:03.030790Z","submitted_at":"2025-05-07T18:09:13Z","title":"Higher symmetries and anomalies in quantum lattice systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.04719","snapshot_observed_at":"2026-08-06T13:17:31.407127Z","title":"Kapustin, (2025), arXiv:2505.04719 [math-ph]","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.407127Z"},"links":{"cited_paper":"/paper/2505.04719","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:e92e3eacd0f3ff6e119f2a2b13e40a7ec3d3ff33d6db10724f381c02957e8188","observation_id":"e327e005-ece0-45e2-8169-ab44fdec87bd","resolution":{"observed_at":"2026-08-06T13:17:31.407127Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.07430","last_updated":"2025-07-14T19:33:05Z","snapshot_observed_at":"2026-08-06T18:38:55.369420Z","submitted_at":"2025-07-10T04:56:21Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-08-06T13:17:31.409328Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.409328Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:ece6f5ad7a0dcfcb063677e11a8e656c95fba3f7606d7ac7956ef4f479a2d6ca","observation_id":"738a9e3f-f40f-4277-82cd-add225e7871c","resolution":{"observed_at":"2026-08-06T13:17:31.409328Z","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":"2026-08-06T13:17:31.765730Z","title":null,"venue":null,"work_id":"f21ce51b-225a-4073-b0ac-989dfb00d19a","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.411483Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:0d84d50636a9a27566a940879e970e9dd2deae4283b737d3ae3bf12baf938349","observation_id":"c819bcf6-822c-4bc1-9cf4-489cc55210a1","resolution":{"observed_at":"2026-08-06T13:17:31.767924Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.760387Z","title":"equivalent","venue":null,"work_id":"b2a55c70-76a8-4a1a-a809-584b78473e3c","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.413427Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:c97c7688dcbe47e862503573a95e388140ca253f538f43e4c2dab200e96925a1","observation_id":"99266557-866b-4da8-baef-0e10375b83c9","resolution":{"observed_at":"2026-08-06T13:17:31.762294Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.754431Z","title":null,"venue":null,"work_id":"a7a5a02b-99c6-45fa-bc4b-fc3a247c6edc","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.415715Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:847276c6e2984bf5fff5b5a3b31f76e2307e71fc35636e4f9aa4e542dfd78321","observation_id":"545d1d27-1507-4528-a1eb-2a709f2c5dc3","resolution":{"observed_at":"2026-08-06T13:17:31.756373Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.747904Z","title":null,"venue":null,"work_id":"c0e2a914-bfba-4ce6-a71b-cde3046dacc0","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.417692Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:9ba34a78555f3620dea0b425b0372be9a9e156c218fddd1f3f0779dc46d0838f","observation_id":"c6ff6e21-7424-4d72-b597-a959eacfe46a","resolution":{"observed_at":"2026-08-06T13:17:31.749731Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.742157Z","title":"We now show that dynamical gaugeability implies background gaugeability","venue":null,"work_id":"0f14ce27-38ba-457c-97d1-756b0cd55b63","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.419429Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:09b4dfc0a0ef5a73823d79b9196838e5f221aed99c706d516d48fd1db4de7574","observation_id":"0ac4fb7e-337a-480d-86a7-b95d03ea3f42","resolution":{"observed_at":"2026-08-06T13:17:31.744295Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.736656Z","title":null,"venue":null,"work_id":"2515014f-434d-40de-9b51-7f7dbd605bdf","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.421348Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:570225270817a755d799a0d0025e36a828ac466dfdb3b17ea93a7be8d69f8bbd","observation_id":"eb18a1b2-eae2-4c2b-a3a6-506b3aca8e48","resolution":{"observed_at":"2026-08-06T13:17:31.738652Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.730846Z","title":"symmetry disentangler","venue":null,"work_id":"ec5a5374-28b0-4f49-aee7-86bfc0a2cc9e","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.423140Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:f0c176fffb7a9abe9f10203eda32392d7966b3b0db3216e66f900e52f80b9700","observation_id":"96b749da-05c5-4856-90ed-20fc6f107a6e","resolution":{"observed_at":"2026-08-06T13:17:31.732780Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.724886Z","title":"bulk-boundary correspondence","venue":null,"work_id":"5d17ef18-488c-4229-83b8-55df5a5d5b7a","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.425140Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:310fc67141555b0a2b249c5a8f8e0b64d65f2c2012ff6a40923199a6a807ef81","observation_id":"d00d2b8a-a391-405b-86d0-be62eeccfa6b","resolution":{"observed_at":"2026-08-06T13:17:31.727061Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.712932Z","title":"In the 2D honeycomb lattice system, the G-spin on each plaquette is simply a qubit, where the |1⟩ state is identified with |↑⟩ and the |g⟩ state with |↓⟩","venue":null,"work_id":"89d509e5-ac6d-418d-ad42-c4a9c03114d2","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.429582Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:a7e9b4c80bdf8123934415be3055d93aaf07b6316470f542b2957f8d380769c9","observation_id":"7cc5372b-91a6-4176-adc8-9ebcdbf3f427","resolution":{"observed_at":"2026-08-06T13:17:31.715225Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.707316Z","title":"quasi-diagonal","venue":null,"work_id":"8f820d7e-f024-4ca0-9e93-1e8073ba2797","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.431844Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:790ca6fed9c32eb49073dee24ae1470d1caa35c8d146702213d3c4de5c43c9de","observation_id":"13e9e0ca-85bc-421c-ab0f-129e9c12bd26","resolution":{"observed_at":"2026-08-06T13:17:31.709242Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.694320Z","title":"We do this by constructing an explicit gapped, symmetric Hamil- tonian with a product state as its unique ground state","venue":null,"work_id":"7b90a735-3fc9-45c8-bd67-4eb76179e557","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.435682Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:840644f158c73c91eb239900f39b263426c869263f37e77888d751a7a94004d5","observation_id":"9ce8e3ae-890d-4941-a8cd-843898133986","resolution":{"observed_at":"2026-08-06T13:17:31.696823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.687876Z","title":"flow” F(u) of the single particle unitary matrix ujk associated withU : Ind(U ) = 2 F (u). (77) Here the matrix ujk is defined by U †cjU = ∑ jkujkck, while the “flow","venue":null,"work_id":"c9ba4bf1-fed6-4d5d-96ab-26eff5ae245e","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.437623Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:907998deee74dd17e115660d57078e603f0e4bf0c0249a705a2995e088488463","observation_id":"592d751e-2d70-4ebd-92d6-1319bf3f795a","resolution":{"observed_at":"2026-08-06T13:17:31.690221Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.674985Z","title":"Gross, V","venue":null,"work_id":"b4f29292-f136-4c84-a5d7-8018f19262a1","year":2012},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.441620Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:129db20547bebffb058c2c14823187e5886e82b35f235c7fc79303b9437c95e9","observation_id":"dc0a1e86-ed70-4445-87d7-ba5f612ca784","resolution":{"observed_at":"2026-08-06T13:17:31.677051Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.668016Z","title":null,"venue":null,"work_id":"f488e88e-4bca-41bc-8b5b-fe0eae4f28a4","year":2016},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.444225Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:8b75789187f71e59c761b902b2c036bd826580d988772a4d1e2dc99532a428c2","observation_id":"9eb8b750-872c-421e-8914-67e25201affd","resolution":{"observed_at":"2026-08-06T13:17:31.670261Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.661752Z","title":"If we define an FDQC in terms of layers with gates that have disjoint support, then we must split each of the above six layers into two layers each","venue":null,"work_id":"9a9b672f-66d5-4421-bfdf-c5a729541b51","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.446540Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:def7efa2809f1c809ca267dbb10e5551ccf211249a824756393638b79672259d","observation_id":"a3e13dfd-45eb-4121-a73a-ff88868add85","resolution":{"observed_at":"2026-08-06T13:17:31.664096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.655826Z","title":null,"venue":null,"work_id":"4be51bcd-c055-447f-9610-8df5df35756c","year":1979},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.448663Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:e6285e014877daca3b2933ef1906c677f9ec67f9bc8a9215b150eceac17525ec","observation_id":"baccb778-17a0-4b6b-8f3e-75f3ae878beb","resolution":{"observed_at":"2026-08-06T13:17:31.657727Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.648809Z","title":"In particular,n is finite","venue":null,"work_id":"8da05bc4-d989-487f-bdc7-9c2df6080b05","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.450564Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:ab52537ebca12be82e5d1e9dd36da02a0588f5aafdd18d0fa429ca282186605c","observation_id":"f8dcaaf3-968e-4b74-963a-48af8bf5cdaf","resolution":{"observed_at":"2026-08-06T13:17:31.651252Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2503.09717","last_updated":"2025-03-12T18:08:22Z","snapshot_observed_at":"2026-08-07T17:09:16.918628Z","submitted_at":"2025-03-12T18:08:22Z","title":"Disentangling anomaly-free symmetries of quantum spin chains","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.09717","snapshot_observed_at":"2026-08-06T13:17:31.452357Z","title":"Seifnashri and W","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.452357Z"},"links":{"cited_paper":"/paper/2503.09717","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:85e076afab32a909710ec54a6515f011065db160c493ccb2d5afe32042866b97","observation_id":"21b24faf-1569-4373-9cbe-5eedc3249035","resolution":{"observed_at":"2026-08-06T13:17:31.452357Z","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":"2026-08-06T13:17:31.783814Z","title":"Zhang, Phys","venue":null,"work_id":"2f14a663-5bb7-4f11-a156-e819418b2a12","year":2023},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.454189Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:c5f7343498378b0a78cc7ea872b59fbac4b15496d5da8c628dde181a003d08d9","observation_id":"29fb087b-7edd-48da-baff-ae4509d90249","resolution":{"observed_at":"2026-08-06T13:17:31.786093Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.718997Z","title":null,"venue":null,"work_id":"3fefcc09-282a-4614-9706-229e99edde7e","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.427583Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:51396aa1f0661271b0c7f5b1b5f6fa8a427fcee2cd7808f9d7aa54242fb1450e","observation_id":"468d72df-44e8-456c-b026-b769bdb715f8","resolution":{"observed_at":"2026-08-06T13:17:31.721303Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1712.07950","last_updated":"2018-09-19T20:36:09Z","snapshot_observed_at":"2026-08-05T09:51:49.000025Z","submitted_at":"2017-12-21T14:16:03Z","title":"Symmetry Protected Topological phases and Generalized Cohomology","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1712.07950","snapshot_observed_at":"2026-08-06T13:17:31.456020Z","title":"Gaiotto and T","venue":null,"work_id":null,"year":2019},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.456020Z"},"links":{"cited_paper":"/paper/1712.07950","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:acdb16f60171ad13b325f7b5709c6a06c4197e4cd5ebd0473459f6e070990f8b","observation_id":"2b9812b3-bb49-4e24-8187-02cfe3a1d109","resolution":{"observed_at":"2026-08-06T13:17:31.456020Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2208.07367","last_updated":"2022-12-09T03:19:09Z","snapshot_observed_at":"2026-07-06T13:42:05.210724Z","submitted_at":"2022-08-15T17:59:59Z","title":"Codimension-2 defects and higher symmetries in (3+1)D topological phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2208.07367","snapshot_observed_at":"2026-08-06T13:17:31.458297Z","title":"Barkeshli, Y .-A","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":57,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.458297Z"},"links":{"cited_paper":"/paper/2208.07367","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:f19e915d302b68e13d003cd9548f940f6690324d86a673fa6cfdbf969256fa98","observation_id":"eeda1908-5d0c-418f-a253-ea141e9fdcf0","resolution":{"observed_at":"2026-08-06T13:17:31.458297Z","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":"2026-08-06T13:17:31.777611Z","title":null,"venue":null,"work_id":"09ea2f55-23a5-4430-aedd-ba6ca394bb32","year":2017},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":58,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.460034Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:eb81d12450d2f7d913d22e1271a633fb80f9b8cd172feae9d5dba4b9bd7ea1e4","observation_id":"9164f6a1-9171-472f-9879-dfc8db1d3191","resolution":{"observed_at":"2026-08-06T13:17:31.779621Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.642199Z","title":"[ 12] also considered slower decay, but in this work we will assume that the off-diagonal matrix elements decays superpolynomially","venue":null,"work_id":"c4e591ba-eeca-4411-8a3a-a13b187bd961","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":59,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.462577Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:05fdac54687bc304c3cebdad411f8050cd0f6f854d264421437f1dad29952d5d","observation_id":"a41fe613-1fb8-40a1-a570-3489409cadb2","resolution":{"observed_at":"2026-08-06T13:17:31.644502Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.464566Z","title":"Kitaev, Annals of Physics 321, 2 (2006)","venue":null,"work_id":null,"year":2006},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":60,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.464566Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:92edd20dcb72cf39d062aba0d2ee0c0c7878ab9df6b3ffa62739d257bed9080c","observation_id":"55ae35c4-fee0-44d9-b8cd-5a083e70357d","resolution":{"observed_at":"2026-08-06T13:17:31.464566Z","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":"2026-08-06T13:17:31.632413Z","title":null,"venue":null,"work_id":"f4637fa7-0a1a-4b89-a3c8-075813caff75","year":2014},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.466502Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:2263d5eea57ca63bebf4acffe819a8f1bafe46669cdcff16269bd94e987d4e7e","observation_id":"248c3c9c-a1c0-4c65-94fa-ab8e816bbe12","resolution":{"observed_at":"2026-08-06T13:17:31.634532Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.626231Z","title":"Fidkowski, H","venue":null,"work_id":"94dcdd3e-0767-4260-9c29-8d381c2a0bb2","year":2019},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":62,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.469026Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:a6a8f7099f79b209cb11cf38879545803b03757d75ec596e0b6a6f48be9d4418","observation_id":"ca605d65-6fef-4585-bbb9-a7fa40e9dba1","resolution":{"observed_at":"2026-08-06T13:17:31.628340Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.619647Z","title":null,"venue":null,"work_id":"bbd17d3a-2e3c-497c-9016-7d6ef5e0e920","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":63,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.470948Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:da4dc74dcc6d3876d4306c690d9cc79b2099f8da504650d69d0ddbac95408ba3","observation_id":"a2f8e66f-1fcd-4a6a-8534-a554fc8fa5f5","resolution":{"observed_at":"2026-08-06T13:17:31.622266Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.472856Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":64,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.472856Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:4260ecbc90325b9189c7482f203be3ec7bb0884e72e8b0efeadae32c85938f78","observation_id":"a156c10d-d95e-44f2-9757-7f16acfbd694","resolution":{"observed_at":"2026-08-06T13:17:31.472856Z","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":"2026-08-06T13:17:31.609626Z","title":"Zhang and M","venue":null,"work_id":"1d7cfa6d-17b1-4005-9f4a-42dc48a87955","year":2023},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.474750Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:41ba8b5e2b123e28e77670aaf7cad7adcdd874dbe245c680d46a7c3dcd10bb2f","observation_id":"ce7c8150-8590-43d3-841b-5c964bb7c122","resolution":{"observed_at":"2026-08-06T13:17:31.611688Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.824939Z","title":null,"venue":null,"work_id":"c4982a7a-b82c-4ae4-ad67-3f5e48fd9f88","year":2012},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.476745Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:37c767d26cc36d600bdf82fa42a909b3c0504f871f92c7bc443e56a16b54c575","observation_id":"519a2424-c504-4224-890f-536c5908fc58","resolution":{"observed_at":"2026-08-06T13:17:31.827454Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.603110Z","title":"Qi, New Journal of Physics 15, 065002 (2013)","venue":null,"work_id":"2368f398-713c-4dc1-9466-aacda54f1735","year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":67,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.478493Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:9833ca1fcc09547fb7d2599cf8f6b1fe61f3936696e5e0ff7264a3b2df18704e","observation_id":"8e569cf6-4a0b-453f-825d-d753246bd599","resolution":{"observed_at":"2026-08-06T13:17:31.605248Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+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":"2026-08-06T13:17:31.596675Z","title":"Y ao and S","venue":null,"work_id":"9919b873-df4d-4681-a5d9-aef7d1bec96a","year":2013},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":68,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.480465Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:2d4cc516d6304b37ec48e59521a88f4eef0f6d1779ec12ba4ac47f6c614a924f","observation_id":"77720c1e-a711-43b7-b3cc-f9cbba7ac0fa","resolution":{"observed_at":"2026-08-06T13:17:31.598969Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1304.4569","last_updated":"2013-04-16T19:34:37Z","snapshot_observed_at":"2026-07-06T03:11:19.070505Z","submitted_at":"2013-04-16T19:34:37Z","title":"The effect of interactions on 2D fermionic symmetry-protected topological phases with Z2 symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1304.4569","snapshot_observed_at":"2026-08-06T13:17:31.482305Z","title":"Gu and M","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":69,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.482305Z"},"links":{"cited_paper":"/paper/1304.4569","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:1ae75a8004fb8c28a4e932fef9e65f462885a19309f2cb87407d6b3fac8d072d","observation_id":"915bc346-d6be-44d8-b0bf-0ae1b2a5794f","resolution":{"observed_at":"2026-08-06T13:17:31.482305Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1604.02145","last_updated":"2016-06-22T15:27:50Z","snapshot_observed_at":"2026-07-06T04:52:07.526190Z","submitted_at":"2016-04-07T20:00:00Z","title":"Discrete spin structures and commuting projector models for 2d fermionic symmetry protected topological phases","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1604.02145","snapshot_observed_at":"2026-08-06T13:17:31.484485Z","title":"Tarantino and L","venue":null,"work_id":null,"year":2016},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":70,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.484485Z"},"links":{"cited_paper":"/paper/1604.02145","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:fb44bea76633d67a4d5b2bd0ff1505ca51c206ddae56dfe4cda852722f5dcb58","observation_id":"5de105b5-4213-4e75-b024-501422c1b566","resolution":{"observed_at":"2026-08-06T13:17:31.484485Z","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":"2026-08-06T13:17:31.681204Z","title":"( 72) and find that Θ = 2 , which is not a fourth power of a rational number or √ 2, or their combinations","venue":null,"work_id":"1907b1c7-feaf-43b8-976d-d7a20ab4da86","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":71,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.439670Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:826df1b910f114f55ecc5e8dad77cfa9af3ef2a32b0e4bf90021a21241859110","observation_id":"e5e508ab-7b28-495b-b47a-b590c5885e3b","resolution":{"observed_at":"2026-08-06T13:17:31.683878Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0010440","last_updated":"2000-10-30T00:01:44Z","snapshot_observed_at":"2026-08-05T13:57:02.419317Z","submitted_at":"2000-10-27T08:59:57Z","title":"Unpaired Majorana fermions in quantum wires","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0010440","snapshot_observed_at":"2026-08-06T13:17:31.486685Z","title":"Kitaev, Phys","venue":null,"work_id":null,"year":2001},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":72,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.486685Z"},"links":{"cited_paper":"/paper/cond-mat/0010440","citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:81422209f0b3a1aa6d270a03abf5885eee64f756fd2c9eccb8eb797507c8f367","observation_id":"16a8f5e4-a074-4a7d-b94f-0c5f58fbbfed","resolution":{"observed_at":"2026-08-06T13:17:31.486685Z","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":"2026-08-06T13:17:31.700954Z","title":"We now show that the Zn symmetry (","venue":null,"work_id":"a95f0633-fd25-4d4e-9ad4-35ee1d476e92","year":null},"citing_paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability","version":1},"reference_index":73,"source":"pdf_text","source_observed_at":"2026-08-06T13:17:31.433891Z"},"links":{"citing_paper":"/paper/2507.21267"},"observation_digest":"sha256:089f09b1a4a4e8058c6b9416fb07c698840872f4dc30350483d41bb84d0f362c","observation_id":"749b36d2-7365-4437-896e-3cce7b1a9b67","resolution":{"observed_at":"2026-08-06T13:17:31.703110Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-07T06:34:17.273281+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.21267","last_updated":"2025-07-28T18:48:39Z","latest_version":1,"primary_category":"cond-mat.str-el","snapshot_observed_at":"2026-08-06T13:17:29.963401Z","submitted_at":"2025-07-28T18:48:39Z","title":"Anomaly-free symmetries with obstructions to gauging and onsiteability"},"reference_resolution":{"displayed":65,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":33,"verified_exact":1,"verified_fuzzy":31},"total_outbound_references":65},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 65 of 65 outbound references and 13 inbound Pith citation observations for arXiv:2507.21267."}