{"as_of":"2026-08-08T07:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:88ed041a861fb64650110a362a07bcca86d3779e4ce995afeb0ec625abd3029c","coverage":[{"denominator":55,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":55,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:49:53.489966Z","state":"measured"},{"denominator":68,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":68,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-08-06T15:13:23.191344Z","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":"2026-07-04T03:19:31.779854Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"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":"2026-08-06T15:13:23.191344Z","title":"Anomaly diagnosis via symmetry re striction in two-dimensional lattice systems","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.16475","last_updated":"2025-07-22T11:28:59Z","snapshot_observed_at":"2026-08-06T15:06:20.367196Z","submitted_at":"2025-07-22T11:28:59Z","title":"On two-dimensional tensor network group symmetries","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T15:13:23.191344Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2507.16475"},"observation_digest":"sha256:ece799ce76a08544dc0230573673b1e05d54cd6f9113bde8f497d21e7f5f2967","observation_id":"759d5681-b112-441d-b409-0241c596d4ce","resolution":{"observed_at":"2026-08-06T15:13:23.191344Z","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":{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":3,"source":"pdf_text","source_observed_at":"2026-05-18T03:18:47.456335Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2510.23701"},"observation_digest":"sha256:b6d5d9bb77a5f5485a1604c832dc859a88a08379fee83363b8d5ccfdf5184122","observation_id":"4d76e211-fffb-400b-8b39-558f788fb2eb","resolution":{"observed_at":"2026-05-18T03:20:48.865139Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2026-08-03T09:26:55.559948Z","title":"Kawagoe and W","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":35,"source":"pdf_text","source_observed_at":"2026-08-03T09:26:55.559948Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2601.14359"},"observation_digest":"sha256:6899409d31cd5173145f383f2ac3b8fcb0d0df51f610c4e4313d2b5eb17477c4","observation_id":"c44e31b6-58c8-4170-b422-0ab685c4ee42","resolution":{"observed_at":"2026-08-03T09:26:55.559948Z","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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":134,"source":"pdf_text","source_observed_at":"2026-05-16T03:25:08.257953Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2602.11696"},"observation_digest":"sha256:604e1efc067e7ef1e9e67ff6a06bf57dda1f8fff0b4d9e35959a5750eec92597","observation_id":"1a14c22d-dd17-40db-a6be-c3124b1eeace","resolution":{"observed_at":"2026-05-16T03:27:13.393969Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":41,"source":"pdf_text","source_observed_at":"2026-05-13T22:38:46.850119Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2604.00347"},"observation_digest":"sha256:db8ecb7b1cafa0ff58e4645c4e40dcb9bc8eb49fd8a8480150b89db425091571","observation_id":"65442d39-aff3-4c64-9a97-3549196e87a0","resolution":{"observed_at":"2026-05-13T22:43:23.441648Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","year":2025},"citing_paper":{"arxiv_id":"2604.02856","last_updated":"2026-04-03T08:22:30Z","snapshot_observed_at":"2026-07-06T22:52:10.923214Z","submitted_at":"2026-04-03T08:22:30Z","title":"Type-IV 't Hooft Anomalies on the Lattice: Emergent Higher-Categorical Symmetries and Applications to LSM Systems","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-13T18:16:10.478388Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2604.02856"},"observation_digest":"sha256:391391dc013e1b5e7d74c6f8e7990bb4911f9743db8d0ea7d03e76f0b9ec320a","observation_id":"c1f4b8cf-ec0b-4e25-ac0c-af838fa0eb49","resolution":{"observed_at":"2026-05-13T18:18:06.257731Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":114,"source":"pdf_text","source_observed_at":"2026-05-20T16:34:21.544962Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2605.16482"},"observation_digest":"sha256:e30671bddfa902eac621a41b7d5540d0a3e647ac25279185cc57bfb0426bff40","observation_id":"f9f1a8d9-7ed0-4730-a881-6f208f81fe38","resolution":{"observed_at":"2026-05-20T16:38:39.889594Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":114,"source":"pdf_text","source_observed_at":"2026-06-30T19:16:14.613475Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2605.16482"},"observation_digest":"sha256:071ee04b4ed99023576d38de910e907031a8b476a038d4608df0d6f420baf0d8","observation_id":"1be813c6-3f63-42bf-9be2-f9996f68aed5","resolution":{"observed_at":"2026-07-01T14:55:47.638400Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","year":2025},"citing_paper":{"arxiv_id":"2605.28925","last_updated":"2026-05-27T18:00:00Z","snapshot_observed_at":"2026-08-06T07:30:36.589203Z","submitted_at":"2026-05-27T18:00:00Z","title":"A local description of strong symmetries and strong-to-weak symmetry breaking in quantum many-body systems","version":1},"reference_index":92,"source":"pdf_text","source_observed_at":"2026-06-29T11:42:51.655279Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2605.28925"},"observation_digest":"sha256:91a75da9f525db3076381551435bc5c0f1a57e8ba358633507f387b0dec342bb","observation_id":"c08ab78d-35b9-42f8-9297-389f72cfac9d","resolution":{"observed_at":"2026-06-29T11:43:23.141209Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":59,"source":"pdf_text","source_observed_at":"2026-06-27T08:37:53.035253Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2606.11527"},"observation_digest":"sha256:6c158eb106d71cdc4aae558b7703e94636c1c5b6175d73562eda4bcb2b987a0e","observation_id":"5041c215-571b-4140-8ed8-5192825cbe08","resolution":{"observed_at":"2026-07-03T12:58:08.441914Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","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":23,"source":"pdf_text","source_observed_at":"2026-06-27T09:09:32.548222Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2606.12510"},"observation_digest":"sha256:c8b41fcf66310dcd1df978ae0ff624c2410d2373eeace81a8e524a2a3ed807f7","observation_id":"4e5d41b1-ba80-4d22-beb5-1276a97d5d09","resolution":{"observed_at":"2026-07-03T11:58:07.156587Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"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":"2507.07430","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2507.07430","snapshot_observed_at":"2026-07-04T03:19:31.779854Z","title":"Anomaly diagnosis via symmetry restriction in two-dimensional lattice systems","venue":null,"work_id":"d86b8da1-f620-4ca5-be75-4745774f9be2","year":2025},"citing_paper":{"arxiv_id":"2606.19657","last_updated":"2026-06-17T23:42:14Z","snapshot_observed_at":"2026-08-08T04:02:53.388728Z","submitted_at":"2026-06-17T23:42:14Z","title":"$K$-Theoretic Obstructions to Linearizing QCA Representations","version":1},"reference_index":11,"source":"arxiv_source","source_observed_at":"2026-06-26T18:09:01.358199Z"},"links":{"cited_paper":"/paper/2507.07430","citing_paper":"/paper/2606.19657"},"observation_digest":"sha256:f7a601021c85c61ec0acd44602bc7db15fc71778903e00411410dc0f704d5b12","observation_id":"e8ccc303-c28d-4558-b730-1949e734b822","resolution":{"observed_at":"2026-07-04T03:19:31.784393Z","resolver_source":"arxiv_id","status":"metadata_mismatch"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.07430/citation-record","integrity":"/paper/2507.07430/integrity","json":"/paper/2507.07430/citation-record.json","paper":"/paper/2507.07430"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:50.293286Z","title":null,"venue":null,"work_id":null,"year":1961},"citing_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},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.293286Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:b58d59fa3fa846f838a7c94f42e9743d1900b9eb8c8aed7e3fade1df7d4d90fe","observation_id":"71de4487-c898-4fe1-a043-116e66a4c64f","resolution":{"observed_at":"2026-08-06T18:49:50.293286Z","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":"2026-08-06T18:49:50.334992Z","title":"Affleck and E","venue":null,"work_id":null,"year":1986},"citing_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},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.334992Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:a36b7a34ee79825f52263b1a187fb2409205e382022dc3664d13314923915980","observation_id":"6f1dcfc2-7fb1-4c61-bf1e-e9e28f4a8081","resolution":{"observed_at":"2026-08-06T18:49:50.334992Z","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":"2026-08-06T18:49:50.372066Z","title":"Oshikawa, Commensurability, Excitation Gap, and Topology in Quantum Many- Particle Systems on a Periodic Lattice , Phys","venue":null,"work_id":null,"year":2000},"citing_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},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.372066Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:c8ed5d4bc14aed8e2317ada94c74f9363240bf8c05d15413e5720e3b9c1d0063","observation_id":"cf47a0e2-9bd5-4d97-bc99-2d37511ff54a","resolution":{"observed_at":"2026-08-06T18:49:50.372066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"cond-mat/0305505","last_updated":"2004-02-09T17:38:53Z","snapshot_observed_at":"2026-08-02T08:34:05.500285Z","submitted_at":"2003-05-21T19:10:30Z","title":"Lieb-Schultz-Mattis in Higher Dimensions","version":6},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"cond-mat/0305505","snapshot_observed_at":"2026-08-06T18:49:50.399394Z","title":null,"venue":null,"work_id":null,"year":2004},"citing_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},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.399394Z"},"links":{"cited_paper":"/paper/cond-mat/0305505","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:9676b77158c6f133deeb40622bfac951ea2f6afb8253ca38857fdf5b79eb5b7b","observation_id":"d8c6d707-10b8-494b-90df-439638974f8d","resolution":{"observed_at":"2026-08-06T18:49:50.399394Z","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":"2026-08-06T18:49:50.426492Z","title":"Ogata and H","venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.426492Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:64a662b8303431c5384199f893fad1910018487658f805e85127154192fa0a68","observation_id":"cbff7c83-a0fc-42c3-926c-4b53508a8f3f","resolution":{"observed_at":"2026-08-06T18:49:50.426492Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2004.06458","last_updated":"2020-04-26T14:26:10Z","snapshot_observed_at":"2026-08-07T18:40:13.958368Z","submitted_at":"2020-04-14T13:02:49Z","title":"General Lieb-Schultz-Mattis type theorems for quantum spin chains","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2004.06458","snapshot_observed_at":"2026-08-06T18:49:50.455351Z","title":"Ogata, Y","venue":null,"work_id":null,"year":2021},"citing_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},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.455351Z"},"links":{"cited_paper":"/paper/2004.06458","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:5b0c38f8335c598f49ea8950002860fd5d132fb8ff65564f1e47f6dec0f55fb3","observation_id":"3c77f31e-d722-42b6-8037-9cde69fc8023","resolution":{"observed_at":"2026-08-06T18:49:50.455351Z","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":"2026-08-06T18:49:50.482603Z","title":"Kapustin and N","venue":null,"work_id":null,"year":2024},"citing_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},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.482603Z"},"links":{"cited_paper":"/paper/2401.02533","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:1bf7dbbc613f7f2e459e55cfa13c5d7267f213ac1c65e282cda018027a284bda","observation_id":"c7c1b616-d082-4218-9462-2566c622f742","resolution":{"observed_at":"2026-08-06T18:49:50.482603Z","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":"2026-08-06T18:49:50.523586Z","title":null,"venue":null,"work_id":null,"year":1985},"citing_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},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.523586Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:040a228618edb2c39a8dd416352a72da76e77df8165a7c9bf57b6bd2ccc80853","observation_id":"0040e413-0dcc-401e-9857-cdc510eb69c7","resolution":{"observed_at":"2026-08-06T18:49:50.523586Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevb.85.045104","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:55.278484Z","title":null,"venue":null,"work_id":"ff022c49-3974-447e-afe2-157bcd82a548","year":2012},"citing_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},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.565910Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:431fa137e8cb0055b0ff50a942c7da19485c509a2e542a594dfdabf09e404f79","observation_id":"9cf98769-8374-4269-b11f-c0ba07c8976b","resolution":{"observed_at":"2026-08-06T18:49:55.312777Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:50.597610Z","title":"Levin and Z.-C","venue":null,"work_id":null,"year":2012},"citing_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},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.597610Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:7037745225d597c54915b1d31ce13c18e2b5ac492c69cbe715cc27e040ff180a","observation_id":"87d5f23e-049a-4ecd-a940-0bc8f9c2e809","resolution":{"observed_at":"2026-08-06T18:49:50.597610Z","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":"2026-08-06T18:49:50.641013Z","title":"Chen, Z.-C","venue":null,"work_id":null,"year":2013},"citing_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},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.641013Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:5dc7c5efa85b6e875d64a2169ae0c104a6ca2f483053742ed48778266bfcce00","observation_id":"03fa992d-4160-4255-8c92-bb0280eb4e41","resolution":{"observed_at":"2026-08-06T18:49:50.641013Z","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":"2026-08-06T18:49:50.675639Z","title":"Vishwanath and T","venue":null,"work_id":null,"year":2013},"citing_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},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.675639Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:ef56555b8f6297a4602fd0a075db2cad44f198e1671ce90a53b2ea902a1e308a","observation_id":"2b6b42f0-d015-43f7-b28b-1ad3332c1152","resolution":{"observed_at":"2026-08-06T18:49:50.675639Z","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":"2026-08-06T18:49:50.704166Z","title":null,"venue":null,"work_id":null,"year":2013},"citing_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},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.704166Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:1dd3f8e6c63e33f0ec4750a28d3b6afc347fbef7cf67e25b6bf915e4914249dc","observation_id":"540c44f0-8383-4918-b10e-713ceaa903f8","resolution":{"observed_at":"2026-08-06T18:49:50.704166Z","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":"2026-08-06T18:49:50.743940Z","title":"Chen, Z.-C","venue":null,"work_id":null,"year":2011},"citing_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},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.743940Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:aca5dc6edf15e9142b5676337026dc1c2f353c7ae010f12736684d43bf7616e8","observation_id":"cf734c82-541c-402e-9f67-aa3fa7f706b9","resolution":{"observed_at":"2026-08-06T18:49:50.743940Z","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":"2026-08-06T18:49:50.779924Z","title":"Schuch, D","venue":null,"work_id":null,"year":2011},"citing_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},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.779924Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:c6d773f8fca6212058e26ebd701da3e25a6fab10028886a2d7a876c78c2fde2f","observation_id":"c64b1a8a-b689-4b34-bead-64a9e07c3372","resolution":{"observed_at":"2026-08-06T18:49:50.779924Z","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":"2026-08-06T18:49:50.814732Z","title":"Pollmann, E","venue":null,"work_id":null,"year":2012},"citing_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},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.814732Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:724650436f94e13edae148cb4cbda42748d5fcc18ad300ce6113d395153a1ae8","observation_id":"44883e40-77ee-4392-b49a-8c55ba387aee","resolution":{"observed_at":"2026-08-06T18:49:50.814732Z","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":"2026-08-06T18:49:50.859755Z","title":"Kapustin and R","venue":null,"work_id":null,"year":2014},"citing_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},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.859755Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:8e7d3fac355475bfbd2b72a0f138355d27030ba481eff272ded21a0a0ba68c27","observation_id":"ca5cc340-9f8f-4ab6-afdb-32f3e8b6c303","resolution":{"observed_at":"2026-08-06T18:49:50.859755Z","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":"2026-08-06T18:49:50.891349Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_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},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.891349Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:5359d0712923b7bef98a6d99dfaee9743eff9760ff09bf11026231f178c60383","observation_id":"b96647e8-1471-4de3-9b50-3c37f31b9f10","resolution":{"observed_at":"2026-08-06T18:49:50.891349Z","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":"2026-08-06T18:49:50.938348Z","title":"Chen, Z.-X","venue":null,"work_id":null,"year":2011},"citing_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},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.938348Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:a99cba68d236484e096d12b6468db893bcfccd328021488b507b1d983c483a63","observation_id":"71b6efcf-6b7d-42e8-9899-251d41fc2709","resolution":{"observed_at":"2026-08-06T18:49:50.938348Z","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":"10.1103/physrevb.104.115156","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:55.081243Z","title":"Kawagoe and M","venue":null,"work_id":"a7bd0146-0765-48fc-89a7-d93aab81b519","year":2021},"citing_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},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:50.982901Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:430d6056d74c82623f7081fb8fc6bd10c26f5f86da008c94d20f07efed6752c8","observation_id":"2632b76b-f6fe-42c5-93ea-44965f645e3e","resolution":{"observed_at":"2026-08-06T18:49:55.125768Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:51.028455Z","title":"Seifnashri, Lieb-schultz-mattis anomalies as obstructions to gauging (non-on-site) symmetries, SciPost Physics 16(4) (2024), doi:10.21468/scipostphys.16.4.098","venue":null,"work_id":null,"year":2024},"citing_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},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.028455Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:35a53a66cd3692df2c3ad410935519840056b9cf657a2c99c017af95c10252de","observation_id":"0a828b5e-0adc-46ac-b2d2-5705e0ec8252","resolution":{"observed_at":"2026-08-06T18:49:51.028455Z","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":"10.1103/physrevb.88.075125","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.954673Z","title":null,"venue":null,"work_id":"52400399-37bf-4cd0-b7ad-c8aea2583d55","year":2013},"citing_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},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.044612Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:72c6999140212fcca6cb37643f04c99654d7d93de2fcafea2394d7527e61da66","observation_id":"564ce089-2718-4d3c-bdb6-293ecff8501e","resolution":{"observed_at":"2026-08-06T18:49:54.988670Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevlett.120.156601","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.873103Z","title":"Bultinck, R","venue":null,"work_id":"c8dd5a3c-1b0e-4555-8485-0ea022ac61c8","year":2018},"citing_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},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.064831Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:73ce3b08241b86d61ea512cde3c75d7a7a7e7628b6158beb13d1212cb9128a5a","observation_id":"2cfbecd4-aaa6-4bc0-9092-70e9e75ef73e","resolution":{"observed_at":"2026-08-06T18:49:54.904124Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:51.122712Z","title":"Tiwari, X","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.122712Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:8dae98856d96e3cd37ea9fc1427a08928bcea125f14145b34f6d713ff0b58db2","observation_id":"e396bf9e-bb9c-44c2-8923-050331d1c708","resolution":{"observed_at":"2026-08-06T18:49:51.122712Z","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":"10.1103/physrevd.103.125001","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.785272Z","title":"Lin and S.-H","venue":null,"work_id":"d4120154-be4e-4a1e-9d9f-c6032174c405","year":2021},"citing_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},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.188410Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:75d06e1caf606d671e2c0cf8d6bc008e8f5861ebf15474cadcf6fe9ca26fc7aa","observation_id":"1edda9a2-56ec-496d-82bd-42989d5395e8","resolution":{"observed_at":"2026-08-06T18:49:54.814334Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.1103/physrevb.90.165134","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.706039Z","title":"Hsieh, O","venue":null,"work_id":"8c3af3af-4b67-41d7-896e-ba352cab31f6","year":2014},"citing_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},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.233369Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:16f824d951e93863cff75bae61f8799a11a73188e367edd404c79b37f125d488","observation_id":"c7741f7f-fd01-4435-8600-a99bcadbe751","resolution":{"observed_at":"2026-08-06T18:49:54.729535Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":"10.48550/arxiv.2412.01886","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.619074Z","title":"Kobayashi, Y","venue":null,"work_id":"bbd0dca8-dad5-4da9-9e22-4b427e189536","year":2025},"citing_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},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.289924Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:ce414f44c3ea0754f4a26bea85d210899cdbe69f1056d7cd17298eb6f8494f31","observation_id":"3b6e5038-2d5e-4b44-8f09-43f2842cc1b1","resolution":{"observed_at":"2026-08-06T18:49:54.651312Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:51.366100Z","title":"Seifnashri and W","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.366100Z"},"links":{"cited_paper":"/paper/2503.09717","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:134b40bbbdfe24d9dc22bc6526be89955197add1c0000007c24a60a4cba5784f","observation_id":"bc170b93-7833-4caf-a3e5-3620f82ca287","resolution":{"observed_at":"2026-08-06T18:49:51.366100Z","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":"2026-08-06T18:49:51.431333Z","title":"Gross, V","venue":null,"work_id":null,"year":2012},"citing_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},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.431333Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:c7f3376bc88494b6bca552272ed7c25f13c2b5ddb02af8b2fdb4cc0ba3105a73","observation_id":"8ae1d4a4-92fe-4ded-8237-8babfb1a146b","resolution":{"observed_at":"2026-08-06T18:49:51.431333Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"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":"2026-08-06T18:49:51.475783Z","title":"Kapustin, Higher symmetries and anomalies in quantum lattice systems , doi:10.48550/arXiv.2505.04719 (2025), 2505.04719","venue":null,"work_id":null,"year":2025},"citing_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},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.475783Z"},"links":{"cited_paper":"/paper/2505.04719","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:1d78267f99ec60f68efd8968f4403955d6d834d23d4d3f0ef7721af4dadcb549","observation_id":"cb774d95-1561-493d-87e4-d524e463298e","resolution":{"observed_at":"2026-08-06T18:49:51.475783Z","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":"2026-08-06T18:49:55.738317Z","title":"Shirley, C","venue":null,"work_id":"c27c0bb4-4ed8-4f72-a194-997ed910bf40","year":null},"citing_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},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.543994Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:587e09d5b99be9b9273b9a4413e6eff29013eea042650a801dbea3c2e82a705b","observation_id":"5a608e64-ad95-4566-bb7a-4a62bf2a2829","resolution":{"observed_at":"2026-08-06T18:49:55.770872Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:51.593968Z","title":"Farrelly, A review of quantum cellular automata , Quantum 4, 368 (2020), doi:10.22331/q-2020-11-30-368","venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.593968Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:c5cd19cbe69dadbc4356692b296aea5a4c3b0b18fa3236afef9f4982c67f2234","observation_id":"e89b748c-e092-459b-abf7-eac8584276b9","resolution":{"observed_at":"2026-08-06T18:49:51.593968Z","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":"2026-08-06T18:49:51.649269Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_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},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.649269Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:53e4b4ca8e89fcf90bfd62f24773c12ef685050b1b57b26363c4132df79438d6","observation_id":"6a181512-47a4-4518-a416-1b59f9a17200","resolution":{"observed_at":"2026-08-06T18:49:51.649269Z","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":"2026-08-06T18:49:51.695928Z","title":"Freedman and M","venue":null,"work_id":null,"year":2020},"citing_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},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.695928Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:204239d0035a4b4bef115f7fcb6aa15c7a19d4b77cacd7b5182dbd6196a3168c","observation_id":"f7c3c375-dabc-425f-ba54-3a0a48430c81","resolution":{"observed_at":"2026-08-06T18:49:51.695928Z","resolver_source":null,"status":"malformed_identifier"},"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":"2026-08-06T18:49:51.736894Z","title":null,"venue":null,"work_id":null,"year":1982},"citing_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},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.736894Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:7dedea771a942be5a5c43600ed5c4f182e62cad59fae8ebf3060392d2870057a","observation_id":"09dc798f-fc66-4535-baff-7fa9bb513aff","resolution":{"observed_at":"2026-08-06T18:49:51.736894Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0403322","last_updated":"2005-03-14T13:46:39Z","snapshot_observed_at":"2026-07-07T05:39:51.686830Z","submitted_at":"2004-03-19T14:51:27Z","title":"Conformal Orbifold Theories and Braided Crossed G-Categories","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0403322","snapshot_observed_at":"2026-08-06T18:49:51.870317Z","title":"Muger, Conformal orbifold theories and braided crossed G-categories , Com- mun","venue":null,"work_id":null,"year":2005},"citing_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},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.870317Z"},"links":{"cited_paper":"/paper/math/0403322","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:5dd6beed55c6ae7240c146fa47abd822b1dbbe53d1308f0c59be76b8de2c1817","observation_id":"a0a7b501-0266-410c-9b94-e670a3883ebf","resolution":{"observed_at":"2026-08-06T18:49:51.870317Z","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":"10.1007/s00023-022-01193-x","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.345464Z","title":"Ranard, M","venue":null,"work_id":"dc1e5cb3-1e9d-4dd6-8074-08fbc11c7d39","year":2022},"citing_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},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:51.974767Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:257b5860ad5169521456ea64bd2aee90b8340392e813cdc1f8abaa0d26a3f284","observation_id":"1ada0cb3-eef6-4d95-9255-c1021e8aad6e","resolution":{"observed_at":"2026-08-06T18:49:54.397641Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:55.652993Z","title":"Kitaev, Toward topological classification of phases with short-range entanglement , Lecture at KITP (2011), doi:https://online.kitp.ucsb.edu/online/topomat11/kitaev","venue":null,"work_id":"3759d1c6-06c7-4ee4-9539-90c8bb840b78","year":2011},"citing_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},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.080590Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:4f52a02f3b06c7a9dfa24adea1ec0dfc0f622e0f2fa6c9f59b6832e232b0e47e","observation_id":"36682bc3-87d7-41bd-bab8-45f2fe1a0f9c","resolution":{"observed_at":"2026-08-06T18:49:55.688494Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:55.572872Z","title":"Kitaev, On the classification of short-range entangled states , Lecture at SCGP (2013), doi:http://scgp.stonybrook.edu/archives/7874","venue":null,"work_id":"d9fd57cb-6d34-4b5f-a07c-f1e51374275a","year":2013},"citing_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},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.218886Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:2f6a21bcafddfaad5376f19f73699b9f3afb678ed8a44cbaed8b6269c1084931","observation_id":"b3c0ed59-ecba-4738-9202-6d556276bf7a","resolution":{"observed_at":"2026-08-06T18:49:55.608401Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:52.321516Z","title":"Chen, Z.-C","venue":null,"work_id":null,"year":2010},"citing_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},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.321516Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:26d6d80dcee1176a396dc1b5c32eb61caa72925cc72f36720e5533a835604a85","observation_id":"040a9829-85a2-4ab5-ae0d-239bdca8b80c","resolution":{"observed_at":"2026-08-06T18:49:52.321516Z","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":"2026-08-06T18:49:52.450973Z","title":"Kapustin, N","venue":null,"work_id":null,"year":2021},"citing_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},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.450973Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:2d7118b5435fea7b79ce7cf8e4a6c2e6c2e7fc17cd9ef6829c6fc197fa42541b","observation_id":"46bed41f-ca0d-481d-a3dc-09153d45e20d","resolution":{"observed_at":"2026-08-06T18:49:52.450973Z","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":"2026-08-06T18:49:52.539309Z","title":null,"venue":null,"work_id":null,"year":2001},"citing_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},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.539309Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:279a9196fa0a56e8af6c51e93090c1f7e2125c8b1883a593f835f6d70509c720","observation_id":"52b810a8-3491-4abf-95da-871de096e6e6","resolution":{"observed_at":"2026-08-06T18:49:52.539309Z","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":"2026-08-06T18:49:52.573698Z","title":"Yoshida, Gapped boundaries, group cohomology and fault-tolerant logical gates , Annals of Physics 377, 387–413 (2017), doi:10.1016/j.aop.2016.12.014","venue":null,"work_id":null,"year":2017},"citing_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},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.573698Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:198b647c5830a50696b0089ce10f8dc94fd2e6068b33e75ff4d60f157138d069","observation_id":"2465fc60-77ef-4d31-871d-9b1fa016cdde","resolution":{"observed_at":"2026-08-06T18:49:52.573698Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9511195","last_updated":"1995-11-27T20:08:59Z","snapshot_observed_at":"2026-08-02T23:11:11.790468Z","submitted_at":"1995-11-27T20:08:59Z","title":"Topological interactions in broken gauge theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9511195","snapshot_observed_at":"2026-08-06T18:49:52.624763Z","title":"de Wild Propitius, Topological interactions in broken gauge theories , doi:10.48550/arXiv.hep-th/9511195 (1995), hep-th/9511195","venue":null,"work_id":null,"year":1995},"citing_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},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.624763Z"},"links":{"cited_paper":"/paper/hep-th/9511195","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:07ac9b8b5426f34d1c127fa70c9bdde4a2a3408792825e5299afc26dcc0a3548","observation_id":"21315ff7-0787-40e6-abd4-9858b3cf2364","resolution":{"observed_at":"2026-08-06T18:49:52.624763Z","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":"10.1103/physrevb.91.165119","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:54.116605Z","title":"Wang and M","venue":null,"work_id":"b0ee54d7-06ba-481a-a4d8-84728e3a8717","year":2015},"citing_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},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.699161Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:a84a1632a20aa1c80693b64ff8e99117b398768c84b8bf921b915e7c507766aa","observation_id":"168e89bf-def8-43e3-b345-cc8a25664563","resolution":{"observed_at":"2026-08-06T18:49:54.221381Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:52.757437Z","title":"Chen, Y.-M","venue":null,"work_id":null,"year":2014},"citing_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},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.757437Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:d5d7c7d3645a80c70a1c1a392c55a7f2afe23e2c0988162adf8cec930c09b0ac","observation_id":"80519122-028d-47a4-bcd6-e9be679cfb6c","resolution":{"observed_at":"2026-08-06T18:49:52.757437Z","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":"10.48550/arxiv.2408.00825","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:53.893502Z","title":null,"venue":null,"work_id":"31ee24b6-f3e7-4dbe-a2a2-d404836dfefa","year":2024},"citing_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},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.868785Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:7a4fc3f1f5fba61517f3dbd18cf0f4fcd3eff02cc60d5415bc5b570b4c28d251","observation_id":"5f4b1bee-bf7c-49da-98cc-245f94b3afbd","resolution":{"observed_at":"2026-08-06T18:49:53.972921Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:52.971799Z","title":"Gaiotto and T","venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:52.971799Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:e778ce100f578bda4bf81a9de234a6ddd5d27e6088a1bb07857f4259931d0d4a","observation_id":"2a5cbb72-4a98-49ae-b9b3-60880c0c7a85","resolution":{"observed_at":"2026-08-06T18:49:52.971799Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1902.05957","last_updated":"2019-02-15T19:00:03Z","snapshot_observed_at":"2026-07-06T07:33:25.489427Z","submitted_at":"2019-02-15T19:00:03Z","title":"1d lattice models for the boundary of 2d \"Majorana\" fermion SPTs: Kramers-Wannier duality as an exact $Z_2$ symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1902.05957","snapshot_observed_at":"2026-08-06T18:49:53.030654Z","title":"majorana","venue":null,"work_id":null,"year":2019},"citing_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},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.030654Z"},"links":{"cited_paper":"/paper/1902.05957","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:a37708a52a4cc11566d47a8c09dd8fc166d3b2ab87362bd2c0b1980fb41ca151","observation_id":"0a372f23-3f99-4b86-ba3e-12c01967c00f","resolution":{"observed_at":"2026-08-06T18:49:53.030654Z","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":"2026-08-06T18:49:53.095077Z","title":"Gaiotto, A","venue":null,"work_id":null,"year":2015},"citing_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},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.095077Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:be9217f9ddd16e5eb1cdca622dc8144901e5707f41b40260337e8144877f7810","observation_id":"ce902658-5410-414d-b6cf-f884b257e298","resolution":{"observed_at":"2026-08-06T18:49:53.095077Z","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":"2026-08-06T18:49:53.156591Z","title":"McGreevy, Generalized symmetries in condensed matter , Annual Review of Condensed Matter Physics 14(1), 57–82 (2023), doi:10.1146/annurev-conmatphys- 040721-021029","venue":null,"work_id":null,"year":2023},"citing_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},"reference_index":51,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.156591Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:1811f8fe1aa00213d4ae9e3655ee29e6a7cd5e2014e6190416beb5f7d9aa9d8c","observation_id":"7d5ddf1f-084f-46d0-9530-35b11b62d221","resolution":{"observed_at":"2026-08-06T18:49:53.156591Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.09545","last_updated":"2022-05-19T13:15:29Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2022-05-19T13:15:29Z","title":"Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.09545","snapshot_observed_at":"2026-08-06T18:49:53.199126Z","title":"Cordova, T","venue":null,"work_id":null,"year":2022},"citing_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},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.199126Z"},"links":{"cited_paper":"/paper/2205.09545","citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:b3e1342623064d5750495b0bfbb7fbed4b8b9fe4200dd613b8cb5be8f831e40c","observation_id":"c080ddbe-bccc-4ef9-90dc-1ea4cbf76c32","resolution":{"observed_at":"2026-08-06T18:49:53.199126Z","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":"2026-08-06T18:49:53.286791Z","title":"Khalaf, H","venue":null,"work_id":null,"year":2018},"citing_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},"reference_index":53,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.286791Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:3b4ce6301f789276feff2bb13a075f9ac33fc5cc6cec8a6bdd27acaaf4319c11","observation_id":"5507af84-9eb0-4378-a819-732d6b96b3eb","resolution":{"observed_at":"2026-08-06T18:49:53.286791Z","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":"10.1103/physrevx.7.011020","metadata_source":"doi_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T18:49:53.569711Z","title":"Song, S.-J","venue":null,"work_id":"62554388-a1f5-4393-8c36-b30c12882126","year":2017},"citing_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},"reference_index":54,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.401179Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:e17dcf19a00fc40987f6168f308093f9acf4522cd2ddd2c1de5acca7298e2764","observation_id":"570e8a31-2bdf-478c-adde-b594cc329d91","resolution":{"observed_at":"2026-08-06T18:49:53.647095Z","resolver_source":"doi","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+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":"2026-08-06T18:49:55.489801Z","title":null,"venue":null,"work_id":"62603e86-5aad-4968-a9ff-2052ae165ba1","year":null},"citing_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},"reference_index":55,"source":"pdf_text","source_observed_at":"2026-08-06T18:49:53.489966Z"},"links":{"citing_paper":"/paper/2507.07430"},"observation_digest":"sha256:fcec0ce060e94900f861535f81406286967a4ef5eef4af9968c22ef4548ecbb5","observation_id":"eacb01c4-038a-42b7-80ce-6ad0722d5cf6","resolution":{"observed_at":"2026-08-06T18:49:55.524900Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2507.07430","last_updated":"2025-07-14T19:33:05Z","latest_version":2,"primary_category":"cond-mat.str-el","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"},"reference_resolution":{"displayed":55,"state_counts":{"malformed_identifier":3,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":11,"verified_fuzzy":3},"total_outbound_references":55},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 13 inbound Pith citation observations for arXiv:2507.07430."}