{"as_of":"2026-08-22T20:11:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:8f2bc570820365087e41f85f0b0ba31a193b7f0cce4b5e92fda530f03d7bf837","coverage":[{"denominator":16,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":16,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-14T14:55:03.853703Z","state":"measured"},{"denominator":23,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":23,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-22T06:32:14.747728+00:00","state":"measured"},{"denominator":7,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":7,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T13:57:59.379600Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"arxiv_reference","source_observed_at":"2026-05-18T03:20:48.968545Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-08-12T13:57:59.379600Z","title":"Tsui and X.-G","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2411.15848","last_updated":"2025-06-27T13:01:13Z","snapshot_observed_at":"2026-08-18T03:21:29.775034Z","submitted_at":"2024-11-24T14:01:37Z","title":"Classifying Logical Gates in Quantum Codes via Cohomology Operations and Symmetry","version":3},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-08-12T13:57:59.379600Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2411.15848"},"observation_digest":"sha256:6e5e4c4611a30c143536891f44086e0f7be35efe59ec9c9c657c5ce3480888cc","observation_id":"24ab2e2f-2383-4794-9bed-8f729f9bdf58","resolution":{"observed_at":"2026-08-12T13:57:59.379600Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-08-07T05:43:06.367123Z","title":"Lattice models that realize Zn-1 symmetry-protected topological states for even n,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2506.07688","last_updated":"2025-06-09T12:20:01Z","snapshot_observed_at":"2026-08-10T04:19:57.965020Z","submitted_at":"2025-06-09T12:20:01Z","title":"Generalized Symmetries Phase Transitions with Local Quantum Fields","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-07T05:43:06.367123Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2506.07688"},"observation_digest":"sha256:47b6302ae3d8240260c8d4fcda748086c9933f02d1278d4654ed2a40e7a10740","observation_id":"83ef0fc0-1eee-435a-b01a-2872ae8d206d","resolution":{"observed_at":"2026-08-07T05:43:06.367123Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":"1908.02613","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lattice models that realizeZ n-1 symmetry-protected topological states for evenn","venue":null,"work_id":"278d9c9f-7705-4aa3-88ec-6d39ce906ff9","year":2020},"citing_paper":{"arxiv_id":"2510.23701","last_updated":"2025-10-27T18:00:00Z","snapshot_observed_at":"2026-08-15T18:47:06.541211Z","submitted_at":"2025-10-27T18:00:00Z","title":"Onsiteability of Higher-Form Symmetries","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-05-18T03:18:47.456335Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2510.23701"},"observation_digest":"sha256:0c6b4852d7d3fcbcb25bf6a66a94ef1a33bbe5280872b4982bad57360c5b3576","observation_id":"f5dfdbe3-c02a-474d-89ed-643b80eac5e9","resolution":{"observed_at":"2026-05-18T03:20:48.971914Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":"1908.02613","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Lattice models that realizeZ n-1 symmetry-protected topological states for evenn","venue":null,"work_id":"278d9c9f-7705-4aa3-88ec-6d39ce906ff9","year":2020},"citing_paper":{"arxiv_id":"2511.15783","last_updated":"2026-05-11T09:13:04Z","snapshot_observed_at":"2026-08-10T22:33:09.025950Z","submitted_at":"2025-11-19T19:00:00Z","title":"Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-05-17T20:18:27.901205Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2511.15783"},"observation_digest":"sha256:05b8499c61b8ea9c24d11eeac258dee794f566a41abc8645de2b5773dd037bf6","observation_id":"606e0b52-3f5c-499f-9881-274529634e9a","resolution":{"observed_at":"2026-05-17T20:20:11.653100Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-08-01T07:04:52.505379Z","title":"Lattice models that realize Zn-1 symmetry-protected topological states for evenn,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21698","last_updated":"2026-07-31T14:13:23Z","snapshot_observed_at":"2026-08-20T14:17:26.525097Z","submitted_at":"2026-07-23T18:00:00Z","title":"Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-01T07:04:52.505379Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2607.21698"},"observation_digest":"sha256:076c0763eb96576136fb9df9127956cd6ad9c30ee7d0d6e660ccd9b8a8579b34","observation_id":"a7a04d04-c695-47ff-9c9d-61eaeddb4f0a","resolution":{"observed_at":"2026-08-01T07:04:52.505379Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-08-03T01:57:30.405997Z","title":"Lattice models that realize Zn-1 symmetry-protected topological states for evenn,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21698","last_updated":"2026-07-31T14:13:23Z","snapshot_observed_at":"2026-08-20T14:17:26.525097Z","submitted_at":"2026-07-23T18:00:00Z","title":"Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-08-03T01:57:30.405997Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2607.21698"},"observation_digest":"sha256:e018909181d77342a73d13f81f201d3984457e934e13ee200f0d66893bb05f80","observation_id":"147be398-e939-43c1-a0a9-870683667b8e","resolution":{"observed_at":"2026-08-03T01:57:30.405997Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1908.02613","snapshot_observed_at":"2026-08-01T06:57:48.954892Z","title":"Lattice models that realizeZ n-1 symmetry-protected topological states for evenn,","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.21728","last_updated":"2026-07-23T18:24:51Z","snapshot_observed_at":"2026-08-15T01:24:07.490361Z","submitted_at":"2026-07-23T18:24:51Z","title":"Quantum Cellular Automata from Kramers-Wannier Dualities and Modular Relations","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-01T06:57:48.954892Z"},"links":{"cited_paper":"/paper/1908.02613","citing_paper":"/paper/2607.21728"},"observation_digest":"sha256:903d5dfda19dab0282c8f11b6cd138e3c54275a3d187aebecf9c554ca05235ba","observation_id":"0e10f66b-fe0b-4747-a03e-3f271afd4f26","resolution":{"observed_at":"2026-08-01T06:57:48.954892Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/1908.02613/citation-record","integrity":"/paper/1908.02613/integrity","json":"/paper/1908.02613/citation-record.json","paper":"/paper/1908.02613"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-14T14:55:04.163049Z","title":"4a, the resulting positions of the two final anyons are exchanged in the two processes","venue":null,"work_id":"ab089b3b-b87f-47e9-b3d8-77a25d8085e3","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.774502Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:d95a7bd33dbfacaaf8c66fcc21031b0091c62c64baff4e5c38136d81d8ee4756","observation_id":"d1ec349f-bcff-407d-9b89-7a9046ee582b","resolution":{"observed_at":"2026-08-14T14:55:04.168748Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.180785Z","title":"boundary state","venue":null,"work_id":"b4f4488c-bed2-4d6f-8b76-6f65357f50cd","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.768303Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:1c955d3d45ab89ee4c706f20c1d310d256dd8bcddfb05e772c627844ce23d2d5","observation_id":"b94c1e16-c81b-452b-89c9-70bc4fec3050","resolution":{"observed_at":"2026-08-14T14:55:04.185760Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.145099Z","title":"38: The 3+1D bulk state that we have constructed is a Zn-1-SPT state labeled by m∈{ 0, 1,··· , 2n−1}, protected by an on-site (anomaly- free) Zn-1-symmetry","venue":null,"work_id":"b0b46dfa-6c7d-4365-afb0-92f1fea173a2","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.779719Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:0c61a38390ac86d4d0b9283495a8a10c40e4e977085a1c9185f07d8e7a7c5fd5","observation_id":"6ee2cee5-5f6a-47d2-b9cd-e99e794646e3","resolution":{"observed_at":"2026-08-14T14:55:04.151078Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.125317Z","title":null,"venue":null,"work_id":"a3eb6663-0604-458c-a69d-576a5d43a390","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.785360Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:5a465e7d0625292122dfb45c0d8d90f790abfc663b8265fca77af6492625f2d9","observation_id":"f7a126cc-0f23-4ab7-9059-d6416436404f","resolution":{"observed_at":"2026-08-14T14:55:04.130857Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.105703Z","title":null,"venue":null,"work_id":"6798d35f-44a8-426c-84e9-f7a46d514b5e","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.791299Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:9769d8dd0ae7546d7943eb8a996c423998bc52b41346f5e39a290ac81823a702","observation_id":"b6ae61cf-8b78-4284-ae23-46d8c171be23","resolution":{"observed_at":"2026-08-14T14:55:04.111692Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.086386Z","title":null,"venue":null,"work_id":"87c5f477-fa05-47b7-a643-2b1f994c3fa6","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.796922Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:1be13570b6868ddef484afde1441e6e4438a2c57380ec6ab624612b80b21c269","observation_id":"dacd6f47-e143-4587-87bb-e4961441a1a3","resolution":{"observed_at":"2026-08-14T14:55:04.092496Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.067500Z","title":"S-structure","venue":null,"work_id":"ce17dc7f-f583-4046-bffe-c1e69b296c57","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.802546Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:ec35f6f40b2e6b389725317a0d3fc081f5f1ac07c167854b1b1ddff28c3bd131","observation_id":"4a757e40-041e-41bb-a48f-b0bdb5c5767d","resolution":{"observed_at":"2026-08-14T14:55:04.073287Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.049498Z","title":"no-crossing","venue":null,"work_id":"ae1b45ae-1663-4587-9c41-a83e9b170edd","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.807792Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:86aec2a7526345e2852c70e34bcca14a1b3dfb14af0971ced73c015953560e79","observation_id":"29db271b-3507-4113-84ea-14690d3e6177","resolution":{"observed_at":"2026-08-14T14:55:04.055018Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.031198Z","title":"quotient- remainder","venue":null,"work_id":"8e266028-1d22-447c-85dc-dc385bb26176","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.812943Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:c3afef36473c426988fcc5dce23ab5092ab68c2ccef132d73499a382fe5b3173","observation_id":"e5c26478-2fa5-4b45-8629-c87319e53162","resolution":{"observed_at":"2026-08-14T14:55:04.037008Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:04.011350Z","title":"The space-time has boundaries at t = 0,T , where the field configurations are given by{a0} and{aT}","venue":null,"work_id":"672ee6c6-2373-4c84-9c71-add6e328ef37","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.819538Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:3f2a5dced009e8702554ad54bd470ee1728558d59e1f0243d8ea00430fe3b9f6","observation_id":"533296b4-2f3e-40b2-bff6-0c421ff9dbc7","resolution":{"observed_at":"2026-08-14T14:55:04.017945Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:03.988747Z","title":"In order to define the transfer ma- trix, we need to specify the background gauge field ˆB on the spacetime M3×I","venue":null,"work_id":"4e4a2824-d27b-469f-b1d5-e57dad9d0e2e","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.825512Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:0e457a0edb03c02f4de8c55a33cf70d3160d33e3214a1f6b37614686a9cadc6a","observation_id":"1105ce75-5c44-4c07-bab2-9bdf1acdcb1a","resolution":{"observed_at":"2026-08-14T14:55:03.995660Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:03.969780Z","title":"Define|ψ0⟩ = 1 Nψ ∑ {a} e2πi ∫ M3φ3[a]|{a}⟩ with normal- ization Nψ = √ nNl,M3","venue":null,"work_id":"021bd490-6e9a-47e3-bf7e-536fbf8313d9","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.831018Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:70774a3a3db5a5eda714b2dea63b4fba82ed5486320a6185e02317c9abb4bcf1","observation_id":"e718b735-da48-4384-9508-d19fdb08cbe7","resolution":{"observed_at":"2026-08-14T14:55:03.975647Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:03.948746Z","title":null,"venue":null,"work_id":"d530ed96-3316-4826-9f51-e4606fca7457","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.836318Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:faf519d1d678660b5275485644c0224016c5ce658e70e1cb652ef12c902518bc","observation_id":"5e029b91-c726-44c3-ad9d-627c2c40aa1c","resolution":{"observed_at":"2026-08-14T14:55:03.954670Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:03.929593Z","title":"⃗ rij = ⃗ n+ ˆα 2 denote the mid-point of ij = (⃗0, ˆα)⃗ n, ⃗1 2 := ( 1 2, 1 2, 1 2), and Fβγ(⃗ r) := daZn(⃗0, ˆβ, ˆβ + ˆγ)⃗ r− ˆβ 2− ˆγ 2 − (β↔γ)","venue":null,"work_id":"fc550480-780b-4422-ab95-6aa5df7a8769","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.841571Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:c23836f6fcfdefa0f9211dfba94f6ac33539ef3adff952ecf05988f700c01446","observation_id":"5457c734-6cd9-4b7e-b2dd-f605390107f7","resolution":{"observed_at":"2026-08-14T14:55:03.935672Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+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":"2026-08-14T14:55:03.909883Z","title":"reference","venue":null,"work_id":"fc1a1a49-e248-475e-9946-ab5d1ffdd631","year":null},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.847857Z"},"links":{"citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:47f0f269ad1844e0dd22a34b85b93ae21728c485bb0041afa90710fea15c614c","observation_id":"921e55c9-e7a0-4de9-bbe2-32652185ff3c","resolution":{"observed_at":"2026-08-14T14:55:03.916658Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"0903.1069","last_updated":"2009-03-08T17:46:52Z","snapshot_observed_at":"2026-08-15T15:05:00.024487Z","submitted_at":"2009-03-05T20:11:33Z","title":"Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0903.1069","snapshot_observed_at":"2026-08-14T14:55:03.853703Z","title":"symmetry twist","venue":null,"work_id":null,"year":1989},"citing_paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-14T14:55:03.853703Z"},"links":{"cited_paper":"/paper/0903.1069","citing_paper":"/paper/1908.02613"},"observation_digest":"sha256:deb36013669eaa9fc46136e433e43851643b4d424e2227b298f3d49146b86533","observation_id":"2624a3ab-b21a-4c1e-8652-46b7394ad3dc","resolution":{"observed_at":"2026-08-14T14:55:03.853703Z","resolver_source":null,"status":"malformed_identifier"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"1908.02613","last_updated":"2020-01-08T06:51:33Z","latest_version":2,"primary_category":"cond-mat.str-el","snapshot_observed_at":"2026-08-17T11:34:59.740206Z","submitted_at":"2019-08-06T17:59:14Z","title":"Lattice models that realize $\\mathbb{Z}_n$-1-symmetry protected topological states for even $n$"},"reference_resolution":{"displayed":16,"state_counts":{"malformed_identifier":1,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":4,"verified_exact":0,"verified_fuzzy":11},"total_outbound_references":16},"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":"2026-08-22T06:32:14.747728+00:00","source":"crossref"},{"observed_at":"2026-08-22T06:32:06.552537+00:00","source":"retraction_watch"}],"thesis":"As of 22 August 2026, this Paper Citation Record lists 16 of 16 outbound references and 7 inbound Pith citation observations for arXiv:1908.02613."}