{"as_of":"2026-08-16T17:28:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a1668c88389f8c6825462b9b1e0c57c93bd640100f045a030beeb852816e0a42","coverage":[{"denominator":0,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":9,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":9,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-16T06:30:59.297886+00:00","state":"measured"},{"denominator":9,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T19:47:17.938067Z","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":"2026-05-19T03:13:14.184513Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-12T20:28:56.092298Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.09685","last_updated":"2025-04-16T19:43:02Z","snapshot_observed_at":"2026-08-13T00:57:54.184459Z","submitted_at":"2024-11-14T18:52:31Z","title":"The Higher Structure of Symmetries of Axion-Maxwell Theory","version":2},"reference_index":121,"source":"pdf_text","source_observed_at":"2026-08-12T20:28:56.092298Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2411.09685"},"observation_digest":"sha256:ee03b358399acf8ff90e0a88d8521f326395a94d818630f3df7e0c6e22d00999","observation_id":"e37dec30-bd2e-4c21-b88e-b45df7551abc","resolution":{"observed_at":"2026-08-12T20:28:56.092298Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-12T11:41:19.533655Z","title":"Putrov and R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2411.18056","last_updated":"2025-03-17T00:31:30Z","snapshot_observed_at":"2026-08-16T01:16:03.229875Z","submitted_at":"2024-11-27T05:05:55Z","title":"SymTFT Approach to 2D Orbifold Groupoids: `t Hooft Anomalies, Gauging, and Partition Functions","version":2},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-12T11:41:19.533655Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2411.18056"},"observation_digest":"sha256:f7cfdf5e34f6049a010dce3772a38982ad91bb8f8d0b9dbd2c5d31ca50f96f21","observation_id":"43198604-6f74-4829-9637-f48abf1773d0","resolution":{"observed_at":"2026-08-12T11:41:19.533655Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-10T20:40:50.175763Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs,","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.07787","last_updated":"2025-01-14T02:05:45Z","snapshot_observed_at":"2026-08-10T22:56:41.547558Z","submitted_at":"2025-01-14T02:05:45Z","title":"SymSETs and self-dualities under gauging non-invertible symmetries","version":1},"reference_index":65,"source":"pdf_text","source_observed_at":"2026-08-10T20:40:50.175763Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2501.07787"},"observation_digest":"sha256:04f67481d8e86741fa6f8f038b7b00a91370a1b132377695bc96ddb1c3e5ff16","observation_id":"8a0765fc-5e38-4638-87fd-37df2fa556cb","resolution":{"observed_at":"2026-08-10T20:40:50.175763Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-15T19:47:17.938067Z","title":"Putrov and R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2506.15158","last_updated":"2025-07-23T05:15:26Z","snapshot_observed_at":"2026-08-16T13:59:26.643754Z","submitted_at":"2025-06-18T06:02:38Z","title":"ADE triality via (non-)invertible symmetry gauging","version":2},"reference_index":75,"source":"pdf_text","source_observed_at":"2026-08-15T19:47:17.938067Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2506.15158"},"observation_digest":"sha256:6a93eb18df14ce1307c308f2930d800a37cd9a5267a9e92ea2192e4f6b5bc44c","observation_id":"d4cbe559-563e-4788-825c-463798a7f363","resolution":{"observed_at":"2026-08-15T19:47:17.938067Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-06T21:09:17.763956Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.01142","last_updated":"2025-07-01T19:00:39Z","snapshot_observed_at":"2026-08-13T08:06:39.024636Z","submitted_at":"2025-07-01T19:00:39Z","title":"Gauging Non-Invertible Symmetries in (2+1)d Topological Orders","version":1},"reference_index":105,"source":"pdf_text","source_observed_at":"2026-08-06T21:09:17.763956Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2507.01142"},"observation_digest":"sha256:71038696fdf17e1ef59692b768a2c1e7ce10d695851e494416c0b9d89c6b0fc0","observation_id":"ff65fb03-a72d-46cf-bf3a-709784bfe9d1","resolution":{"observed_at":"2026-08-06T21:09:17.763956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-15T16:39:36.608522Z","title":"Putrov and R","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2509.04581","last_updated":"2026-06-02T07:23:48Z","snapshot_observed_at":"2026-08-16T17:09:15.982512Z","submitted_at":"2025-09-04T18:03:57Z","title":"Symmetric entanglers for non-invertible SPT phases","version":3},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-15T16:39:36.608522Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2509.04581"},"observation_digest":"sha256:e8b8ccb2ae3f56852a91ff2ea35c2cde2c5fd6c99d51256ce1b7d2be1e4192e7","observation_id":"2dbcecdc-c3a9-4e8c-b500-6054623dd0e7","resolution":{"observed_at":"2026-08-15T16:39:36.608522Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-08-05T05:32:59.961861Z","title":"Putrov and R","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.05408","last_updated":"2026-07-14T04:31:00Z","snapshot_observed_at":"2026-08-16T16:11:59.871383Z","submitted_at":"2025-09-05T18:00:02Z","title":"SymTFT actions, Condensable algebras and Categorical anomaly resolutions","version":3},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-08-05T05:32:59.961861Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2509.05408"},"observation_digest":"sha256:78bd6323a147ef4fd5757b35b12cfe1de157f631ca395bd56f7feb22e5ef1f9c","observation_id":"6df7e7c0-fbc1-4a60-b096-75a24dd75169","resolution":{"observed_at":"2026-08-05T05:32:59.961861Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":"2405.04619","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Non- anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","venue":null,"work_id":"1cf74b3b-e99e-4ff2-bfb2-0e6390172b0e","year":2026},"citing_paper":{"arxiv_id":"2602.11696","last_updated":"2026-04-07T06:24:20Z","snapshot_observed_at":"2026-08-11T02:07:07.982426Z","submitted_at":"2026-02-12T08:22:02Z","title":"Symmetry Spans and Enforced Gaplessness","version":2},"reference_index":52,"source":"pdf_text","source_observed_at":"2026-05-16T03:25:08.257953Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2602.11696"},"observation_digest":"sha256:02fa1ae0dfdf6394a35f4ed39d67f3f7a4ecdc66f38147470fb09b0d055564a8","observation_id":"c6f8e411-fde2-4fd7-9756-d5857976cbd0","resolution":{"observed_at":"2026-05-16T03:27:13.094959Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","version":1},"cited_work":{"arxiv_id":"2405.04619","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2405.04619","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Non- anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs","venue":null,"work_id":"1cf74b3b-e99e-4ff2-bfb2-0e6390172b0e","year":2026},"citing_paper":{"arxiv_id":"2605.15194","last_updated":"2026-05-14T17:59:45Z","snapshot_observed_at":"2026-08-12T13:36:57.077289Z","submitted_at":"2026-05-14T17:59:45Z","title":"Non-Invertible Symmetries on Tensor-Product Hilbert Spaces and Quantum Cellular Automata","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-05-15T02:51:36.560672Z"},"links":{"cited_paper":"/paper/2405.04619","citing_paper":"/paper/2605.15194"},"observation_digest":"sha256:bd3b8433e6e3a7c9b4e5510cfe640416f567b0b949b7b7b63d9bf5278b74a873","observation_id":"b52f08a3-f442-468c-9a3a-b4ce30d419d9","resolution":{"observed_at":"2026-05-15T02:53:33.667478Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2405.04619/citation-record","integrity":"/paper/2405.04619/integrity","json":"/paper/2405.04619/citation-record.json","paper":"/paper/2405.04619"},"outbound":[],"paper":{"arxiv_id":"2405.04619","last_updated":"2024-05-07T19:05:07Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-16T13:54:33.923439Z","submitted_at":"2024-05-07T19:05:07Z","title":"Non-anomalous non-invertible symmetries in 1+1D from gapped boundaries of SymTFTs"},"reference_resolution":{"displayed":0,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":0},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-16T06:30:59.297886+00:00","source":"crossref"},{"observed_at":"2026-08-16T06:30:54.164669+00:00","source":"retraction_watch"}],"thesis":"As of 16 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 9 inbound Pith citation observations for arXiv:2405.04619."}