{"as_of":"2026-08-10T12:38:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:30cf3fc1dcfde87de054bf34b45d8228d0c9034c6379cdec4908089199abbf80","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":"2026-08-10T06:31:04.303077+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":"2026-08-07T05:43:06.347201Z","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":"2026-07-02T13:57:00.234251Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-08-07T05:43:06.347201Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories,","venue":null,"work_id":null,"year":null},"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":15,"source":"pdf_text","source_observed_at":"2026-08-07T05:43:06.347201Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2506.07688"},"observation_digest":"sha256:60f400f4640ad25841fcceb9be8429832d4e8d544dfe26bb275c440d7722dff7","observation_id":"5e7e185f-38ae-487c-9e47-923963b27ca1","resolution":{"observed_at":"2026-08-07T05:43:06.347201Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2511.15783","last_updated":"2026-05-11T09:13:04Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2025-11-19T19:00:00Z","title":"Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-17T20:18:27.901205Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2511.15783"},"observation_digest":"sha256:baad1684d8b339ff94da687e078cee838e640fe9b8ff75bd7fc9cc35385ec4b9","observation_id":"86ca2ea4-fdbc-473a-be7d-0323f16425fe","resolution":{"observed_at":"2026-05-17T20:20:11.625688Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2603.12323","last_updated":"2026-04-20T21:42:38Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2026-03-12T18:00:02Z","title":"On the SymTFTs of Finite Non-Abelian Symmetries","version":2},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-15T11:33:18.662351Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2603.12323"},"observation_digest":"sha256:7230ed107871c79e6be8a786364064f8897e5dd76044741f0fbda087921d90b5","observation_id":"7c99a0de-dec4-44b4-a525-15633a4b73d8","resolution":{"observed_at":"2026-05-15T11:35:31.508561Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2604.02414","last_updated":"2026-07-09T20:27:45Z","snapshot_observed_at":"2026-08-09T15:00:39.925445Z","submitted_at":"2026-04-02T18:00:00Z","title":"On Lagrangians of Non-abelian Dijkgraaf-Witten Theories","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-05-13T21:08:00.081723Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2604.02414"},"observation_digest":"sha256:7a00878bcd062bcde5f484095702398f51a149e6866f0362d066bc337de5e8a0","observation_id":"18e0ed97-e5d4-4571-a42f-e3ac25d36aa6","resolution":{"observed_at":"2026-05-13T21:08:17.138064Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-13T13:50:27.597426Z","title":"Cordova, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2604.02414","last_updated":"2026-07-09T20:27:45Z","snapshot_observed_at":"2026-08-09T15:00:39.925445Z","submitted_at":"2026-04-02T18:00:00Z","title":"On Lagrangians of Non-abelian Dijkgraaf-Witten Theories","version":2},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-07-13T13:50:27.597426Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2604.02414"},"observation_digest":"sha256:72c942343b7bbdb3f74ad41195d059a8c5247a22c97b9e2e99e479caa135f9d4","observation_id":"14981d1f-2b1b-46b4-ab9c-22fc0912312f","resolution":{"observed_at":"2026-07-13T13:50:27.597426Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2605.06653","last_updated":"2026-06-24T13:52:20Z","snapshot_observed_at":"2026-08-08T13:23:42.843051Z","submitted_at":"2026-05-07T17:56:48Z","title":"From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs","version":1},"reference_index":4,"source":"arxiv_source","source_observed_at":"2026-05-08T07:40:29.165507Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2605.06653"},"observation_digest":"sha256:c6126a5e25aa27b25e5d4b6413aba7e52f191c42fe1f508ae3fa268365f7c0d8","observation_id":"11d53778-b0d9-4b9d-8fa6-ae3c2f2fe3ea","resolution":{"observed_at":"2026-05-11T20:56:13.609375Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2605.12601","last_updated":"2026-08-04T13:44:39Z","snapshot_observed_at":"2026-08-09T04:12:34.234927Z","submitted_at":"2026-05-12T18:00:04Z","title":"Lattice Gauging Interfaces and Noninvertible Defects in Higher Dimensions","version":1},"reference_index":61,"source":"pdf_text","source_observed_at":"2026-05-14T20:37:24.809017Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2605.12601"},"observation_digest":"sha256:6d69af54f233ffe31e89bb30968d46301697d1f4cdad2ee516f2745674b2df08","observation_id":"800b1439-62b9-479d-9ad7-df9db5e08f4f","resolution":{"observed_at":"2026-05-14T20:37:58.390380Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":"2412.16681","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-07-02T13:57:00.234251Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","venue":null,"work_id":"7a11972d-2517-4d62-91ea-b50c223782d0","year":2024},"citing_paper":{"arxiv_id":"2606.05543","last_updated":"2026-07-15T02:48:01Z","snapshot_observed_at":"2026-08-02T12:26:57.733415Z","submitted_at":"2026-06-04T00:58:08Z","title":"Notes on (-2)-form symmetries","version":1},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-06-28T00:46:19.482598Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2606.05543"},"observation_digest":"sha256:8d056ac801da38fd966def8783afec376fa9e8c9cbbbffc4d4cf2e372350cdca","observation_id":"30a50185-26e2-4856-8753-67ccebf2e006","resolution":{"observed_at":"2026-07-02T13:57:00.235657Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.16681","snapshot_observed_at":"2026-08-02T12:27:00.074087Z","title":"Cordova, D","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.05543","last_updated":"2026-07-15T02:48:01Z","snapshot_observed_at":"2026-08-02T12:26:57.733415Z","submitted_at":"2026-06-04T00:58:08Z","title":"Notes on (-2)-form symmetries","version":2},"reference_index":100,"source":"pdf_text","source_observed_at":"2026-08-02T12:27:00.074087Z"},"links":{"cited_paper":"/paper/2412.16681","citing_paper":"/paper/2606.05543"},"observation_digest":"sha256:7f98042c5d308bd09df5457a529c00851bb73641a9cc98dcae9e6b4399d13d03","observation_id":"72d41aca-d5f4-4659-92a3-4ac97fdbb3c0","resolution":{"observed_at":"2026-08-02T12:27:00.074087Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2412.16681/citation-record","integrity":"/paper/2412.16681/integrity","json":"/paper/2412.16681/citation-record.json","paper":"/paper/2412.16681"},"outbound":[],"paper":{"arxiv_id":"2412.16681","last_updated":"2024-12-21T16:16:52Z","latest_version":1,"primary_category":"cond-mat.str-el","snapshot_observed_at":"2026-08-09T07:28:09.465991Z","submitted_at":"2024-12-21T16:16:52Z","title":"Non-Invertible Symmetries as Condensation Defects in Finite-Group Gauge Theories"},"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":"2026-08-10T06:31:04.303077+00:00","source":"crossref"},{"observed_at":"2026-08-10T06:30:57.382061+00:00","source":"retraction_watch"}],"thesis":"As of 10 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 9 inbound Pith citation observations for arXiv:2412.16681."}