{"as_of":"2026-08-18T22:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:90db02fe1c86878b1f2a9fd1a423e0b1d48963a05e2b9de5e90372185f3d76d8","coverage":[{"denominator":11,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":11,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-10T19:36:11.403157Z","state":"measured"},{"denominator":12,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":12,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-18T06:34:40.430872+00:00","state":"measured"},{"denominator":1,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T18:17:46.568649Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-08-06T18:17:47.627392Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"cited_work":{"arxiv_id":"2501.10113","doi":null,"metadata_source":"pith","pith_arxiv_id":"2501.10113","snapshot_observed_at":"2026-08-06T18:17:47.627392Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","venue":"math.QA","work_id":"ad663df3-d684-4330-b658-5ec23758773c","year":2025},"citing_paper":{"arxiv_id":"2507.08722","last_updated":"2025-07-11T16:21:54Z","snapshot_observed_at":"2026-08-14T02:28:43.832411Z","submitted_at":"2025-07-11T16:21:54Z","title":"Generalized Yetter-Drinfeld modules, the center of bi-actegories and groupoid-crossed braided bicategories","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T18:17:46.568649Z"},"links":{"cited_paper":"/paper/2501.10113","citing_paper":"/paper/2507.08722"},"observation_digest":"sha256:46d344cae6834eee4e2f4894443fff05eae4b0741c4eedfcfe761c11f1c5f430","observation_id":"271b6fb4-2c3f-439c-8979-4c1ada98b512","resolution":{"observed_at":"2026-08-06T18:17:47.680766Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2501.10113/citation-record","integrity":"/paper/2501.10113/integrity","json":"/paper/2501.10113/citation-record.json","paper":"/paper/2501.10113"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-10T19:36:11.564742Z","title":"Abrams, Two-dimensional topological quantum ﬁeld theories a nd Frobenius algebras, Journal of Knot Theory and Its Ramiﬁcations 5 (5), (1996), 569–587","venue":null,"work_id":"82cd158c-a22b-4134-af38-3908e7de4f57","year":1996},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.362887Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:7b8bb65f29b18f2f57666c292ad1ff03fcbfcf5b754e711b4ef33739be190e21","observation_id":"e2c5c772-793e-420d-8f5e-544a247b4603","resolution":{"observed_at":"2026-08-10T19:36:11.568029Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.552927Z","title":"Brightwell and P","venue":null,"work_id":"644f562d-0fd9-430a-8102-769893189b71","year":2000},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.368243Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:d62b500d95911b69a99779ae1a503f7a009274d7d6094eb13f084b045d85b59e","observation_id":"09921370-1fdf-4aee-83c7-71e1f2d6807e","resolution":{"observed_at":"2026-08-10T19:36:11.557090Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.541205Z","title":"Kassel, Quantum Groups, Springer-Verlag, New York 1995","venue":null,"work_id":"053d8225-17af-4661-a793-b8335e0c1859","year":1995},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.372512Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:a20af3866fbd347d584387caf17d28cbe29584845486ab2197f5a73811c11167","observation_id":"44e4d711-a3d2-4b84-9fcc-37755e37c8fd","resolution":{"observed_at":"2026-08-10T19:36:11.545350Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.529401Z","title":"Kock, Frobenius Algebras and 2D Topological Quantum Field The ories, Cambridge University Press , Cambridge (2003)","venue":null,"work_id":"997e36b5-5605-45e5-b0dd-74191319a2e0","year":2003},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.375884Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:22fb5ace7dc58c3a6f78de9945b7a9428e041b6decd77b20073d85d86e49381e","observation_id":"0280e941-377c-4635-8821-67085a0ee441","resolution":{"observed_at":"2026-08-10T19:36:11.533823Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.517259Z","title":"Lauda and H","venue":null,"work_id":"a2f2b3dd-e99d-4dee-8e16-8a5b8cec93d0","year":2008},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.379304Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:4307dd5aa8c1e80222813a4cef304c881b875824c2d98d9e10defd78d75f69ca","observation_id":"019ce2cc-fd29-4c9e-918f-5364c515c3db","resolution":{"observed_at":"2026-08-10T19:36:11.521742Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.503295Z","title":"Mac Lane, Categories for the Working Mathematician, Gradua te Texts in Mathematics 5, Springer- Verlag, New York 1998","venue":null,"work_id":"817f700f-14bc-491e-9dc7-a56a1a51e731","year":1998},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.385234Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:84453b377541946313463124c470ee227b80c17476759122a8f543f4dce7894a","observation_id":"8907c668-6eef-44dc-b312-7df10ac0491d","resolution":{"observed_at":"2026-08-10T19:36:11.508253Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.490888Z","title":"Porter and V","venue":null,"work_id":"0998455b-4615-4a2a-b33e-b6fb8c590045","year":2006},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.389153Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:902f4e2aed37235d817fcbfd6e7f113bf0eb0106d7e9e64ea78f56faec02653c","observation_id":"9f1ad072-f062-4e46-aab0-e209fba9a22f","resolution":{"observed_at":"2026-08-10T19:36:11.495320Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.479797Z","title":"Rodrigues, Homotopy Quantum Field Theories and the Homotop y Cobordism Category in Dimension 1 + 1, J","venue":null,"work_id":"59d2f164-cbc2-4083-b4aa-6a70baa2c201","year":2003},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.392437Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:0a82e05ca8a5f78519baa4e8f89d989f65f8b988f4b0bea5f2c5fa553b630a3e","observation_id":"58cb400a-81b9-4dc9-b185-b53f827328aa","resolution":{"observed_at":"2026-08-10T19:36:11.483987Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.467697Z","title":"Staic and V","venue":null,"work_id":"0ace0663-0b55-48d8-8e12-3b08c27903ea","year":2010},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.396000Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:eba3ba25528a447045b5e829e8f59aeaf0d5419031e140af7feabd949756a386","observation_id":"ed90de9f-1f33-4635-87c2-aa99817b1c7a","resolution":{"observed_at":"2026-08-10T19:36:11.471794Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"math/9910010","last_updated":"1999-10-04T12:34:51Z","snapshot_observed_at":"2026-08-02T13:51:48.407018Z","submitted_at":"1999-10-04T12:34:51Z","title":"Homotopy field theory in dimension 2 and group-algebras","version":1},"cited_work":{"arxiv_id":"math/9910010","doi":null,"metadata_source":"pith","pith_arxiv_id":"math/9910010","snapshot_observed_at":"2026-08-10T19:36:11.437921Z","title":"Homotopy field theory in dimension 2 and group-algebras","venue":"math.QA","work_id":"518500e2-067f-4029-b819-405678589da4","year":1999},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.398887Z"},"links":{"cited_paper":"/paper/math/9910010","citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:e10a66e79cce48e25b9e822cfbe0bd93e696eca1d198bfd21edf6ebcad8f30fc","observation_id":"95cc9a0c-7d48-460e-b76e-cbba1d7e4ecf","resolution":{"observed_at":"2026-08-10T19:36:11.444846Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+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":"2026-08-10T19:36:11.454931Z","title":"Turaev, Homotopy Quantum Field Theory, EMS Tracts in Math ematics, 2010","venue":null,"work_id":"208d9745-c4dc-4852-bef9-78c2f16c53a0","year":2010},"citing_paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-10T19:36:11.403157Z"},"links":{"citing_paper":"/paper/2501.10113"},"observation_digest":"sha256:930caad8a77e0bba99bad28f4809d9d191e861c20994ed1209f24b6eba85c9b8","observation_id":"500e5281-7639-4a5e-aae2-8b14c5b277a4","resolution":{"observed_at":"2026-08-10T19:36:11.459984Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2501.10113","last_updated":"2025-01-17T10:55:48Z","latest_version":1,"primary_category":"math.QA","snapshot_observed_at":"2026-08-17T07:13:55.690973Z","submitted_at":"2025-01-17T10:55:48Z","title":"2D HQFTs and Frobenius $(\\mathcal{G},\\mathcal{V})$-categories"},"reference_resolution":{"displayed":11,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":10},"total_outbound_references":11},"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":"2026-08-18T06:34:40.430872+00:00","source":"crossref"},{"observed_at":"2026-08-18T06:34:34.496301+00:00","source":"retraction_watch"}],"thesis":"As of 18 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 1 inbound Pith citation observation for arXiv:2501.10113."}