{"as_of":"2026-08-09T19:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d5b2ed952a3ae281fd753396a43cb9c260c69b9664155b71cf0b0826e9058600","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":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-08T17:21:04.896717Z","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":"2026-06-29T19:23:53.993895Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.03457","snapshot_observed_at":"2026-08-08T17:21:04.896717Z","title":"An extension theory for partial groups,","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2502.05958","last_updated":"2025-02-09T16:55:01Z","snapshot_observed_at":"2026-08-08T17:10:56.994435Z","submitted_at":"2025-02-09T16:55:01Z","title":"Simplicial effects and weakly associative partial groups","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-08T17:21:04.896717Z"},"links":{"cited_paper":"/paper/2105.03457","citing_paper":"/paper/2502.05958"},"observation_digest":"sha256:89e324e00564266bbedc700d8ef2050fcabab5d9a7ae5925bf966a3185d9ab95","observation_id":"69378378-9b4b-48fa-a712-06724f6096d3","resolution":{"observed_at":"2026-08-08T17:21:04.896717Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.03457","snapshot_observed_at":"2026-08-07T00:26:58.345988Z","title":"Broto, A","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2506.14304","last_updated":"2025-08-26T02:16:14Z","snapshot_observed_at":"2026-08-07T00:15:43.194477Z","submitted_at":"2025-06-17T08:30:45Z","title":"Partial Group Symmetry in Figures I: Semidirect Products and the Six Coins","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-07T00:26:58.345988Z"},"links":{"cited_paper":"/paper/2105.03457","citing_paper":"/paper/2506.14304"},"observation_digest":"sha256:87338fea5a4e9d40d5c3d74dabd57b1e1e59433344b3d74050198a0e38ab4086","observation_id":"15d0fc66-8c9a-4130-bca7-1ea18d928c95","resolution":{"observed_at":"2026-08-07T00:26:58.345988Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.03457","snapshot_observed_at":"2026-08-06T19:37:43.873240Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.05437","last_updated":"2025-09-04T14:14:50Z","snapshot_observed_at":"2026-08-08T12:13:52.887453Z","submitted_at":"2025-07-07T19:38:51Z","title":"Higher Segal spaces and partial groups","version":2},"reference_index":3,"source":"arxiv_source","source_observed_at":"2026-08-06T19:37:43.873240Z"},"links":{"cited_paper":"/paper/2105.03457","citing_paper":"/paper/2507.05437"},"observation_digest":"sha256:4cee89b04230aa00675299b03090b4587ba1a58207860f76976d14ab97fd904f","observation_id":"02e468d6-2341-440f-a500-e2431e2740cb","resolution":{"observed_at":"2026-08-06T19:37:43.873240Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2105.03457","snapshot_observed_at":"2026-08-02T19:18:43.080055Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2603.03167","last_updated":"2026-07-07T16:51:51Z","snapshot_observed_at":"2026-08-09T11:14:38.041648Z","submitted_at":"2026-03-03T17:16:50Z","title":"Binary partial groups","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T19:18:43.080055Z"},"links":{"cited_paper":"/paper/2105.03457","citing_paper":"/paper/2603.03167"},"observation_digest":"sha256:80559e2acb08b2848ca8b62432c90a44e28452f6511d9e6cff9552b0886809c0","observation_id":"5792cbd4-44ce-43f9-8f9b-816901cb8f52","resolution":{"observed_at":"2026-08-02T19:18:43.080055Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups","version":1},"cited_work":{"arxiv_id":"2105.03457","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2105.03457","snapshot_observed_at":"2026-06-29T19:23:53.993895Z","title":"An extension theory for partial groups","venue":null,"work_id":"350334ee-3bac-41e1-91f8-252b2063e30c","year":null},"citing_paper":{"arxiv_id":"2605.26199","last_updated":"2026-07-07T16:57:27Z","snapshot_observed_at":"2026-08-06T11:04:02.536094Z","submitted_at":"2026-05-25T17:12:46Z","title":"On partial groups of small order","version":1},"reference_index":6,"source":"arxiv_source","source_observed_at":"2026-06-29T19:18:30.555799Z"},"links":{"cited_paper":"/paper/2105.03457","citing_paper":"/paper/2605.26199"},"observation_digest":"sha256:0e27862d36a6d6e7df0ceb09eea3603f4dc974ae2f70a17f4ccb6247af2a6c2e","observation_id":"8377d948-2562-4658-a679-4a5567afb5af","resolution":{"observed_at":"2026-06-29T19:23:53.995508Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2105.03457/citation-record","integrity":"/paper/2105.03457/integrity","json":"/paper/2105.03457/citation-record.json","paper":"/paper/2105.03457"},"outbound":[],"paper":{"arxiv_id":"2105.03457","last_updated":"2021-05-07T18:14:06Z","latest_version":1,"primary_category":"math.AT","snapshot_observed_at":"2026-07-06T11:07:21.848674Z","submitted_at":"2021-05-07T18:14:06Z","title":"An extension theory for partial groups"},"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":"2026-08-09T06:31:02.800959+00:00","source":"crossref"},{"observed_at":"2026-08-09T06:30:57.326959+00:00","source":"retraction_watch"}],"thesis":"As of 9 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2105.03457."}