{"as_of":"2026-08-09T15:07:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:5adba6106d44c026b04bbf628bad19f937ee3ccab840497de1fad5a8a862d409","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":4,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":4,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-09T06:31:02.800959+00:00","state":"measured"},{"denominator":4,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":4,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-07T00:26:58.360313Z","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":"2026-06-29T19:23:54.004054Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1507.04392","last_updated":"2015-09-02T23:33:19Z","snapshot_observed_at":"2026-07-06T04:23:59.000858Z","submitted_at":"2015-07-15T20:48:50Z","title":"An extension theory for partial groups and localities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.04392","snapshot_observed_at":"2026-08-07T00:26:58.360313Z","title":"Gonz´ alez, An extension theory for partial groups and localities, arXiv:1507.04392, 2015","venue":null,"work_id":null,"year":2015},"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":6,"source":"pdf_text","source_observed_at":"2026-08-07T00:26:58.360313Z"},"links":{"cited_paper":"/paper/1507.04392","citing_paper":"/paper/2506.14304"},"observation_digest":"sha256:aff61944d1a75ab232b4d91a1bb4a7104dda624e4d254c54d89f8fe2e07cf79e","observation_id":"57ed9096-17bf-439a-935d-3395b8444094","resolution":{"observed_at":"2026-08-07T00:26:58.360313Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1507.04392","last_updated":"2015-09-02T23:33:19Z","snapshot_observed_at":"2026-07-06T04:23:59.000858Z","submitted_at":"2015-07-15T20:48:50Z","title":"An extension theory for partial groups and localities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.04392","snapshot_observed_at":"2026-08-06T19:37:43.980270Z","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":21,"source":"arxiv_source","source_observed_at":"2026-08-06T19:37:43.980270Z"},"links":{"cited_paper":"/paper/1507.04392","citing_paper":"/paper/2507.05437"},"observation_digest":"sha256:efb1dc19ba551088d6adca37178aa390388e57e2eb92821f19307e5f6c0b899f","observation_id":"391ae2e5-6051-40e1-ac92-69fd2a822784","resolution":{"observed_at":"2026-08-06T19:37:43.980270Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1507.04392","last_updated":"2015-09-02T23:33:19Z","snapshot_observed_at":"2026-07-06T04:23:59.000858Z","submitted_at":"2015-07-15T20:48:50Z","title":"An extension theory for partial groups and localities","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1507.04392","snapshot_observed_at":"2026-08-02T19:18:43.601823Z","title":"PARTIAL GROUPS AS PARTIAL GROUPS 7","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":9,"source":"pdf_text","source_observed_at":"2026-08-02T19:18:43.601823Z"},"links":{"cited_paper":"/paper/1507.04392","citing_paper":"/paper/2603.03167"},"observation_digest":"sha256:e372a6aa97b37ec087a296eb69be4329c1023b6b482f996cef3ebbc53b1ee028","observation_id":"09f03f1b-2da1-4acb-b0c3-0e935a4ea483","resolution":{"observed_at":"2026-08-02T19:18:43.601823Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1507.04392","last_updated":"2015-09-02T23:33:19Z","snapshot_observed_at":"2026-07-06T04:23:59.000858Z","submitted_at":"2015-07-15T20:48:50Z","title":"An extension theory for partial groups and localities","version":2},"cited_work":{"arxiv_id":"1507.04392","doi":null,"metadata_source":"pith","pith_arxiv_id":"1507.04392","snapshot_observed_at":"2026-06-29T19:23:54.004054Z","title":"An extension theory for partial groups and localities","venue":"math.AT","work_id":"7f0e71e4-497b-4992-bb32-a939747fc53e","year":2015},"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":17,"source":"arxiv_source","source_observed_at":"2026-06-29T19:18:30.555799Z"},"links":{"cited_paper":"/paper/1507.04392","citing_paper":"/paper/2605.26199"},"observation_digest":"sha256:9cb20d444c734f710308b9266dab44de00467118bab3967ff80bb8fa7a021a4d","observation_id":"c9a6c1be-ac07-4f09-ade5-f0881a5e159c","resolution":{"observed_at":"2026-06-29T19:23:54.005421Z","resolver_source":"local_arxiv","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/1507.04392/citation-record","integrity":"/paper/1507.04392/integrity","json":"/paper/1507.04392/citation-record.json","paper":"/paper/1507.04392"},"outbound":[],"paper":{"arxiv_id":"1507.04392","last_updated":"2015-09-02T23:33:19Z","latest_version":2,"primary_category":"math.AT","snapshot_observed_at":"2026-07-06T04:23:59.000858Z","submitted_at":"2015-07-15T20:48:50Z","title":"An extension theory for partial groups and localities"},"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 4 inbound Pith citation observations for arXiv:1507.04392."}