{"as_of":"2026-08-07T10:31:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:d5790064e951dd50141de5ee614539a1f1648f9b6846041859af8b02c731acd9","coverage":[{"denominator":9,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":9,"source":"paper_references, paper_reference_links","source_observed_at":"2026-07-15T10:39:49.531101Z","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":"2026-08-07T06:34:17.273281+00:00","state":"measured"},{"denominator":0,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":0,"source":"paper_references, paper_reference_links","source_observed_at":null,"state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"cited_works","source_observed_at":null,"state":"measured"}],"external_citation_measurements":[],"inbound":[],"links":{"evidence":"/evidence","html":"/paper/2606.22088/citation-record","integrity":"/paper/2606.22088/integrity","json":"/paper/2606.22088/citation-record.json","paper":"/paper/2606.22088"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"Manifolds of Negative Curvature","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:6e0fa96e1d7240d1fdb29e53237b3af246ba52d92a9d186673449873d9428f95","observation_id":"131fdca9-0741-436c-843c-4bae7113fb16","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"Topological and Geometric Properties of Graph- Manifolds","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:0e211b4e144405751e8ed0001bce8b293304a85622ab4ab6f53a9ac939b2d1ae","observation_id":"76347ef2-6a13-4e8b-be74-8c2e76ed8ba3","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"Deforming Homotopy Involutions of 3-Manifolds to Involutions","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:88daf562373746a05d68f81441a7650cdff739e3d05791ac569f12e4f9f62ede","observation_id":"610f2578-93dd-4836-86b5-0f0a31b1907a","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"The Nielsen realization problem","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:24c8431e22453005b01033e1d19a5e2fec6a98e9d4ef17d2ddb6ecddf6ab151e","observation_id":"690e8681-7b74-4cf6-9e87-146a2772e246","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"3-Manifolds with(out) Metrics of Nonpositive Curvature","venue":null,"work_id":null,"year":1995},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:2b768f76f4d63495e6eec6ec595f68fe1c6f74c141315fc162db7c9a92007e4a","observation_id":"b82b8833-7114-4812-a684-3eb9b6176a56","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0211159","last_updated":"2002-11-11T16:11:49Z","snapshot_observed_at":"2026-07-07T05:32:21.443158Z","submitted_at":"2002-11-11T16:11:49Z","title":"The entropy formula for the Ricci flow and its geometric applications","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0211159","snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"[Per03a] G","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"cited_paper":"/paper/math/0211159","citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:133a4048a20196c0862da7b87e59f39077e414578dea92c4a7de3f27c4b37d40","observation_id":"00711101-f5e1-40b2-be95-f5abe3df54a9","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"math/0307245","last_updated":"2003-07-17T15:26:38Z","snapshot_observed_at":"2026-07-07T05:35:59.786340Z","submitted_at":"2003-07-17T15:26:38Z","title":"Finite extinction time for the solutions to the Ricci flow on certain three-manifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"math/0307245","snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"[Per03b] G","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"cited_paper":"/paper/math/0307245","citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:92a94413ddd84a0c85cf477d6ed8d3c9a6aea60312bc2c08ba6f130735238595","observation_id":"3c3f307d-901f-4ced-a192-b16e3ddc54bb","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"Compact Group Actions and the Topology of Mani- folds with Non-Positive Curvature","venue":null,"work_id":null,"year":1979},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:38c8b976a7529ce6fc5f9f43ae780393a092d4b9cc73478db6dfdcc5e5e30d0a","observation_id":"98b58705-09b4-49a3-9b33-68df69f438f9","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-07-15T10:39:49.531101Z","title":"Das Nielsensche Realisierungsproblem f¨ ur hinreichend große 3-Mannigfaltigkeiten","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-07-15T10:39:49.531101Z"},"links":{"citing_paper":"/paper/2606.22088"},"observation_digest":"sha256:6af214c5c623e050c09125e0189164ee84fc13551a9d63857756a48767119e4e","observation_id":"a3938720-9713-4f23-a396-8a8b764ddd3d","resolution":{"observed_at":"2026-07-15T10:39:49.531101Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.22088","last_updated":"2026-07-14T15:16:09Z","latest_version":2,"primary_category":"math.GT","snapshot_observed_at":"2026-08-06T18:35:11.268745Z","submitted_at":"2026-06-20T15:12:54Z","title":"Isometric free finite group actions on non-positively curved 3-manifolds"},"reference_resolution":{"displayed":9,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":9,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":9},"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":"2026-08-07T06:34:17.273281+00:00","source":"crossref"},{"observed_at":"2026-08-07T06:34:11.927384+00:00","source":"retraction_watch"}],"thesis":"As of 7 August 2026, this Paper Citation Record lists 9 of 9 outbound references and 0 inbound Pith citation observations for arXiv:2606.22088."}