{"as_of":"2026-08-08T17:55:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fc4cc5854abe46f284cc75a48f3575a1a283071a33c9d90b54bbdd4497de9c6f","coverage":[{"denominator":12,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":12,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T11:09:14.718205Z","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":"2026-08-08T06:32:00.761636+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/2606.18034/citation-record","integrity":"/paper/2606.18034/integrity","json":"/paper/2606.18034/citation-record.json","paper":"/paper/2606.18034"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T11:09:13.679569Z","title":null,"venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:13.679569Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:76e4cfcd5d4765b9524e253748a3a04fe7e365da64835f7a393bd08c4933e34b","observation_id":"087928f3-dc20-46ec-8556-e38d5d509e25","resolution":{"observed_at":"2026-08-02T11:09:13.679569Z","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":"2026-08-02T11:09:13.856026Z","title":"Bieri, W","venue":null,"work_id":null,"year":1987},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:13.856026Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:0a050fe47a2a432af68b1ce062d9aafe865b01c8a5674d598b3eb7f587610bb7","observation_id":"b7ec5f80-7c84-4f0f-85e6-2334d5ffabd2","resolution":{"observed_at":"2026-08-02T11:09:13.856026Z","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":"2026-08-02T11:09:14.595317Z","title":null,"venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":496,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.595317Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:20625d09dd75c599c79192d684e4326113e50b4d974e4f09d7a3dcf91cf1b08c","observation_id":"4ac252e2-2639-4f07-b20f-87feab6aaef6","resolution":{"observed_at":"2026-08-02T11:09:14.595317Z","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":"2026-08-02T11:09:14.718205Z","title":"Weis,Quasi-isometry invariance of discrete higher filling functions, arXiv preprint (2026), arXiv:2601.15140","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1979,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.718205Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:18e3f99bc876294da1177cbaae0eff3d38576948e8dd09acbc5754d19cf98eff","observation_id":"7c706091-fbe9-46b8-b85c-2b83316caf17","resolution":{"observed_at":"2026-08-02T11:09:14.718205Z","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":"2026-08-02T11:09:14.483604Z","title":"Stallings,On fibering certain3-manifolds, Topology of 3-manifolds and related topics (Proc","venue":null,"work_id":null,"year":1961},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1987,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.483604Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:7e06ea203b540262dde27fafb3359874a0b07d3cc16b604db8c405b7f2b8c7c4","observation_id":"03f268f1-257d-46fa-b6de-fa9eca730693","resolution":{"observed_at":"2026-08-02T11:09:14.483604Z","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":"2026-08-02T11:09:14.301855Z","title":"[MPSV25] F","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1990,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.301855Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:9b0e7bf57450eb4ca99da826439cf725a581d5fef8b79e4eaafb5808df2d9358","observation_id":"d1b5d18a-1eed-4ae5-bef6-cc81f90821e3","resolution":{"observed_at":"2026-08-02T11:09:14.301855Z","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":"2026-08-02T11:09:13.950507Z","title":"[Cal01] D","venue":null,"work_id":null,"year":1982},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1994,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:13.950507Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:30a04e910973b74ff0509df7c096103761febccc4e8a5619eccb7d5ec8e05ac6","observation_id":"9b680ea9-8a33-461a-89c9-dd8970845f88","resolution":{"observed_at":"2026-08-02T11:09:13.950507Z","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":"2026-08-02T11:09:13.772558Z","title":"Bieri,Deficiency and the geometric invariants of a group, J","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":1999,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:13.772558Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:869c0781ee7850b4ccd3d7a47e6107b7d0fa5582ea9cdf22af60043d58cd108c","observation_id":"e4a791d8-5b8a-4bd9-8cbd-8a621d88622d","resolution":{"observed_at":"2026-08-02T11:09:13.772558Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2411.04745","last_updated":"2024-11-07T14:28:23Z","snapshot_observed_at":"2026-07-06T19:46:46.160010Z","submitted_at":"2024-11-07T14:28:23Z","title":"Coarse homological invariants of metric spaces","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.04745","snapshot_observed_at":"2026-08-02T11:09:14.225357Z","title":"[KK05] ,Coarse Alexander duality and duality groups, J","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":2004,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.225357Z"},"links":{"cited_paper":"/paper/2411.04745","citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:dc7b6781a76b1f9906a44eeb6988664cd93f833079acbc2c6304ae066b219a4a","observation_id":"dd644482-6517-4558-9c41-52cd193dd20a","resolution":{"observed_at":"2026-08-02T11:09:14.225357Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2012.15303","last_updated":"2024-04-01T17:35:29Z","snapshot_observed_at":"2026-08-07T23:34:24.240043Z","submitted_at":"2020-12-30T19:48:06Z","title":"Foundations of geometric approximate group theory","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2012.15303","snapshot_observed_at":"2026-08-02T11:09:14.035206Z","title":"Cordes, T","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":2016,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.035206Z"},"links":{"cited_paper":"/paper/2012.15303","citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:cb20666529f7943662fec3359a6d0864c10945e3c1895b81e54390c08f7eda65","observation_id":"9689ee0c-1890-43fa-82f8-c18c90ab75e0","resolution":{"observed_at":"2026-08-02T11:09:14.035206Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.14666","last_updated":"2025-06-17T15:57:09Z","snapshot_observed_at":"2026-08-07T00:13:59.985167Z","submitted_at":"2025-06-17T15:57:09Z","title":"Virtual fibring of Poincar\\'e-duality groups","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.14666","snapshot_observed_at":"2026-08-02T11:09:14.130435Z","title":"[EF97] D","venue":null,"work_id":null,"year":1997},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":2018,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.130435Z"},"links":{"cited_paper":"/paper/2506.14666","citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:f4147b9177fe7115295b5c32c452652fa9463af7c4f1f03bf0213becdd1836be","observation_id":"0b069abb-ca2a-41e2-813a-0c50710e7fdd","resolution":{"observed_at":"2026-08-02T11:09:14.130435Z","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":"2026-08-02T11:09:14.378840Z","title":"QUASIMORPHISMS AND POINCAR ´E DUALITY IN DIMENSION 3 41 [Roe93] J","venue":null,"work_id":null,"year":1993},"citing_paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3","version":2},"reference_index":2023,"source":"pdf_text","source_observed_at":"2026-08-02T11:09:14.378840Z"},"links":{"citing_paper":"/paper/2606.18034"},"observation_digest":"sha256:e8528bcb286c7a40c907414960a8ccb1f06ec96acdb3519021abc7662629530c","observation_id":"1e93a044-7c72-4617-b91d-025706d2658c","resolution":{"observed_at":"2026-08-02T11:09:14.378840Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2606.18034","last_updated":"2026-07-22T11:10:46Z","latest_version":2,"primary_category":"math.GR","snapshot_observed_at":"2026-08-02T11:09:11.896729Z","submitted_at":"2026-06-16T15:10:04Z","title":"Quasimorphisms and Poincar\\'e duality in dimension 3"},"reference_resolution":{"displayed":12,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":12,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":12},"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":"2026-08-08T06:32:00.761636+00:00","source":"crossref"},{"observed_at":"2026-08-08T06:31:55.24221+00:00","source":"retraction_watch"}],"thesis":"As of 8 August 2026, this Paper Citation Record lists 12 of 12 outbound references and 0 inbound Pith citation observations for arXiv:2606.18034."}