{"as_of":"2026-08-15T13:50:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:1a9e78137d7eb742a6a14eac8468945e8f3f8f817fa313e785bfa811d6cb618f","coverage":[{"denominator":1,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":1,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-10T17:25:29.245102Z","state":"measured"},{"denominator":2,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":2,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-15T06:32:42.880941+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":"2026-07-31T03:42:57.165427Z","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":[{"citation":{"cited_paper":{"arxiv_id":"2604.08285","last_updated":"2026-04-09T14:22:49Z","snapshot_observed_at":"2026-08-07T06:24:35.309406Z","submitted_at":"2026-04-09T14:22:49Z","title":"Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2604.08285","snapshot_observed_at":"2026-07-31T03:42:57.165427Z","title":"Yan and X","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.25015","last_updated":"2026-07-27T19:12:52Z","snapshot_observed_at":"2026-08-14T19:17:19.516365Z","submitted_at":"2026-07-27T19:12:52Z","title":"Topological Rigidity of Contractible 3-Manifolds and Handlebody Interiors under Nonnegative Scalar Curvature","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-07-31T03:42:57.165427Z"},"links":{"cited_paper":"/paper/2604.08285","citing_paper":"/paper/2607.25015"},"observation_digest":"sha256:1fcc4a6fa01db9e8e04ff80f7b19e605b2ded4cd563dd2a45e00815a9749a787","observation_id":"36192369-a83e-40ed-b805-5c35ee3d152d","resolution":{"observed_at":"2026-07-31T03:42:57.165427Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2604.08285/citation-record","integrity":"/paper/2604.08285/integrity","json":"/paper/2604.08285/citation-record.json","paper":"/paper/2604.08285"},"outbound":[{"citation":{"cited_paper":{"arxiv_id":"2501.17947","last_updated":"2025-01-29T19:09:55Z","snapshot_observed_at":"2026-08-10T04:29:16.433814Z","submitted_at":"2025-01-29T19:09:55Z","title":"Gradient estimates for scalar curvature","version":1},"cited_work":{"arxiv_id":"2501.17947","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2501.17947","snapshot_observed_at":"2026-06-28T20:52:37.837065Z","title":"Colding,Lower bounds on Ricci curvature and the almost rigidity of warped products, Ann","venue":null,"work_id":"6586e97c-ec2e-46e0-b110-090a054bd634","year":2020},"citing_paper":{"arxiv_id":"2604.08285","last_updated":"2026-04-09T14:22:49Z","snapshot_observed_at":"2026-08-07T06:24:35.309406Z","submitted_at":"2026-04-09T14:22:49Z","title":"Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-10T17:25:29.245102Z"},"links":{"cited_paper":"/paper/2501.17947","citing_paper":"/paper/2604.08285"},"observation_digest":"sha256:be8fb26021e5a5c13e2bf4e438e7b36db394ff8373e716547f535f3a5db194c9","observation_id":"e1310204-6020-4ca4-807e-e87476d8e09e","resolution":{"observed_at":"2026-05-11T06:51:24.041569Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2604.08285","last_updated":"2026-04-09T14:22:49Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-07T06:24:35.309406Z","submitted_at":"2026-04-09T14:22:49Z","title":"Topology of 3-manifolds with nonnegative scalar curvature and positive harmonic functions"},"reference_resolution":{"displayed":1,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":1,"verified_fuzzy":0},"total_outbound_references":1},"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":"2026-08-15T06:32:42.880941+00:00","source":"crossref"},{"observed_at":"2026-08-15T06:32:39.529945+00:00","source":"retraction_watch"}],"thesis":"As of 15 August 2026, this Paper Citation Record lists 1 of 1 outbound references and 1 inbound Pith citation observation for arXiv:2604.08285."}