{"as_of":"2026-08-15T15:12:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:ec93af5504532a6f5a9f8c9c566eb62bb6c2f0fa665c772ae9984b00441c3ddb","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":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":2,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":2,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T15:01:55.490691Z","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":"2026-05-19T18:52:43.081969Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2312.16686","last_updated":"2025-04-09T17:17:11Z","snapshot_observed_at":"2026-08-15T02:39:01.286715Z","submitted_at":"2023-12-27T18:58:54Z","title":"Lojasiewicz inequalities for maps of the 2-sphere","version":2},"cited_work":{"arxiv_id":"2312.16686","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2312.16686","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"arXiv:2312.16686 , year=","venue":null,"work_id":"589e2eac-7620-43ff-b9f6-42fabdac9aee","year":null},"citing_paper":{"arxiv_id":"2605.17001","last_updated":"2026-05-16T13:54:24Z","snapshot_observed_at":"2026-08-15T03:33:15.878149Z","submitted_at":"2026-05-16T13:54:24Z","title":"Strong uniqueness and rectifiability of generalized cylindrical singularities in Ricci flow","version":1},"reference_index":100,"source":"arxiv_source","source_observed_at":"2026-05-19T18:47:45.076682Z"},"links":{"cited_paper":"/paper/2312.16686","citing_paper":"/paper/2605.17001"},"observation_digest":"sha256:54422fe0f12f8b23789a4054cb31c76725bbea906a6772c3cdd56ad0ac5f087e","observation_id":"219fd30b-bdbb-4181-b6d6-9150296267f6","resolution":{"observed_at":"2026-05-19T18:52:43.083603Z","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"}},{"citation":{"cited_paper":{"arxiv_id":"2312.16686","last_updated":"2025-04-09T17:17:11Z","snapshot_observed_at":"2026-08-15T02:39:01.286715Z","submitted_at":"2023-12-27T18:58:54Z","title":"Lojasiewicz inequalities for maps of the 2-sphere","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2312.16686","snapshot_observed_at":"2026-08-06T15:01:55.490691Z","title":"Schulze,Uniqueness of compact tangent flows in mean curvature flow, J","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.04855","last_updated":"2026-08-05T13:48:07Z","snapshot_observed_at":"2026-08-15T06:34:20.856558Z","submitted_at":"2026-08-05T13:48:07Z","title":"Non-uniqueness of geodesic limits and a question of Grayson and Gage","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T15:01:55.490691Z"},"links":{"cited_paper":"/paper/2312.16686","citing_paper":"/paper/2608.04855"},"observation_digest":"sha256:01d402b387d395a22580d60e05ba594f13d503f8136afc31d4a0680ee582164f","observation_id":"763849eb-da61-4a45-996d-5cc3e0a1c8a4","resolution":{"observed_at":"2026-08-06T15:01:55.490691Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"links":{"evidence":"/evidence","html":"/paper/2312.16686/citation-record","integrity":"/paper/2312.16686/integrity","json":"/paper/2312.16686/citation-record.json","paper":"/paper/2312.16686"},"outbound":[],"paper":{"arxiv_id":"2312.16686","last_updated":"2025-04-09T17:17:11Z","latest_version":2,"primary_category":"math.DG","snapshot_observed_at":"2026-08-15T02:39:01.286715Z","submitted_at":"2023-12-27T18:58:54Z","title":"Lojasiewicz inequalities for maps of the 2-sphere"},"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":"2026-08-15T06:32:42.880941+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 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:2312.16686."}