{"as_of":"2026-08-14T23:49:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:fa338e82d505da1eb0c04aba59e162a389cd9a4d992ae29d08cda94746a76abc","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":1,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":1,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-14T06:32:32.682623+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":"2026-05-19T04:49:09.926552Z","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":"2026-05-19T04:52:03.717657Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2504.06089","last_updated":"2025-04-08T14:30:03Z","snapshot_observed_at":"2026-08-07T16:07:29.695774Z","submitted_at":"2025-04-08T14:30:03Z","title":"A Monotonicity Formula for the Extrinsic Biharmonic Map Heat Flow","version":1},"cited_work":{"arxiv_id":"2504.06089","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2504.06089","snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Mäder–Baumdicker and N","venue":null,"work_id":"a0cec5c4-2fd4-4739-82a2-b27247aa501b","year":2025},"citing_paper":{"arxiv_id":"2507.12068","last_updated":"2026-05-07T00:38:54Z","snapshot_observed_at":"2026-08-08T01:34:30.683192Z","submitted_at":"2025-07-16T09:24:35Z","title":"Analyzing the Geometry of Immersions of Co-Dimension One via Shape Operator Dynamics","version":4},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-19T04:49:09.926552Z"},"links":{"cited_paper":"/paper/2504.06089","citing_paper":"/paper/2507.12068"},"observation_digest":"sha256:fd47a75d27953e3c9161d6e491a5a956c0d05e086386a844439f1b19385284fb","observation_id":"c2c643de-f32c-459e-869c-a47aee117522","resolution":{"observed_at":"2026-05-19T04:52:03.719367Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2504.06089/citation-record","integrity":"/paper/2504.06089/integrity","json":"/paper/2504.06089/citation-record.json","paper":"/paper/2504.06089"},"outbound":[],"paper":{"arxiv_id":"2504.06089","last_updated":"2025-04-08T14:30:03Z","latest_version":1,"primary_category":"math.DG","snapshot_observed_at":"2026-08-07T16:07:29.695774Z","submitted_at":"2025-04-08T14:30:03Z","title":"A Monotonicity Formula for the Extrinsic Biharmonic Map Heat Flow"},"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":"2026-08-14T06:32:32.682623+00:00","source":"crossref"},{"observed_at":"2026-08-14T06:32:18.44784+00:00","source":"retraction_watch"}],"thesis":"As of 14 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 1 inbound Pith citation observation for arXiv:2504.06089."}