{"as_of":"2026-08-20T04:22:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:40f45317c51048409374a6737c737ff86041620a3fa654aec26ec172e0fa3378","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":"2026-08-19T06:32:44.657259+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":"2026-08-07T05:27:47.298354Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-03T19:58:53.616787Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"1506.03409","last_updated":"2015-08-13T14:07:12Z","snapshot_observed_at":"2026-08-18T00:30:18.774532Z","submitted_at":"2015-06-10T17:54:24Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1506.03409","snapshot_observed_at":"2026-08-07T05:27:47.298354Z","title":"Ivanisvili and A","venue":null,"work_id":null,"year":2015},"citing_paper":{"arxiv_id":"2506.08494","last_updated":"2025-06-10T06:41:31Z","snapshot_observed_at":"2026-08-07T05:06:52.950135Z","submitted_at":"2025-06-10T06:41:31Z","title":"Multiversion of the Hausdorff--Young inequality","version":1},"reference_index":85,"source":"arxiv_source","source_observed_at":"2026-08-07T05:27:47.298354Z"},"links":{"cited_paper":"/paper/1506.03409","citing_paper":"/paper/2506.08494"},"observation_digest":"sha256:62572c89fdcebb847d35756144743b4a52fc2278f28693d6e499c3ea55ef8a6c","observation_id":"b38a2f2b-9c20-4a25-b60a-7b3e5059244e","resolution":{"observed_at":"2026-08-07T05:27:47.298354Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1506.03409","last_updated":"2015-08-13T14:07:12Z","snapshot_observed_at":"2026-08-18T00:30:18.774532Z","submitted_at":"2015-06-10T17:54:24Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems","version":2},"cited_work":{"arxiv_id":"1506.03409","doi":null,"metadata_source":"pith","pith_arxiv_id":"1506.03409","snapshot_observed_at":"2026-07-03T19:58:53.616787Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems","venue":"math.AP","work_id":"6e9dc8a4-d8b5-4001-b8fb-54ce6fc17636","year":2015},"citing_paper":{"arxiv_id":"2607.01458","last_updated":"2026-07-01T20:28:24Z","snapshot_observed_at":"2026-08-03T20:11:34.768631Z","submitted_at":"2026-07-01T20:28:24Z","title":"Sharp Lower Bounds for Sumsets in Hypercubes","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-07-03T19:54:50.533265Z"},"links":{"cited_paper":"/paper/1506.03409","citing_paper":"/paper/2607.01458"},"observation_digest":"sha256:bd070feb13e0d108ed6a8d868f8d78c903ca577024d6055a036611ff41af9bf1","observation_id":"47dde07a-6c15-44bf-8dc4-b921184f8b16","resolution":{"observed_at":"2026-07-03T19:58:53.618408Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/1506.03409/citation-record","integrity":"/paper/1506.03409/integrity","json":"/paper/1506.03409/citation-record.json","paper":"/paper/1506.03409"},"outbound":[],"paper":{"arxiv_id":"1506.03409","last_updated":"2015-08-13T14:07:12Z","latest_version":2,"primary_category":"math.AP","snapshot_observed_at":"2026-08-18T00:30:18.774532Z","submitted_at":"2015-06-10T17:54:24Z","title":"Bellman partial differential equation and the hill property for classical isoperimetric problems"},"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":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 2 inbound Pith citation observations for arXiv:1506.03409."}