{"as_of":"2026-08-08T15:00:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e54b61a89b6f1182f1fb32e0386dda255d41df352faab1615febe95bdc2f1681","coverage":[{"denominator":5,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-01T14:41:27.692783Z","state":"measured"},{"denominator":5,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":5,"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/2607.18694/citation-record","integrity":"/paper/2607.18694/integrity","json":"/paper/2607.18694/citation-record.json","paper":"/paper/2607.18694"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-01T14:41:26.968404Z","title":null,"venue":null,"work_id":null,"year":1996},"citing_paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-01T14:41:26.968404Z"},"links":{"citing_paper":"/paper/2607.18694"},"observation_digest":"sha256:a8be1d301f510a14cd12a2ddcf5a15afaaf85189a672050d192657af2694bbd9","observation_id":"b87cd2fb-0cca-43e4-9749-82b06d14e3c5","resolution":{"observed_at":"2026-08-01T14:41:26.968404Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2510.23022","last_updated":"2026-07-15T18:42:26Z","snapshot_observed_at":"2026-08-04T08:08:11.750902Z","submitted_at":"2025-10-27T05:34:04Z","title":"Possible Sizes of Sumsets","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2510.23022","snapshot_observed_at":"2026-08-01T14:41:27.120923Z","title":"Rajagopal, Possible sizes of sumsets,Discrete Analysis(2026), Paper No","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-01T14:41:27.120923Z"},"links":{"cited_paper":"/paper/2510.23022","citing_paper":"/paper/2607.18694"},"observation_digest":"sha256:0d150bb77738995abc322c49a27a22854a6f97ea136f2bab3ea5fb75cb72114f","observation_id":"36ae889c-e44d-4d6f-acf3-23938065df93","resolution":{"observed_at":"2026-08-01T14:41:27.120923Z","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":"2026-08-01T14:41:27.290476Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-01T14:41:27.290476Z"},"links":{"citing_paper":"/paper/2607.18694"},"observation_digest":"sha256:5bff61f650fb8be6d3c013ceb2a14a91186c3e58f70834a261d7bf809689f289","observation_id":"34a3d453-d8a9-4636-adca-41a750862ec3","resolution":{"observed_at":"2026-08-01T14:41:27.290476Z","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":"2026-08-01T14:41:27.515550Z","title":"Schinina, On the sumset of sets of size k,Integers26(2026), Paper No","venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-01T14:41:27.515550Z"},"links":{"citing_paper":"/paper/2607.18694"},"observation_digest":"sha256:74b03f92e8b691a74545a6d08bc58eaa1834439cab20c90fe89e7bef788d75c4","observation_id":"29fff04f-8de5-431c-87a0-15024a299e84","resolution":{"observed_at":"2026-08-01T14:41:27.515550Z","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":"2026-08-01T14:41:27.692783Z","title":"Tang and Y","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-01T14:41:27.692783Z"},"links":{"citing_paper":"/paper/2607.18694"},"observation_digest":"sha256:46423d2a32b169d0f10eb17a279fc38825dcc6cda69b5ef4cb2ee14df6308ea7","observation_id":"98254cd6-56f6-418b-b9cd-952eb3686538","resolution":{"observed_at":"2026-08-01T14:41:27.692783Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.18694","last_updated":"2026-07-21T04:25:11Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-05T10:30:17.834662Z","submitted_at":"2026-07-21T04:25:11Z","title":"A Local Classification of Four-Element Multiple Sumsets"},"reference_resolution":{"displayed":5,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":5,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":5},"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 5 of 5 outbound references and 0 inbound Pith citation observations for arXiv:2607.18694."}