{"as_of":"2026-08-13T23:03:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:0fe280a2b652ab0a85af405e4960ab9656de543696340d0a3994f153169b4581","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":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":"2026-08-13T06:32:02.005865+00:00","state":"measured"},{"denominator":5,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":5,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-12T12:11:42.220439Z","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":"2026-05-15T07:55:15.302503Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08360","snapshot_observed_at":"2026-08-12T12:11:42.220439Z","title":"Frantzikinakis, O","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2411.17523","last_updated":"2025-08-07T10:57:19Z","snapshot_observed_at":"2026-08-12T11:58:45.032900Z","submitted_at":"2024-11-26T15:33:48Z","title":"Partition regularity of homogeneous quadratics: Current trends and challenges","version":4},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-12T12:11:42.220439Z"},"links":{"cited_paper":"/paper/2407.08360","citing_paper":"/paper/2411.17523"},"observation_digest":"sha256:ea84cf17c9f5c30746e5c02c3872aa905c8815bd75b1ea843d1eef1e2dd9b630","observation_id":"b73eab6b-42cd-4b36-90d7-ec0293af30cf","resolution":{"observed_at":"2026-08-12T12:11:42.220439Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08360","snapshot_observed_at":"2026-08-11T22:31:11.044024Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.03504","last_updated":"2025-08-24T13:46:51Z","snapshot_observed_at":"2026-08-13T18:07:21.856335Z","submitted_at":"2024-12-04T17:45:49Z","title":"On multiplicative recurrence along linear patterns","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T22:31:11.044024Z"},"links":{"cited_paper":"/paper/2407.08360","citing_paper":"/paper/2412.03504"},"observation_digest":"sha256:494a2381609607d5553a3746aa7ae9c439877edb31c3a02178b098974e776355","observation_id":"94ce36ec-08eb-48b5-b889-47185c3ad0b3","resolution":{"observed_at":"2026-08-11T22:31:11.044024Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08360","snapshot_observed_at":"2026-08-11T11:59:25.504393Z","title":"Frantzikinakis, O","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2412.14917","last_updated":"2025-05-09T20:26:41Z","snapshot_observed_at":"2026-08-11T11:46:01.284076Z","submitted_at":"2024-12-19T14:50:43Z","title":"Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem","version":2},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-11T11:59:25.504393Z"},"links":{"cited_paper":"/paper/2407.08360","citing_paper":"/paper/2412.14917"},"observation_digest":"sha256:66875028ce28300dbc8159b57566f9c73cebd0182a1c3375a9b32f3159dc1b5c","observation_id":"08012c0f-a3dd-4389-afa6-a905d5db3f4e","resolution":{"observed_at":"2026-08-11T11:59:25.504393Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2407.08360","snapshot_observed_at":"2026-08-10T12:17:11.452217Z","title":"Frantzikinakis, O","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2501.17203","last_updated":"2025-04-15T06:06:25Z","snapshot_observed_at":"2026-08-10T12:00:52.938627Z","submitted_at":"2025-01-28T00:10:05Z","title":"Homogeneous Patterns in Ramsey Theory","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-10T12:17:11.452217Z"},"links":{"cited_paper":"/paper/2407.08360","citing_paper":"/paper/2501.17203"},"observation_digest":"sha256:062196582b483e9a7d8deb65d4a6c5b51e1a616c32b61e557370cedad13ce79c","observation_id":"beaf8b24-c362-479d-ab58-3caf9aa27e85","resolution":{"observed_at":"2026-08-10T12:17:11.452217Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs","version":3},"cited_work":{"arxiv_id":"2407.08360","doi":null,"metadata_source":"arxiv_reference","pith_arxiv_id":"2407.08360","snapshot_observed_at":"2026-07-28T02:23:12.250165Z","title":"Frantzikinakis, O","venue":null,"work_id":"659810c3-e38f-4d5b-9fe9-ef9549f0b2a9","year":2024},"citing_paper":{"arxiv_id":"2603.20497","last_updated":"2026-04-07T10:28:01Z","snapshot_observed_at":"2026-08-06T09:06:22.100541Z","submitted_at":"2026-03-20T20:58:41Z","title":"Partition regularity in imaginary quadratic rings of integers","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-15T07:51:40.513892Z"},"links":{"cited_paper":"/paper/2407.08360","citing_paper":"/paper/2603.20497"},"observation_digest":"sha256:bbec52a27221d5579457fa33367cd0aa4dabb151d8d71a993f02066f522c4afa","observation_id":"c0fc8f92-752c-4808-b90b-69e5408f4895","resolution":{"observed_at":"2026-07-28T02:23:12.250165Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2407.08360/citation-record","integrity":"/paper/2407.08360/integrity","json":"/paper/2407.08360/citation-record.json","paper":"/paper/2407.08360"},"outbound":[],"paper":{"arxiv_id":"2407.08360","last_updated":"2026-07-27T16:09:59Z","latest_version":3,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T23:24:21.243205Z","submitted_at":"2024-07-11T10:12:34Z","title":"Partition regularity of generalized Pythagorean pairs"},"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":"2026-08-13T06:32:02.005865+00:00","source":"crossref"},{"observed_at":"2026-08-13T06:31:53.387327+00:00","source":"retraction_watch"}],"thesis":"As of 13 August 2026, this Paper Citation Record lists 0 of 0 outbound references and 5 inbound Pith citation observations for arXiv:2407.08360."}