{"as_of":"2026-08-08T12:10:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:a67f0973d26286a29ba23a805419105ec7d223607789001f28cf1119e975d070","coverage":[{"denominator":32,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":32,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-02T00:26:08.937458Z","state":"measured"},{"denominator":33,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":33,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-08T06:32:00.761636+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":"2026-08-07T20:46:45.253779Z","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":"2026-08-07T20:46:45.290117Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"cited_work":{"arxiv_id":"2607.15071","doi":null,"metadata_source":"pith","pith_arxiv_id":"2607.15071","snapshot_observed_at":"2026-08-07T20:46:45.290117Z","title":"Two problems on booksize and triangular edges in Nosal graphs","venue":"math.CO","work_id":"84204386-efe2-42b9-bb56-36420c79b62e","year":2026},"citing_paper":{"arxiv_id":"2608.05947","last_updated":"2026-08-06T12:17:33Z","snapshot_observed_at":"2026-08-08T11:15:24.363881Z","submitted_at":"2026-08-06T12:17:33Z","title":"On a spectral booksize problem fo non bipartite graphs","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-07T20:46:45.253779Z"},"links":{"cited_paper":"/paper/2607.15071","citing_paper":"/paper/2608.05947"},"observation_digest":"sha256:bce03262f0ff5824f9b8f4a6286f4d6143f00b636b51ed5cd120388617bb376a","observation_id":"aeda6584-0f7b-4e89-b000-2dc3193e02d1","resolution":{"observed_at":"2026-08-07T20:46:45.297409Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.","reason":null,"source_receipts":[{"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"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2607.15071/citation-record","integrity":"/paper/2607.15071/integrity","json":"/paper/2607.15071/citation-record.json","paper":"/paper/2607.15071"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-02T00:26:08.856804Z","title":"Babai, B","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.856804Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:f3dd5caf3447d11dcedf2ec472e0ec3f315f235d4bf2f6f6cfd2176b38603b2e","observation_id":"8f343536-005a-47b8-a38e-ca15c2e62cbd","resolution":{"observed_at":"2026-08-02T00:26:08.856804Z","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":"2026-08-02T00:26:08.860753Z","title":"Bollob´ as, Extremal Graph Theory, Academic Press, 1978","venue":null,"work_id":null,"year":1978},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.860753Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:de582f10d156d61c946a2e07d55e8bf0652620e75e49a6d801a0e06bf88fc38d","observation_id":"3dd647f1-9c2a-45ca-b4ba-3c21978b1c5e","resolution":{"observed_at":"2026-08-02T00:26:08.860753Z","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":"2026-08-02T00:26:08.864099Z","title":"Bollob´ as, V","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.864099Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:e555ab936661480117e8e92de549e6cc5096c08905c503083214bbacca403af9","observation_id":"37483039-e421-4e76-a2ef-e1b61ffb9049","resolution":{"observed_at":"2026-08-02T00:26:08.864099Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2607.16746","last_updated":"2026-07-18T10:16:58Z","snapshot_observed_at":"2026-08-06T15:00:38.905668Z","submitted_at":"2026-07-18T10:16:58Z","title":"Supersaturation in Nosal graphs: Triangles and books","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2607.16746","snapshot_observed_at":"2026-08-02T00:26:08.867015Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.867015Z"},"links":{"cited_paper":"/paper/2607.16746","citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:ac9e9802f16bc495ff3d5dadc6516ad4f490f333676ff0e410d0da5698861a7e","observation_id":"9f1cf139-5019-4f58-9c99-00628cb6ac31","resolution":{"observed_at":"2026-08-02T00:26:08.867015Z","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":"2026-08-02T00:26:08.870243Z","title":"Cioab˘ a, D","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.870243Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:68a90460bff4f87a3a577a97a1a98f9f501034cda46f8c72deffb305db4f2dc3","observation_id":"5a91d04b-2254-4070-9410-9d235257f278","resolution":{"observed_at":"2026-08-02T00:26:08.870243Z","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":"2026-08-02T00:26:08.872938Z","title":"Cioab˘ a, D","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.872938Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:0ed59c172db53cf88ed3dbadf63cbe8854e58f1e02f4d182858deec3a2d8af48","observation_id":"5a6ad5ef-120e-4d8a-a7f6-3d216da14e67","resolution":{"observed_at":"2026-08-02T00:26:08.872938Z","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":"2026-08-02T00:26:08.875949Z","title":"Cioab˘ a, L","venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.875949Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:01099111f0646844168badcaed3950d66d4ea66500ea4bf56c22c8bd5d28cf57","observation_id":"cf7489ef-d6d6-415c-ab83-751b4f3452fc","resolution":{"observed_at":"2026-08-02T00:26:08.875949Z","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":"2026-08-02T00:26:08.878451Z","title":"Cvetkovi´ c, P","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.878451Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:f491ef57497f442bbd339745b7641f386bc0377ecbe1a210fd4c131540f5ef0b","observation_id":"fb34259d-0ff4-48f8-ae07-611001ee27ad","resolution":{"observed_at":"2026-08-02T00:26:08.878451Z","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":"2026-08-02T00:26:08.880961Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.880961Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:eb832471c39a49e60dedbf62330d45042d5531fbb61684e02544ba18bb272bd6","observation_id":"1c8d8df7-2114-4f2d-a6d0-f451f7faf8c3","resolution":{"observed_at":"2026-08-02T00:26:08.880961Z","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":"2026-08-02T00:26:08.883336Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.883336Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:401f7c7b464c36574fff99931f6c57f4dafae10d619bd9486572cfddb43f038e","observation_id":"a3c9e5c6-f632-47b1-86ce-bb0414fb2512","resolution":{"observed_at":"2026-08-02T00:26:08.883336Z","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":"2026-08-02T00:26:08.885752Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.885752Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:a30d06c605d04dbc08ccfb5cded3f9d256666e10115e331f6dc4722f298e1b6a","observation_id":"03e56754-5315-454c-a871-8798eca22f06","resolution":{"observed_at":"2026-08-02T00:26:08.885752Z","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":"2026-08-02T00:26:08.888579Z","title":null,"venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.888579Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:505152aa5ea9e41f87e7269030337fc69724ece6c0db1d3ff91b46d8441430b9","observation_id":"0db4156b-5fad-4f5a-964b-f74b253ac86b","resolution":{"observed_at":"2026-08-02T00:26:08.888579Z","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":"2026-08-02T00:26:08.891045Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.891045Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:56c364b5fec3ed57f879809f279dccacc6134c087379a2038ccd8ebb58709b25","observation_id":"85dda783-52a5-4d1d-a243-2d2b09ed1c42","resolution":{"observed_at":"2026-08-02T00:26:08.891045Z","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":"2026-08-02T00:26:08.893183Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.893183Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:0dda0d75eb9d277ee03fd5a7d991092c1f48b341273c2c8753fa3826e9624756","observation_id":"fdcdefa5-cfe4-4ad9-94fa-844931fd7309","resolution":{"observed_at":"2026-08-02T00:26:08.893183Z","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":"2026-08-02T00:26:08.895511Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.895511Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:3d770dbcdf3f2f6b6be67cbd29e3620e6201f15986f556ee5a64ef205dfd1d69","observation_id":"d2e0c181-ba4c-4662-96fd-8b100c5f1aad","resolution":{"observed_at":"2026-08-02T00:26:08.895511Z","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":"2026-08-02T00:26:08.898600Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.898600Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:a2aca3ba0be84c69945e1a375139891bbba21bd964f28ac847e92b06aab0bc7c","observation_id":"47cdc460-72ab-474e-a012-f42914268fe0","resolution":{"observed_at":"2026-08-02T00:26:08.898600Z","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":"2026-08-02T00:26:08.901136Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.901136Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:c44a5761e1c618eefdb08c824599f623a43b40082acda53058bcef2546bfa648","observation_id":"fdad3c88-0ff1-43e0-b7cd-adf6fda613b1","resolution":{"observed_at":"2026-08-02T00:26:08.901136Z","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":"2026-08-02T00:26:08.903458Z","title":null,"venue":null,"work_id":null,"year":2020},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.903458Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:4eb5d586024e39d11c4e0fcaa0c017901b8fe7ac028ea2da51424af3b831e6a6","observation_id":"de34195e-91ea-433b-aab9-97680b027b61","resolution":{"observed_at":"2026-08-02T00:26:08.903458Z","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":"2026-08-02T00:26:08.905717Z","title":"Lov´ asz, M","venue":null,"work_id":null,"year":1975},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.905717Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:c709ac1d33afd062a49c3b0f112fd5f09357891fcb5239bf4849c476742b62a1","observation_id":"22b6b37c-1e1a-4483-9b7f-97c989e1cc6e","resolution":{"observed_at":"2026-08-02T00:26:08.905717Z","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":"2026-08-02T00:26:08.908041Z","title":"Lov´ asz, M","venue":null,"work_id":null,"year":1983},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.908041Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:8fdd6faf83fb4a7aed296f35e11e9c762c658988447bca9f0f385259425f6ee2","observation_id":"905c214a-670c-46a1-bba1-91a9cc0f30c2","resolution":{"observed_at":"2026-08-02T00:26:08.908041Z","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":"2026-08-02T00:26:08.910437Z","title":"Mubayi, Counting substructures I: color critical graphs, Adv","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.910437Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:967b343f318529a1710defdb29cb74d6e7a145db5dd8d5fdfd6e76d2448216ad","observation_id":"e5bae955-49cb-408f-bfe8-f61c00313f36","resolution":{"observed_at":"2026-08-02T00:26:08.910437Z","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":"2026-08-02T00:26:08.912766Z","title":"Nikiforov, Some inequalities for the largest eigenvalue of a graph, Comb","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.912766Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:628a61c6be009d95e8b52e547a179ceefb077286e48a9253c0ccc1ff95eb16b4","observation_id":"eade9e8e-16e5-4ecc-8258-fcc80c12d66f","resolution":{"observed_at":"2026-08-02T00:26:08.912766Z","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":"2026-08-02T00:26:08.915438Z","title":"Nikiforov, A contribution to the Zarankiewicz problem, Linear Algebra Appl","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.915438Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:31f7f557b510a88b7a4a8dfe9808b713d4caabe5a354028a9eabda859d1104d6","observation_id":"d6a56f2b-ea97-48d1-b3dd-b0cb6fd9a040","resolution":{"observed_at":"2026-08-02T00:26:08.915438Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2104.12171","last_updated":"2021-04-25T14:22:17Z","snapshot_observed_at":"2026-07-06T11:03:26.012948Z","submitted_at":"2021-04-25T14:22:17Z","title":"On a theorem of Nosal","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2104.12171","snapshot_observed_at":"2026-08-02T00:26:08.917795Z","title":"Nikiforov, On a theorem of Nosal, arXiv:2104.12171, 2021","venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.917795Z"},"links":{"cited_paper":"/paper/2104.12171","citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:b7630278b9a11afb56c6143ebd35c7fd11e5510d82c6409505d2fb8b28155fc7","observation_id":"52f97ac5-6bb8-43cd-a85e-dccaa6f4e7dc","resolution":{"observed_at":"2026-08-02T00:26:08.917795Z","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":"2026-08-02T00:26:08.920757Z","title":null,"venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.920757Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:dc3d789a4f78dc70cbfc1ceb6fca8cefa4a2b1fd57c7e484b46f515962cdebea","observation_id":"1d0dcd79-cf6b-4f0a-9f5f-d3948e8853c1","resolution":{"observed_at":"2026-08-02T00:26:08.920757Z","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":"2026-08-02T00:26:08.923040Z","title":"Nosal, Eigenvalues of graphs, Master’s thesis, University of Calgary, 1970","venue":null,"work_id":null,"year":1970},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.923040Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:f16f838c303a4233ba42f2c5836845d0deb5b80d2c0bdfddb7712c4b74214aca","observation_id":"f9ac0ef2-1d40-4912-b0dc-29a5f5d21caf","resolution":{"observed_at":"2026-08-02T00:26:08.923040Z","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":"2026-08-02T00:26:08.925623Z","title":"Pikhurko, Z.B","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.925623Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:3a7289da8a66fc10eba6cdee04c23756d9c1876a172b5d784c8fa80f2a3505c7","observation_id":"7516aab3-eee9-46af-bdf7-7bd219aeb944","resolution":{"observed_at":"2026-08-02T00:26:08.925623Z","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":"2026-08-02T00:26:08.928087Z","title":null,"venue":null,"work_id":null,"year":2026},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.928087Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:9619cc8dcb43b07e885063e8e6c617f623b445fcaaf108635f8ad5423fa847ce","observation_id":"4d3c3ef8-8267-4378-a6fa-bfea91624c67","resolution":{"observed_at":"2026-08-02T00:26:08.928087Z","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":"2026-08-02T00:26:08.930443Z","title":null,"venue":null,"work_id":null,"year":2021},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.930443Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:a24152b64244cc392fbe05c0400e99ca7aebddf9df7b19a3d183522f74e4ee24","observation_id":"a3f831d5-045f-4be3-a891-b199d0d2bba3","resolution":{"observed_at":"2026-08-02T00:26:08.930443Z","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":"2026-08-02T00:26:08.932793Z","title":null,"venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.932793Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:939ca6db67086c59616148b82814cf8f6c2c8fc81829d3d07e6f704652477a75","observation_id":"821c7c41-6d63-42e5-b2c3-3b7fc05abc4c","resolution":{"observed_at":"2026-08-02T00:26:08.932793Z","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":"2026-08-02T00:26:08.935075Z","title":"Zhang, On the first two eigenvalues of regular graphs, Linear Algebra Appl","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.935075Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:68f703bd057c9f3d6939bd5486b15043d615e8ec9b669703267f02e455fa6340","observation_id":"f3024e90-4146-483d-a8fe-b4e88df1809d","resolution":{"observed_at":"2026-08-02T00:26:08.935075Z","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":"2026-08-02T00:26:08.937458Z","title":"Zhang, The spectral radius, maximum average degree and cycles of consecutive lengths of graphs, Graphs Comb","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs","version":2},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-02T00:26:08.937458Z"},"links":{"citing_paper":"/paper/2607.15071"},"observation_digest":"sha256:2f12f660e5cef7957e300174896880fad1dcb3d25b35b3d160f8d66df2f1abc1","observation_id":"4df8513d-e10a-4760-bac2-fa8e654885e8","resolution":{"observed_at":"2026-08-02T00:26:08.937458Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2607.15071","last_updated":"2026-07-21T02:40:01Z","latest_version":2,"primary_category":"math.CO","snapshot_observed_at":"2026-08-02T00:26:08.310192Z","submitted_at":"2026-07-16T14:43:37Z","title":"Two problems on booksize and triangular edges in Nosal graphs"},"reference_resolution":{"displayed":32,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":32,"verified_exact":0,"verified_fuzzy":0},"total_outbound_references":32},"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 32 of 32 outbound references and 1 inbound Pith citation observation for arXiv:2607.15071."}