{"as_of":"2026-08-12T05:14:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:86abf47c9f9971716a22944fe88d5b29c318a1ff440ab82aae4d106462a91d27","coverage":[{"denominator":26,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":26,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-11T00:42:02.369772Z","state":"measured"},{"denominator":26,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":26,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-11T06:34:44.6726+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/2608.07607/citation-record","integrity":"/paper/2608.07607/integrity","json":"/paper/2608.07607/citation-record.json","paper":"/paper/2608.07607"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.864820Z","title":"New bounds for Zarankiewicz numbers via reinforced LLM evolutionary search, 2026","venue":null,"work_id":"7edd219f-14b2-4b55-beb0-c7658a959ea5","year":2026},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.252304Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:3b00d54300e0e6547f9e4fbeda741dd67e65d63024fbb7a223d272282d1c2d33","observation_id":"3f6c5c01-0e2f-4dad-b421-994aa343fd9a","resolution":{"observed_at":"2026-08-11T00:42:02.869449Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2202.05507","last_updated":"2024-04-09T18:19:26Z","snapshot_observed_at":"2026-08-11T12:42:35.967100Z","submitted_at":"2022-02-11T08:43:53Z","title":"Exact values for unbalanced Zarankiewicz numbers","version":2},"cited_work":{"arxiv_id":"2202.05507","doi":null,"metadata_source":"pith","pith_arxiv_id":"2202.05507","snapshot_observed_at":"2026-08-11T00:42:02.572656Z","title":"Exact values for unbalanced Zarankiewicz numbers","venue":"math.CO","work_id":"ee6fe164-b520-4335-b070-82a1c472ab53","year":2022},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.257920Z"},"links":{"cited_paper":"/paper/2202.05507","citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:79a61b83ccd115cf3539e40f9ad3777b0d31bd4a5339cff8fed88a303ab73567","observation_id":"7b4b7559-aa27-4fd4-bfc2-b2c4a7443da2","resolution":{"observed_at":"2026-08-11T00:42:02.577354Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2310.12685","last_updated":"2024-07-12T03:45:20Z","snapshot_observed_at":"2026-08-05T20:53:23.566356Z","submitted_at":"2023-10-19T12:31:28Z","title":"Zarankiewicz numbers near the triple system threshold","version":2},"cited_work":{"arxiv_id":"2310.12685","doi":null,"metadata_source":"pith","pith_arxiv_id":"2310.12685","snapshot_observed_at":"2026-08-11T00:42:02.551839Z","title":"Zarankiewicz numbers near the triple system threshold","venue":"math.CO","work_id":"b9ad6d2b-4c96-4055-b66f-45356ecd92e3","year":2023},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.263636Z"},"links":{"cited_paper":"/paper/2310.12685","citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:da66089a21c7a023309aaf64ddeca0f638c4f37f764c4fea97025b9cf7d034db","observation_id":"60e6eebd-4043-4a1a-8ce2-e5018d0347b5","resolution":{"observed_at":"2026-08-11T00:42:02.557580Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.850875Z","title":"Discrete Mathematics and its Applications","venue":null,"work_id":"17d0a4b8-50d9-4822-aab0-b068d34cbd81","year":2007},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.269703Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:5deb8547d91112b0c66017c01306dfdec9ea082be2db5c20fcf3ecd306668397","observation_id":"69436837-f7d2-4c2c-a3e1-46101373edab","resolution":{"observed_at":"2026-08-11T00:42:02.855499Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.836049Z","title":"Collins, Alexander W","venue":null,"work_id":"6b4e26a3-f5d6-4e87-ae89-9463fee7ffa5","year":2016},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.275068Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:b857deef3fbe0e374bf55480dc6cbf55392237af5131105840c6f5805dab7c0f","observation_id":"8ace5d29-0ed1-42f9-a93d-73cb96d6dc76","resolution":{"observed_at":"2026-08-11T00:42:02.840729Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2007.12816","last_updated":"2021-04-11T19:43:34Z","snapshot_observed_at":"2026-08-11T15:50:52.182641Z","submitted_at":"2020-07-25T00:45:04Z","title":"Some remarks on the Zarankiewicz problem","version":3},"cited_work":{"arxiv_id":"2007.12816","doi":null,"metadata_source":"pith","pith_arxiv_id":"2007.12816","snapshot_observed_at":"2026-08-11T00:42:02.531208Z","title":"Some remarks on the Zarankiewicz problem","venue":"math.CO","work_id":"5149e780-eb97-464d-9e51-03c0242f1ac2","year":2020},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.279696Z"},"links":{"cited_paper":"/paper/2007.12816","citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:388ebbfe8eaaa24416a91d2c4a3723aa2e36f3cd1c634ad0e4a2828797799763","observation_id":"3d39b00c-7fd8-4eb7-bffc-edf5146a3654","resolution":{"observed_at":"2026-08-11T00:42:02.536396Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.822239Z","title":"Teilweise Lösung eines verallgemeinerten Problems von K","venue":null,"work_id":"9d8c3611-3781-4638-af13-42d551afd00c","year":1956},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.284828Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:181cd2c51aae0370d2cfb4822019eef8d63e4bffe2f90c49bf906c57616e3ee1","observation_id":"fe69888f-a2e2-4b41-ae95-9a6a91f5d069","resolution":{"observed_at":"2026-08-11T00:42:02.826532Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.808174Z","title":"The Zarankiewicz problem, cages, and geometries.Annales Universitatis Scientiarum Budapestinensis de Rolando Eötvös Nominatae, Sectio Mathematica, 56(1):3–37, 2013","venue":null,"work_id":"dd92162f-ce43-44c1-afcb-f4c2ca5439b5","year":2013},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.289955Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:14cf1e4b0dca2173437bfc232a6407f62c98f30c18dcaa5d9110f242c599dee9","observation_id":"3973ba5f-a57f-42dd-9957-d8c7b84ed917","resolution":{"observed_at":"2026-08-11T00:42:02.812820Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":"2411.18842","doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.504738Z","title":"Improved upper bounds on Zarankiewicz numbers.Discrete Math- ematics, 349(5):114924, 2026","venue":null,"work_id":"ab07bfd5-c2e6-4753-8956-9403174ed497","year":2026},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.294399Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:08b34e69849f6fd083da5c57a9bfa095948298edb800c47b45133be648ef2781","observation_id":"b804ccd5-ff7d-4176-b1d4-54c5d8f898f2","resolution":{"observed_at":"2026-08-11T00:42:02.514889Z","resolver_source":"raw_fallback","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.794103Z","title":"An upper bound on Zarankiewicz’ prob- lem.Combinatorics, Probability and Computing, 5(1):29– 33, 1996","venue":null,"work_id":"ab3764e8-1af2-4335-b39e-c001c2d625a5","year":1996},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.299176Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:064162613b92608f10f484eb00a6fdc0a124da0f404cca7a96324ade08163373","observation_id":"febdbfd5-c1d5-4eee-812d-cee8953ca34d","resolution":{"observed_at":"2026-08-11T00:42:02.799274Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1611.06827","last_updated":"2020-02-28T16:16:10Z","snapshot_observed_at":"2026-07-06T05:19:29.105134Z","submitted_at":"2016-11-21T15:12:33Z","title":"The existence of designs via iterative absorption: hypergraph $F$-designs for arbitrary $F$","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1611.06827","snapshot_observed_at":"2026-08-11T00:42:02.303507Z","title":"The existence of designs via iterative absorption: hypergraph F-designs for arbitrary F.Memoirs of the American Mathematical Society, 284(1406), 2023","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.303507Z"},"links":{"cited_paper":"/paper/1611.06827","citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:548a700e94335cdc20789d363a234222d4abb112731a5ab90c45819b76c3036d","observation_id":"757f74f8-152e-4367-833e-93704c21ecc4","resolution":{"observed_at":"2026-08-11T00:42:02.303507Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.780680Z","title":"Henning, and Or- trud R","venue":null,"work_id":"f6943479-ae32-4b80-9d41-46cff9350c17","year":2000},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.308414Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:3e63c769c6188f75c0f708fc264706d7b755b8b27523ea5163b736fd995984c0","observation_id":"de57e55e-2aa3-4cef-b8d5-da599d6a2b25","resolution":{"observed_at":"2026-08-11T00:42:02.785114Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.767202Z","title":null,"venue":null,"work_id":"5b0fa32d-7103-419b-8bd5-aa250bf4bd19","year":null},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.312781Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:80df162f2c34cc682e7290aa099b66e35749634ec227ce56b8163b7a8e55b6f7","observation_id":"677b6e91-8777-4252-b981-0299d5d69218","resolution":{"observed_at":"2026-08-11T00:42:02.771533Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.738216Z","title":"On quadruple systems.Canadian Journal of Mathematics, 12:145–157, 1960","venue":null,"work_id":"5cb2d1b7-69b7-4c54-b7f8-7407c4b95a7a","year":1960},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.320604Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:3b6f82196754be7dbb0bbaac85cfadd103bdc3179ab733e0ced2d823c287cd3b","observation_id":"bf9c2897-6a31-4b51-b3a6-e4aaf6745630","resolution":{"observed_at":"2026-08-11T00:42:02.743143Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.722611Z","title":"A class of three-designs.Journal of Combinatorial Theory, Series A, 26(1):1–19, 1979","venue":null,"work_id":"e1bf1dd3-3160-44cb-b803-5d41087aff0f","year":1979},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.324383Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:088ba5bdcecdca224698476efec45dc901c504e2808ba7fa22fc549336290994","observation_id":"0a5c94c8-b0ae-46d1-817e-4e2866ce1ae9","resolution":{"observed_at":"2026-08-11T00:42:02.727756Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.706714Z","title":"On a combinatorical problem","venue":null,"work_id":"ce11213f-95d0-4e7c-80d4-43be2437dae1","year":1958},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.328442Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:66aa250a8006716aff48a42ae4e813f44267944e964c03d3fb380f897c5a3513","observation_id":"b5c641ad-560e-4e48-a3a7-587d93127703","resolution":{"observed_at":"2026-08-11T00:42:02.711571Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.691556Z","title":null,"venue":null,"work_id":"5b424da9-9ff2-48f0-8664-f6d74657e3b6","year":1978},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.332436Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:50e82c4873a219ea439445ec6b0d53003e1be408eba4b7f5304a369266c67d33","observation_id":"30715fae-e6fc-49de-a6cc-a4478a2d842b","resolution":{"observed_at":"2026-08-11T00:42:02.696363Z","resolver_source":"raw_fallback","status":"unresolved"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2411.18291","last_updated":"2024-11-27T12:28:53Z","snapshot_observed_at":"2026-07-06T19:57:55.925634Z","submitted_at":"2024-11-27T12:28:53Z","title":"A short proof of the existence of designs","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2411.18291","snapshot_observed_at":"2026-08-11T00:42:02.336658Z","title":"The existence of designs, 2014","venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.336658Z"},"links":{"cited_paper":"/paper/2411.18291","citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:8a2976f1bd21ef7ed8ea0beec7b90ceefa8866b14da1dda28f34574cb87a1311","observation_id":"924af2a9-8f00-48fa-bc06-81bacd51c771","resolution":{"observed_at":"2026-08-11T00:42:02.336658Z","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":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.675721Z","title":"Sós, and Pál Turán","venue":null,"work_id":"85d0bb99-dce5-4389-ae2d-ba380fc6a7a4","year":1954},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.341789Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:7b7da64b3e60bdc4162fab74173b2e35328afdaae0c6a848db7d7c872ddc3801","observation_id":"d0c6f7ce-28ca-4a77-a8c9-d18199fef621","resolution":{"observed_at":"2026-08-11T00:42:02.680909Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.660310Z","title":"A new result on the problem of Zarankiewicz.Journal of Combinatorial Theory, Series A, 31(2):126–130, 1981","venue":null,"work_id":"4df193ac-7d06-40d1-a4e6-afb7cf48195f","year":1981},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.346451Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:f2254bd06d8bdf6b94463b1be358dbf80e45b481f37ebbc5b9dc57af5676f858","observation_id":"a4805af2-e5b2-47d1-a14e-d05efae56315","resolution":{"observed_at":"2026-08-11T00:42:02.665311Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.645464Z","title":"A contribution to the Zarankiewicz problem.Linear Algebra and its Applications, 432(6):1405–1411, 2010","venue":null,"work_id":"4dc18e17-2659-445c-8898-f0a5dd2241e8","year":2010},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.351020Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:dfdc4bc18b711f0feeafac1556474b5208eb90107976ac09d83540e048f54802","observation_id":"05b1e094-a724-4141-8e79-e9ebbb0e9a23","resolution":{"observed_at":"2026-08-11T00:42:02.650234Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.630854Z","title":"Über ein Problem von K","venue":null,"work_id":"fd2e8f74-cf66-4a48-a0be-19bcedeef568","year":1958},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.355964Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:4fe9c8429e3355b605ad48bbe1f42c621cfda6289480f49fb7be9b111f2b2d1a","observation_id":"c2c2ca1f-23f9-4dd9-a2f3-6bfe64345896","resolution":{"observed_at":"2026-08-11T00:42:02.635286Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.616854Z","title":"A problem of Zarankiewicz.Journal of Combinatorial Theory, Series A, 18(2):187–198, 1975","venue":null,"work_id":"d643770e-f72f-4826-b4c1-642bb8ba6271","year":1975},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.360623Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:982eb9334e2a8ef64252c9afb7bfdabfeb29b2ccd454b6b4a7538a400460e2d7","observation_id":"19745945-4ba7-41a3-bf8e-a34efb5ff2e5","resolution":{"observed_at":"2026-08-11T00:42:02.621136Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.601181Z","title":"An attack on Zarankiewicz’s problem through SAT solving, 2022","venue":null,"work_id":"7809f212-bb12-4f3f-91d3-1cdf724d1e52","year":2022},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.365224Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:95f5d91f1ef40ed9f49fca264fb83aecc04abec507ebac16bacc483c078a254e","observation_id":"98e58168-c266-4959-a656-229a8573bb64","resolution":{"observed_at":"2026-08-11T00:42:02.606435Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.586978Z","title":"Problem p 101.Colloquium Mathematicum, 2:301, 1951","venue":null,"work_id":"3c67621f-e760-4639-97ea-77d0272cf3c3","year":1951},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.369772Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:f662c1fe7a53d7a1f16f7f85fa386d5d72e38fb69ac1585cc453497ebed6ce73","observation_id":"05e5d10f-c8e1-41ff-8879-2f931410d5be","resolution":{"observed_at":"2026-08-11T00:42:02.591161Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-11T00:42:02.752866Z","title":null,"venue":null,"work_id":"2cad548d-d549-4775-9c6b-a2580fc25663","year":1969},"citing_paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers","version":1},"reference_index":148,"source":"pdf_text","source_observed_at":"2026-08-11T00:42:02.316790Z"},"links":{"citing_paper":"/paper/2608.07607"},"observation_digest":"sha256:758338e48fda25c9e599f8bdeb1ccff218556444aa4b650560d91cf1020153fc","observation_id":"c4eced90-645d-4269-a0f9-9f17bea0264e","resolution":{"observed_at":"2026-08-11T00:42:02.757051Z","resolver_source":"raw_fallback","status":"parse_uncertain"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2608.07607","last_updated":"2026-08-06T20:20:47Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-08-12T04:12:38.246444Z","submitted_at":"2026-08-06T20:20:47Z","title":"A congruence obstruction to Roman's bound for Zarankiewicz numbers"},"reference_resolution":{"displayed":26,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":1,"unresolved":4,"verified_exact":4,"verified_fuzzy":17},"total_outbound_references":26},"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":"2026-08-11T06:34:44.6726+00:00","source":"crossref"},{"observed_at":"2026-08-11T06:34:36.301508+00:00","source":"retraction_watch"}],"thesis":"As of 12 August 2026, this Paper Citation Record lists 26 of 26 outbound references and 0 inbound Pith citation observations for arXiv:2608.07607."}