{"as_of":"2026-08-06T01:01:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:e6506e8c5c30829ecac21e058f2523b2a4642a06ca4683e1aff0aa7432a9d20c","coverage":[{"denominator":21,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":21,"source":"paper_references, paper_reference_links","source_observed_at":"2026-05-12T00:54:45.537121Z","state":"measured"},{"denominator":21,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":21,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-05T06:32:48.257954+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/2605.08603/citation-record","integrity":"/paper/2605.08603/integrity","json":"/paper/2605.08603/citation-record.json","paper":"/paper/2605.08603"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-06-05T21:23:00.469572Z","title":"Erd˝ os, C","venue":null,"work_id":"92d44c4a-ea34-4d1b-8c51-9228f4938710","year":1961},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:09f617661a467a04b0a4485bf880fcf8686a32c532e8e91887adda7adbfe5ae4","observation_id":"f73ea6ab-6ad3-406a-b4be-529e3f6dd6bf","resolution":{"observed_at":"2026-05-14T09:28:26.448111Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Infinite and Finite Sets","venue":null,"work_id":"8d328362-389d-4e2d-9d6f-4d40980946f9","year":1975},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:bca0d0a3c655141406f3f607092af798a98e6ee098b3818b77892d326b900e13","observation_id":"726bc1f0-8e21-4a66-98e2-5da5b6a817db","resolution":{"observed_at":"2026-05-14T09:28:26.452098Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, On intersecting families of finite sets, Bull","venue":null,"work_id":"68e8313f-7502-4a2e-b356-49dc56edad46","year":1980},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:9ee76fe5d8d8b573b2cae3fd80cb9e17390623078578ea7f4cb08cec44841dbb","observation_id":"3455c3a7-4baa-464f-bc15-f82fa5b90b13","resolution":{"observed_at":"2026-05-14T09:28:26.385553Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, Erd˝ os-Ko-Rado theorem with conditions on the maximal degree, J","venue":null,"work_id":"76bddae2-a100-4e26-a134-29747133729f","year":1987},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:9b266438db0ddd76246ed790100be659b9746bd947034524e2b06c665c057ccb","observation_id":"65d37da0-493a-422d-8e71-a2a4a215e547","resolution":{"observed_at":"2026-05-14T09:28:26.431545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, A near-exponential improvement of a bound of Erd˝ os and Lov´ asz on max- imal intersecting families, Combinatorics, Probability & Computing 28(5) (2019), 733–739","venue":null,"work_id":"8d394854-7c4e-4a48-aade-2552d0629e34","year":2019},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:a5f955c0eb926a0615c808ab2d73d5ac8220ece01eaadb93ce3249df422c905e","observation_id":"cfaa18b0-1bbf-4c2d-a5d8-68876421c056","resolution":{"observed_at":"2026-05-14T09:28:26.435925Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, On the maximum of the sum of the sizes of non-trivial cross-intersecting families, Combinatorica 44 (2024), 15–35","venue":null,"work_id":"a6145892-49d5-4b93-b9da-1e756e1f205d","year":2024},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:5808557f17cbf52cc0f0a446ec23a7bda5b083559f4fc57275a8e4e4bb9d9adc","observation_id":"49aca883-1332-4372-9bec-8ca82950b89c","resolution":{"observed_at":"2026-05-14T09:28:26.439986Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, K","venue":null,"work_id":"8729bc94-1660-4dbc-99c9-78132cb66326","year":1995},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:df7c7d71c3c236ef17ad7beb060c96c81955ddef095ba461935de0a9789c611d","observation_id":"3dc01718-c129-411c-ae8f-40121da53314","resolution":{"observed_at":"2026-05-14T09:28:26.419545Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, N","venue":null,"work_id":"c74152d3-937c-4d72-a5c0-256102b54712","year":1992},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:bff5a1ba9d00112b1d49780d4dd2d135fb84688ab1b0cff84f8039130d9ff969","observation_id":"e5a87013-e604-4e97-9a8d-2eca922cdcec","resolution":{"observed_at":"2026-05-14T09:28:26.415836Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, J","venue":null,"work_id":"8732bc64-aebc-4a6a-b055-163a80a7deb9","year":2023},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:fd549d5bca34159f7e1f7c3e60685eecded6bcff6512476a8c4fc34040cc6c5f","observation_id":"a84229b4-db1f-4407-8900-41c0b4287b4d","resolution":{"observed_at":"2026-05-14T09:28:26.427582Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, J","venue":null,"work_id":"f4d0b71a-3657-4883-8514-24a9cc009464","year":2025},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:7a31d86f0f81fe71fc9355b32cf02aa974bc8284b3636310510c8bd084869337","observation_id":"2e16a451-f1d1-443d-88e1-6050e0b635d9","resolution":{"observed_at":"2026-05-14T09:28:26.404438Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, J","venue":null,"work_id":"718972ae-a72a-406e-9ad6-3c6741b94357","year":2025},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:f714ea1bcf2d1ed9441a3966155805555ac6a4847f5961c4973145b8a5b78738","observation_id":"9543ce28-1c19-4f5d-adf6-1b8ba54fdfbd","resolution":{"observed_at":"2026-05-14T09:28:26.408278Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Frankl, J","venue":null,"work_id":"b2e82d53-21a5-456e-b342-9c196d2cff41","year":null},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:82366c81732c9a3494cbec61a3151fb15883d6770ce3e0bc9634c2397ce07843","observation_id":"441a2f7c-38db-497b-9019-913736820ac5","resolution":{"observed_at":"2026-05-14T09:28:26.401011Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Furuya, M","venue":null,"work_id":"ff478b73-3292-4bc0-b307-3b2fc522ca8e","year":2013},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:feb9a709fbb90bc26189a88994539971deda2ee3946ddc7f89aa9ab12ae99eaa","observation_id":"2f170cc2-7168-4764-b14f-18a141c82e86","resolution":{"observed_at":"2026-05-14T09:28:26.412103Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Hilton, The Erd˝ os-Ko-Rado Theorem with valency conditions, unpublished manuscript","venue":null,"work_id":"c54a7470-32f7-4429-9ac3-5e6882ae6c54","year":1976},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:7b6d73bc8a0c30dafae2b1485d6062fef9a0574cb989ff8d7565b363f44e6f6d","observation_id":"f228ba35-beba-48dc-b974-1aa489cc23da","resolution":{"observed_at":"2026-05-14T09:28:26.424010Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Hilton, E.C","venue":null,"work_id":"acb79184-e9b6-4917-a687-3c9ab8ba7075","year":1967},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:07dc815e23d9ebffc62d61387c0ccca79b5bfb302d2b7cf275211ee5ab9ea5d6","observation_id":"dbc1e1e3-a726-4434-8078-4953e3f24c6d","resolution":{"observed_at":"2026-05-14T09:28:26.443866Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Katona, A theorem of finite sets, Theory of Graphs","venue":null,"work_id":"a8e4b6c9-5a0c-4dcc-be6c-4f0281d62435","year":1966},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:0f40b756c69e30d86aee59e449a24c41eb646a6fa172ce32461babd803c1bd7c","observation_id":"1e191179-e2f3-40fa-acdb-a73cb4bfbd9d","resolution":{"observed_at":"2026-05-14T09:28:26.464096Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Kruskal, The number of simplices in a complex, Mathematical Optimization Techniques 251 (1963), 251–278","venue":null,"work_id":"fb9358d7-91ee-40ef-bcbc-094780c71071","year":1963},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:2fa64c930c6383ce2047ebcb83458e970febfd6205dcf1ce040b585db16e5c7c","observation_id":"c5351e72-d225-4cb5-b855-3d6b938ea0d5","resolution":{"observed_at":"2026-05-14T09:28:26.397655Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Kupavskii, Intersecting families with covering number 3, J","venue":null,"work_id":"354c982c-2b32-487d-a04f-e2dfddff9671","year":2026},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:474ab60a04bb4b631e0eeb9a1b4a277170b12925284bba99c672c2495b295435","observation_id":"96cd1ec1-ef04-470f-9af1-e3448c23b402","resolution":{"observed_at":"2026-05-14T09:28:26.460395Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Lov´ asz, On minimax theorems of combinatorics, Math","venue":null,"work_id":"67bbfbf1-8970-42d5-a1e6-bd1418209fa4","year":1975},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:4a34773b342ac4b7e034f7a1f40b6b65b2b00fa69b62009b03a173dc8efe81f8","observation_id":"2b69fce9-29a6-48f2-ad73-5b5311e41053","resolution":{"observed_at":"2026-05-14T09:28:26.456014Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Sperner, Ein Satz ¨ uber Untermengen einer endlichen Menge, Math","venue":null,"work_id":"77f3fd26-c6a7-407c-861f-a12b69c3e4b9","year":1928},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:0d79d26307320a602103cd5c854f4cf00fe30809539461b752c34ed79d3ba842","observation_id":"0e18f5f9-f2ec-4cb7-87d0-c998e76edd6b","resolution":{"observed_at":"2026-05-14T09:28:26.389782Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+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":"2026-06-05T21:23:00.469572Z","title":"Zakharov, On the size of maximal intersecting families, Combinatorics, Probability & Computing 33 (2024), 32–49","venue":null,"work_id":"019b5524-e072-4c58-bfef-87a00100c592","year":2024},"citing_paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-05-12T00:54:45.537121Z"},"links":{"citing_paper":"/paper/2605.08603"},"observation_digest":"sha256:eae6f21d797bc3e7b59eae14443f892bce65e1cef594d2ce585efc041025c433","observation_id":"fc91f8e6-36c8-4fa6-b4dc-85d31745dd88","resolution":{"observed_at":"2026-05-14T09:28:26.393701Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-05T06:32:48.257954+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"state":"measured"}}],"paper":{"arxiv_id":"2605.08603","last_updated":"2026-05-09T01:51:50Z","latest_version":1,"primary_category":"math.CO","snapshot_observed_at":"2026-07-06T23:20:47.880233Z","submitted_at":"2026-05-09T01:51:50Z","title":"Intersecting families with covering number three II"},"reference_resolution":{"displayed":21,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":0,"verified_exact":0,"verified_fuzzy":21},"total_outbound_references":21},"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":"2026-08-05T06:32:48.257954+00:00","source":"crossref"},{"observed_at":"2026-08-05T06:32:44.755628+00:00","source":"retraction_watch"}],"thesis":"As of 6 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:2605.08603."}