{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:LRSIS2GLV6FVYYSRGBN63UOWNN","short_pith_number":"pith:LRSIS2GL","schema_version":"1.0","canonical_sha256":"5c648968cbaf8b5c6251305bedd1d66b58ca394aec098c352e96a609b66b5d1c","source":{"kind":"arxiv","id":"2311.02246","version":1},"attestation_state":"computed","paper":{"title":"Intersection theorems for uniform subfamilies of hereditary families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii","submitted_at":"2023-11-03T21:29:30Z","abstract_excerpt":"A family $\\mathcal C$ of sets is hereditary if whenever $A\\in \\mathcal C$ and $B\\subset A$, we have $B\\in \\mathcal C$. Chv\\'atal conjectured that the largest intersecting subfamily of a hereditary family is the family of all sets containing a fixed element. This is a generalization of the non-uniform Erd\\H{o}s-Ko-Rado theorem.\n  A natural uniform variant of this question, which is essentially a generalization for the uniform Erd\\H{o}s-Ko-Rado theorem, was suggested by Borg: given a hereditary family $\\mathcal C$, in which all maximal sets have size at least $n$, what is the largest intersectin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2311.02246","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-11-03T21:29:30Z","cross_cats_sorted":[],"title_canon_sha256":"037836cf57da540f7062c6115e97ae54c0d78c0d012481644abb06090e617db4","abstract_canon_sha256":"e41d9283d7f7b7d53814b2e3f4fa66db279278bd6322f14c62d226177c178e69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:09:08.163914Z","signature_b64":"3kGOlZ7w07mS7fGLENyMA/i2CfHhk8Ty3lL/h8t4HeEVPn3VRCh9xTq9a61KropOZlmDo3RPtU0Y45+Jh7ZRCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c648968cbaf8b5c6251305bedd1d66b58ca394aec098c352e96a609b66b5d1c","last_reissued_at":"2026-07-05T07:09:08.163475Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:09:08.163475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection theorems for uniform subfamilies of hereditary families","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrey Kupavskii","submitted_at":"2023-11-03T21:29:30Z","abstract_excerpt":"A family $\\mathcal C$ of sets is hereditary if whenever $A\\in \\mathcal C$ and $B\\subset A$, we have $B\\in \\mathcal C$. Chv\\'atal conjectured that the largest intersecting subfamily of a hereditary family is the family of all sets containing a fixed element. This is a generalization of the non-uniform Erd\\H{o}s-Ko-Rado theorem.\n  A natural uniform variant of this question, which is essentially a generalization for the uniform Erd\\H{o}s-Ko-Rado theorem, was suggested by Borg: given a hereditary family $\\mathcal C$, in which all maximal sets have size at least $n$, what is the largest intersectin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.02246","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.02246/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2311.02246","created_at":"2026-07-05T07:09:08.163526+00:00"},{"alias_kind":"arxiv_version","alias_value":"2311.02246v1","created_at":"2026-07-05T07:09:08.163526+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.02246","created_at":"2026-07-05T07:09:08.163526+00:00"},{"alias_kind":"pith_short_12","alias_value":"LRSIS2GLV6FV","created_at":"2026-07-05T07:09:08.163526+00:00"},{"alias_kind":"pith_short_16","alias_value":"LRSIS2GLV6FVYYSR","created_at":"2026-07-05T07:09:08.163526+00:00"},{"alias_kind":"pith_short_8","alias_value":"LRSIS2GL","created_at":"2026-07-05T07:09:08.163526+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.12380","citing_title":"Forbidden Intersection Theorems for Matrix Spaces","ref_index":11,"is_internal_anchor":false},{"citing_arxiv_id":"2607.00318","citing_title":"A Complete Intersection Theorem for Large Permutation Groups","ref_index":33,"is_internal_anchor":false},{"citing_arxiv_id":"2605.04987","citing_title":"Matchings in permutations","ref_index":21,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN","json":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN.json","graph_json":"https://pith.science/api/pith-number/LRSIS2GLV6FVYYSRGBN63UOWNN/graph.json","events_json":"https://pith.science/api/pith-number/LRSIS2GLV6FVYYSRGBN63UOWNN/events.json","paper":"https://pith.science/paper/LRSIS2GL"},"agent_actions":{"view_html":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN","download_json":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN.json","view_paper":"https://pith.science/paper/LRSIS2GL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2311.02246&json=true","fetch_graph":"https://pith.science/api/pith-number/LRSIS2GLV6FVYYSRGBN63UOWNN/graph.json","fetch_events":"https://pith.science/api/pith-number/LRSIS2GLV6FVYYSRGBN63UOWNN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN/action/storage_attestation","attest_author":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN/action/author_attestation","sign_citation":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN/action/citation_signature","submit_replication":"https://pith.science/pith/LRSIS2GLV6FVYYSRGBN63UOWNN/action/replication_record"}},"created_at":"2026-07-05T07:09:08.163526+00:00","updated_at":"2026-07-05T07:09:08.163526+00:00"}