{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:747AVUXRN4LCNXXEUB6IKRZ2QY","short_pith_number":"pith:747AVUXR","schema_version":"1.0","canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","source":{"kind":"arxiv","id":"1603.06887","version":2},"attestation_state":"computed","paper":{"title":"The First Time KE is Broken up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adi Jarden","submitted_at":"2016-03-22T17:47:49Z","abstract_excerpt":"A relevant collection is a collection, $F$, of sets, such that each set in $F$ has the same cardinality, $\\alpha(F)$. A Konig Egervary (KE) collection is a relevant collection $F$, that satisfies $|\\bigcup F|+|\\bigcap F|=2\\alpha(F)$. An hke (hereditary KE) collection is a relevant collection such that all of his non-empty subsets are KE collections. In \\cite{jlm} and \\cite{dam}, Jarden, Levit and Mandrescu presented results concerning graphs, that give the motivation for the study of hke collections. In \\cite{hke}, Jarden characterize hke collections.\n  Let $\\Gamma$ be a relevant collection su"},"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":"1603.06887","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-22T17:47:49Z","cross_cats_sorted":[],"title_canon_sha256":"17be3afc033413675a3086b7e34b8ed2c76b78f0e92049e288b1817451bed344","abstract_canon_sha256":"05315ec226f6d84f7c15666b173fc778edad49a90f8f94bb4c50b724c30b5ba9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:13.635652Z","signature_b64":"h1TpJspcKdiessQ+7X64IhWzCmkBh36MI+6Y2GOtpMdsUQWMVsjpwnVj1shQy1Yl8jAG7IMGxeQWJzwH7ulWCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","last_reissued_at":"2026-05-18T01:18:13.634783Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:13.634783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The First Time KE is Broken up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Adi Jarden","submitted_at":"2016-03-22T17:47:49Z","abstract_excerpt":"A relevant collection is a collection, $F$, of sets, such that each set in $F$ has the same cardinality, $\\alpha(F)$. A Konig Egervary (KE) collection is a relevant collection $F$, that satisfies $|\\bigcup F|+|\\bigcap F|=2\\alpha(F)$. An hke (hereditary KE) collection is a relevant collection such that all of his non-empty subsets are KE collections. In \\cite{jlm} and \\cite{dam}, Jarden, Levit and Mandrescu presented results concerning graphs, that give the motivation for the study of hke collections. In \\cite{hke}, Jarden characterize hke collections.\n  Let $\\Gamma$ be a relevant collection su"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06887","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1603.06887","created_at":"2026-05-18T01:18:13.634903+00:00"},{"alias_kind":"arxiv_version","alias_value":"1603.06887v2","created_at":"2026-05-18T01:18:13.634903+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06887","created_at":"2026-05-18T01:18:13.634903+00:00"},{"alias_kind":"pith_short_12","alias_value":"747AVUXRN4LC","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_16","alias_value":"747AVUXRN4LCNXXE","created_at":"2026-05-18T12:30:04.600751+00:00"},{"alias_kind":"pith_short_8","alias_value":"747AVUXR","created_at":"2026-05-18T12:30:04.600751+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY","json":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY.json","graph_json":"https://pith.science/api/pith-number/747AVUXRN4LCNXXEUB6IKRZ2QY/graph.json","events_json":"https://pith.science/api/pith-number/747AVUXRN4LCNXXEUB6IKRZ2QY/events.json","paper":"https://pith.science/paper/747AVUXR"},"agent_actions":{"view_html":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY","download_json":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY.json","view_paper":"https://pith.science/paper/747AVUXR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1603.06887&json=true","fetch_graph":"https://pith.science/api/pith-number/747AVUXRN4LCNXXEUB6IKRZ2QY/graph.json","fetch_events":"https://pith.science/api/pith-number/747AVUXRN4LCNXXEUB6IKRZ2QY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/action/storage_attestation","attest_author":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/action/author_attestation","sign_citation":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/action/citation_signature","submit_replication":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/action/replication_record"}},"created_at":"2026-05-18T01:18:13.634903+00:00","updated_at":"2026-05-18T01:18:13.634903+00:00"}