{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:747AVUXRN4LCNXXEUB6IKRZ2QY","short_pith_number":"pith:747AVUXR","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"},"canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","source":{"kind":"arxiv","id":"1603.06887","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06887","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06887v2","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06887","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"747AVUXRN4LC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"747AVUXRN4LCNXXE","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"747AVUXR","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:747AVUXRN4LCNXXEUB6IKRZ2QY","target":"record","payload":{"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"},"canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","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"},"source_kind":"arxiv","source_id":"1603.06887","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhdaOsVo9vYlxoYGvlYemrMKLoAoWJ9sXHau6zaH6JR/LB/4iW5WDr4NV4NS6PSinXe4djI1bJ2oCu+clse7Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:38:32.562093Z"},"content_sha256":"31c0f48eeddd10a5cc8e3197d24112a1fb94d73da27c60a05af058975432fcfb","schema_version":"1.0","event_id":"sha256:31c0f48eeddd10a5cc8e3197d24112a1fb94d73da27c60a05af058975432fcfb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:747AVUXRN4LCNXXEUB6IKRZ2QY","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ewudq+ICuvbJOHG7lxMM6564qptooHVh4n7pF5NH0IRwjbdSF78WRi/JmFEfY3V7Adn9Ux9xCzTx2Z9PIamLBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T23:38:32.562455Z"},"content_sha256":"337e3493834ae04b688882fcb23f54867732ecef7234ce3b5c1a927f34f63743","schema_version":"1.0","event_id":"sha256:337e3493834ae04b688882fcb23f54867732ecef7234ce3b5c1a927f34f63743"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/bundle.json","state_url":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T23:38:32Z","links":{"resolver":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY","bundle":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/bundle.json","state":"https://pith.science/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/747AVUXRN4LCNXXEUB6IKRZ2QY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:747AVUXRN4LCNXXEUB6IKRZ2QY","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"05315ec226f6d84f7c15666b173fc778edad49a90f8f94bb4c50b724c30b5ba9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-22T17:47:49Z","title_canon_sha256":"17be3afc033413675a3086b7e34b8ed2c76b78f0e92049e288b1817451bed344"},"schema_version":"1.0","source":{"id":"1603.06887","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06887","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06887v2","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06887","created_at":"2026-05-18T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"747AVUXRN4LC","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"747AVUXRN4LCNXXE","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"747AVUXR","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:337e3493834ae04b688882fcb23f54867732ecef7234ce3b5c1a927f34f63743","target":"graph","created_at":"2026-05-18T01:18:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Adi Jarden","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-22T17:47:49Z","title":"The First Time KE is Broken up"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06887","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:31c0f48eeddd10a5cc8e3197d24112a1fb94d73da27c60a05af058975432fcfb","target":"record","created_at":"2026-05-18T01:18:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"05315ec226f6d84f7c15666b173fc778edad49a90f8f94bb4c50b724c30b5ba9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-03-22T17:47:49Z","title_canon_sha256":"17be3afc033413675a3086b7e34b8ed2c76b78f0e92049e288b1817451bed344"},"schema_version":"1.0","source":{"id":"1603.06887","kind":"arxiv","version":2}},"canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff3e0ad2f16f1626dee4a07c85473a8638fed577fd90110c68e3edc054cc0b0d","first_computed_at":"2026-05-18T01:18:13.634783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:13.634783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h1TpJspcKdiessQ+7X64IhWzCmkBh36MI+6Y2GOtpMdsUQWMVsjpwnVj1shQy1Yl8jAG7IMGxeQWJzwH7ulWCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:13.635652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06887","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31c0f48eeddd10a5cc8e3197d24112a1fb94d73da27c60a05af058975432fcfb","sha256:337e3493834ae04b688882fcb23f54867732ecef7234ce3b5c1a927f34f63743"],"state_sha256":"78de11ea6c962d0fe7d7e801cb8d7667142fc34db339925149a0a2dd135f4d20"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gukyipxhyh3+229SRVTx+QQfeRDlA8BiQkPatTZEHsU7Jr3X0/iPp3ab8MJ1t14RzZY27De4VDv+dDTKM2Q7Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T23:38:32.564488Z","bundle_sha256":"ff0d349d7cb0637e99529b6d69faef763852a3c3effdb3d28abda2ef5698eb54"}}