{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DTZV7Q5AJZOP3UCZA6T24NBOJW","short_pith_number":"pith:DTZV7Q5A","canonical_record":{"source":{"id":"1605.06361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T14:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"7de1adad3546aa33904ea1965ba3de083da65b64714c825b611f137f24d1e76b","abstract_canon_sha256":"f0acfea8701ce2c13765ad221586639437aa33c041daf31c51cb1187af542a14"},"schema_version":"1.0"},"canonical_sha256":"1cf35fc3a04e5cfdd05907a7ae342e4d8d08802b8c593d8fc6917dd9223b33ac","source":{"kind":"arxiv","id":"1605.06361","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06361","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06361v2","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06361","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"DTZV7Q5AJZOP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTZV7Q5AJZOP3UCZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTZV7Q5A","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DTZV7Q5AJZOP3UCZA6T24NBOJW","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06361","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T14:05:27Z","cross_cats_sorted":[],"title_canon_sha256":"7de1adad3546aa33904ea1965ba3de083da65b64714c825b611f137f24d1e76b","abstract_canon_sha256":"f0acfea8701ce2c13765ad221586639437aa33c041daf31c51cb1187af542a14"},"schema_version":"1.0"},"canonical_sha256":"1cf35fc3a04e5cfdd05907a7ae342e4d8d08802b8c593d8fc6917dd9223b33ac","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:10:57.329520Z","signature_b64":"fswBmj9dcEPLNMUiXDNym7BiTwwlhtk1w6pd+ZkhWkzFjTTOWf2xxlYjJOLYJoVWu417/BYfuUGKusQkMBZhAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1cf35fc3a04e5cfdd05907a7ae342e4d8d08802b8c593d8fc6917dd9223b33ac","last_reissued_at":"2026-05-18T00:10:57.328882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:10:57.328882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06361","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":"2026-05-18T00:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1HH08O1cpRw+nXHZ3nezKepzwSoHqxL5B0OC0EgRrqOlO55UcM01b60Ip8Ks/r1m6Tcl88284SmPdMvQWJKAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:21.175740Z"},"content_sha256":"fe9d6aac28581a99c971636c4a3a8dc1798d9661d4436fe533fe8b3f9e09d365","schema_version":"1.0","event_id":"sha256:fe9d6aac28581a99c971636c4a3a8dc1798d9661d4436fe533fe8b3f9e09d365"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DTZV7Q5AJZOP3UCZA6T24NBOJW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A family of extremal hypergraphs for Ryser's conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Abu-Khazneh, Alexey Pokrovskiy, J\\'anos Bar\\'at, Tibor Szab\\'o","submitted_at":"2016-05-20T14:05:27Z","abstract_excerpt":"Ryser's Conjecture states that for any $r$-partite $r$-uniform hypergraph, the vertex cover number is at most $r{-}1$ times the matching number. This conjecture is only known to be true for $r\\leq 3$ in general and for $r\\leq 5$ if the hypergraph is intersecting. There has also been considerable effort made for finding hypergraphs that are extremal for Ryser's Conjecture, i.e. $r$-partite hypergraphs whose cover number is $r-1$ times its matching number. Aside from a few sporadic examples, the set of uniformities $r$ for which Ryser's Conjecture is known to be tight is limited to those integer"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06361","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":"2026-05-18T00:10:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OyFXrcvjGpRB8FST+it3Gz4x0yaqX6U0dosKJOzUwQfpES+xrT2HDXLawxLFzmZjvhHKK+tga2zGIqGPnQEHBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:21.176589Z"},"content_sha256":"369ddaaf85dc841f7cef0a84b31ff154652b9c7b9140aaa5e9dca59288f8c101","schema_version":"1.0","event_id":"sha256:369ddaaf85dc841f7cef0a84b31ff154652b9c7b9140aaa5e9dca59288f8c101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/bundle.json","state_url":"https://pith.science/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/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":"2026-06-09T10:07:21Z","links":{"resolver":"https://pith.science/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW","bundle":"https://pith.science/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/bundle.json","state":"https://pith.science/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTZV7Q5AJZOP3UCZA6T24NBOJW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DTZV7Q5AJZOP3UCZA6T24NBOJW","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":"f0acfea8701ce2c13765ad221586639437aa33c041daf31c51cb1187af542a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T14:05:27Z","title_canon_sha256":"7de1adad3546aa33904ea1965ba3de083da65b64714c825b611f137f24d1e76b"},"schema_version":"1.0","source":{"id":"1605.06361","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06361","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06361v2","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06361","created_at":"2026-05-18T00:10:57Z"},{"alias_kind":"pith_short_12","alias_value":"DTZV7Q5AJZOP","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DTZV7Q5AJZOP3UCZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DTZV7Q5A","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:369ddaaf85dc841f7cef0a84b31ff154652b9c7b9140aaa5e9dca59288f8c101","target":"graph","created_at":"2026-05-18T00:10:57Z","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":"Ryser's Conjecture states that for any $r$-partite $r$-uniform hypergraph, the vertex cover number is at most $r{-}1$ times the matching number. This conjecture is only known to be true for $r\\leq 3$ in general and for $r\\leq 5$ if the hypergraph is intersecting. There has also been considerable effort made for finding hypergraphs that are extremal for Ryser's Conjecture, i.e. $r$-partite hypergraphs whose cover number is $r-1$ times its matching number. Aside from a few sporadic examples, the set of uniformities $r$ for which Ryser's Conjecture is known to be tight is limited to those integer","authors_text":"Ahmad Abu-Khazneh, Alexey Pokrovskiy, J\\'anos Bar\\'at, Tibor Szab\\'o","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T14:05:27Z","title":"A family of extremal hypergraphs for Ryser's conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06361","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:fe9d6aac28581a99c971636c4a3a8dc1798d9661d4436fe533fe8b3f9e09d365","target":"record","created_at":"2026-05-18T00:10:57Z","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":"f0acfea8701ce2c13765ad221586639437aa33c041daf31c51cb1187af542a14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-20T14:05:27Z","title_canon_sha256":"7de1adad3546aa33904ea1965ba3de083da65b64714c825b611f137f24d1e76b"},"schema_version":"1.0","source":{"id":"1605.06361","kind":"arxiv","version":2}},"canonical_sha256":"1cf35fc3a04e5cfdd05907a7ae342e4d8d08802b8c593d8fc6917dd9223b33ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1cf35fc3a04e5cfdd05907a7ae342e4d8d08802b8c593d8fc6917dd9223b33ac","first_computed_at":"2026-05-18T00:10:57.328882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:57.328882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fswBmj9dcEPLNMUiXDNym7BiTwwlhtk1w6pd+ZkhWkzFjTTOWf2xxlYjJOLYJoVWu417/BYfuUGKusQkMBZhAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:57.329520Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06361","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe9d6aac28581a99c971636c4a3a8dc1798d9661d4436fe533fe8b3f9e09d365","sha256:369ddaaf85dc841f7cef0a84b31ff154652b9c7b9140aaa5e9dca59288f8c101"],"state_sha256":"17bb2e3d5b05ceb85bc63a8140d6c776acb65777b015d288c1a47abbfa118041"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wvJ8NxgNUIFrVxp5vVoLJy/ZVbhLgimpU6i0trEdBV1OtH84T4oaZc7ybpdgkL1n3jNr+DUhtOs/FzT4kCISCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:07:21.187683Z","bundle_sha256":"41f358d1f8bcd834c690ec3a2ea929c46a39951aa95ce23782f284ed366e1a6f"}}