{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VWHZMK45ALAZ2BNOGQELBJEOWL","short_pith_number":"pith:VWHZMK45","canonical_record":{"source":{"id":"1412.3067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"6bc718270ad36cec857ad097a6c7cfcaee8f20eae9e02914dfaa94339bad6677","abstract_canon_sha256":"93724c95ad97833937826f8b0ac44f71b34f1a5e60eb7250b7a094bd1259e5fb"},"schema_version":"1.0"},"canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","source":{"kind":"arxiv","id":"1412.3067","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3067","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3067v2","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3067","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"VWHZMK45ALAZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWHZMK45ALAZ2BNO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWHZMK45","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VWHZMK45ALAZ2BNOGQELBJEOWL","target":"record","payload":{"canonical_record":{"source":{"id":"1412.3067","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","cross_cats_sorted":[],"title_canon_sha256":"6bc718270ad36cec857ad097a6c7cfcaee8f20eae9e02914dfaa94339bad6677","abstract_canon_sha256":"93724c95ad97833937826f8b0ac44f71b34f1a5e60eb7250b7a094bd1259e5fb"},"schema_version":"1.0"},"canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:15.144278Z","signature_b64":"+CjS4S7sM4KAkmprkI+DXnBjhBsJo6zM57PtoyBl3TqBNomDfC7w5zepN5YGAq6GjR2hO55FHYvFhqA14fw1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","last_reissued_at":"2026-05-18T02:30:15.143859Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:15.143859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.3067","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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fPDaCS6bS+pSmD/3F/N412AraSuudhhvuf4TvxTcKvdtb37L5VHKJF3hyX8cj2/ZnVFb45NLpykOLYNFjLYQDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:44:31.706457Z"},"content_sha256":"b75cd9b1afbea709d758468ebf893974b2122a2e2524e718bb1eae6bdd51f895","schema_version":"1.0","event_id":"sha256:b75cd9b1afbea709d758468ebf893974b2122a2e2524e718bb1eae6bdd51f895"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VWHZMK45ALAZ2BNOGQELBJEOWL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Covers in Partitioned Intersecting Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"C.J. Argue, Ron Aharoni","submitted_at":"2014-12-09T19:38:12Z","abstract_excerpt":"Given an integer $r$ and a vector $\\vec{a}=(a_1, \\ldots ,a_p)$ of positive numbers with $\\sum_{i \\le p} a_i=r$, an $r$-uniform hypergraph $H$ is said to be $\\vec{a}$-partitioned if $V(H)=\\bigcup_{i \\le p}V_i$, where the sets $V_i$ are disjoint, and $|e \\cap V_i|=a_i$ for all $e \\in H,~~i \\le p$. A $\\vec{1}$-partitioned hypergraph is said to be $r$-partite. Let $t(\\vec{a})$ be the maximum, over all intersecting $\\vec{a}$-partitioned hypergraphs $H$, of the minimal size of a cover of $H$. A famous conjecture of Ryser is that $t(\\vec{1})\\le r-1$. Tuza conjectured that if $r>2$ then $t(\\vec{a})=r$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3067","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":"2026-05-18T02:30:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gzyIA6Rr67b/rz5aVDYB3/50+go0QnNy4b0NEK/tfM16nIWtfhmzW5d40jx1mH2CHAhsfCZ02CDC4oCkFed5DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T10:44:31.707186Z"},"content_sha256":"2cb3ef093618d6d1e33db6c67e83c66204299203cdba4fa9ec280c5b307ec6b6","schema_version":"1.0","event_id":"sha256:2cb3ef093618d6d1e33db6c67e83c66204299203cdba4fa9ec280c5b307ec6b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/bundle.json","state_url":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/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":"2026-05-23T10:44:31Z","links":{"resolver":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL","bundle":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/bundle.json","state":"https://pith.science/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWHZMK45ALAZ2BNOGQELBJEOWL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VWHZMK45ALAZ2BNOGQELBJEOWL","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":"93724c95ad97833937826f8b0ac44f71b34f1a5e60eb7250b7a094bd1259e5fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","title_canon_sha256":"6bc718270ad36cec857ad097a6c7cfcaee8f20eae9e02914dfaa94339bad6677"},"schema_version":"1.0","source":{"id":"1412.3067","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.3067","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"arxiv_version","alias_value":"1412.3067v2","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3067","created_at":"2026-05-18T02:30:15Z"},{"alias_kind":"pith_short_12","alias_value":"VWHZMK45ALAZ","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWHZMK45ALAZ2BNO","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWHZMK45","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:2cb3ef093618d6d1e33db6c67e83c66204299203cdba4fa9ec280c5b307ec6b6","target":"graph","created_at":"2026-05-18T02:30:15Z","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":"Given an integer $r$ and a vector $\\vec{a}=(a_1, \\ldots ,a_p)$ of positive numbers with $\\sum_{i \\le p} a_i=r$, an $r$-uniform hypergraph $H$ is said to be $\\vec{a}$-partitioned if $V(H)=\\bigcup_{i \\le p}V_i$, where the sets $V_i$ are disjoint, and $|e \\cap V_i|=a_i$ for all $e \\in H,~~i \\le p$. A $\\vec{1}$-partitioned hypergraph is said to be $r$-partite. Let $t(\\vec{a})$ be the maximum, over all intersecting $\\vec{a}$-partitioned hypergraphs $H$, of the minimal size of a cover of $H$. A famous conjecture of Ryser is that $t(\\vec{1})\\le r-1$. Tuza conjectured that if $r>2$ then $t(\\vec{a})=r$","authors_text":"C.J. Argue, Ron Aharoni","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","title":"Covers in Partitioned Intersecting Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3067","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:b75cd9b1afbea709d758468ebf893974b2122a2e2524e718bb1eae6bdd51f895","target":"record","created_at":"2026-05-18T02:30:15Z","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":"93724c95ad97833937826f8b0ac44f71b34f1a5e60eb7250b7a094bd1259e5fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-09T19:38:12Z","title_canon_sha256":"6bc718270ad36cec857ad097a6c7cfcaee8f20eae9e02914dfaa94339bad6677"},"schema_version":"1.0","source":{"id":"1412.3067","kind":"arxiv","version":2}},"canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ad8f962b9d02c19d05ae3408b0a48eb2c8a28dad46674b7d35e1e38aeaade0d4","first_computed_at":"2026-05-18T02:30:15.143859Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:15.143859Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+CjS4S7sM4KAkmprkI+DXnBjhBsJo6zM57PtoyBl3TqBNomDfC7w5zepN5YGAq6GjR2hO55FHYvFhqA14fw1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:15.144278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.3067","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b75cd9b1afbea709d758468ebf893974b2122a2e2524e718bb1eae6bdd51f895","sha256:2cb3ef093618d6d1e33db6c67e83c66204299203cdba4fa9ec280c5b307ec6b6"],"state_sha256":"7f42eb629fe32af7ec43e6fa4ea5b114d4f023584eb099362e5d2fbfa674346a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a48vPoW38XSWKrBiBPDNUX3x8Nkir4kpJpvWUGzYY1DYgtahbYiFMvjsgwoVjwyFh6na0yq+k5Wey/zsl+A3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T10:44:31.710865Z","bundle_sha256":"81af4f83445bd96a3690027db94cb809d2f5699567839ef9a47d62d4f9a96d54"}}