{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:X3CQRJJV6RQ4KN3ZMK4AQWADF5","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":"8ce1a8c1876ee19fdbc45e4cdfd2b283663533ff3ee7380d123d93375e5ecc19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-06T07:29:29Z","title_canon_sha256":"e8add51a17076ae70776388c9c15306e58781a8b5ca4aa05710116722cdcc5ca"},"schema_version":"1.0","source":{"id":"1611.01735","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.01735","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"arxiv_version","alias_value":"1611.01735v1","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.01735","created_at":"2026-05-18T01:00:04Z"},{"alias_kind":"pith_short_12","alias_value":"X3CQRJJV6RQ4","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"X3CQRJJV6RQ4KN3Z","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"X3CQRJJV","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:60aa898a855a02fda06e80abd8b61328736300588c89c7c360d91f4ac5535af6","target":"graph","created_at":"2026-05-18T01:00:04Z","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":"For any posotive integer $m$, let $[m]:=\\{1,\\ldots,m\\}$. Let $n,k,t$ be positive integers. Aharoni and Howard conjectured that if, for $i\\in [t]$, $\\mathcal{F}_i\\subset[n]^k:= \\{(a_1,\\ldots,a_k): a_j\\in [n] \\mbox{ for } j\\in [k]\\}$ and $|\\mathcal{F}_i|>(t-1)n^{k-1}$, then there exist $M\\subseteq [n]^k$ such that $|M|=t$ and $|M\\cap \\mathcal{F}_i|=1$ for $i\\in [t]$ We show that this conjecture holds when $n\\geq 3(k-1)(t-1)$.\n  Let $n, t, k_1\\ge k_2\\geq \\ldots\\geq k_t $ be positive integers. Huang, Loh and Sudakov asked for the maximum $\\Pi_{i=1}^t |{\\cal\n  R}_i|$ over all ${\\cal R}=\\{{\\cal R}_1","authors_text":"Hongliang Lu, Xingxing Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-06T07:29:29Z","title":"On rainbow matchings for hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.01735","kind":"arxiv","version":1},"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":"sha256:9e2d534a1c4eb03088448e77eba4aaf383f677b0af926d7efb438e36963848a9","target":"record","created_at":"2026-05-18T01:00:04Z","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":"8ce1a8c1876ee19fdbc45e4cdfd2b283663533ff3ee7380d123d93375e5ecc19","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-11-06T07:29:29Z","title_canon_sha256":"e8add51a17076ae70776388c9c15306e58781a8b5ca4aa05710116722cdcc5ca"},"schema_version":"1.0","source":{"id":"1611.01735","kind":"arxiv","version":1}},"canonical_sha256":"bec508a535f461c5377962b80858032f4ff7de089401ae1fbf61d05e8fd18bef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bec508a535f461c5377962b80858032f4ff7de089401ae1fbf61d05e8fd18bef","first_computed_at":"2026-05-18T01:00:04.567737Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:04.567737Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h+KugFe72kB7IAt86wrU6sGzi4zFS9JCcJTpBwIb8b2q5NWWCmY/OAzeW5HSdahqkY7DCNCndJZ/EcExzmuSDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:04.568530Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.01735","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e2d534a1c4eb03088448e77eba4aaf383f677b0af926d7efb438e36963848a9","sha256:60aa898a855a02fda06e80abd8b61328736300588c89c7c360d91f4ac5535af6"],"state_sha256":"d1797013ae57af1cc069d04df215cf0a7d8ade0ad3baa463cce1afd98216783c"}