{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HYTGNAQXCLWSMP5U6CJNNQHZBQ","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":"96d6f31ef8556eaf6cee8950b1fb8926b8779fd590ef0d3c62c1c12c22063500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-19T23:37:01Z","title_canon_sha256":"7d204d85b25a402d087eb001eef9ba2fa2316f4f8c9d92b2e0fcd8648ea7f040"},"schema_version":"1.0","source":{"id":"1202.4196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4196","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4196v1","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4196","created_at":"2026-05-17T23:51:44Z"},{"alias_kind":"pith_short_12","alias_value":"HYTGNAQXCLWS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYTGNAQXCLWSMP5U","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYTGNAQX","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:bc1fa131a22c6a2c602a8b35e8157ca0bcfe4dd7398430f2c5193a0b36506d8c","target":"graph","created_at":"2026-05-17T23:51:44Z","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":"In 1965 Erd\\H{o}s conjectured that the number of edges in k-uniform hypergraphs on n vertices in which the largest matching has s edges is maximized for hypergraphs of one of two special types. We settled this conjecture in the affirmative for k=3 and n is large enough.","authors_text":"Katarzyna Mieczkowska, Tomasz Luczak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-19T23:37:01Z","title":"On Erdos' extremal problem on matchings in hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4196","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:b217097341bf4567da1184572d35f95918ac17975563e757f13df56ddc868c1a","target":"record","created_at":"2026-05-17T23:51:44Z","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":"96d6f31ef8556eaf6cee8950b1fb8926b8779fd590ef0d3c62c1c12c22063500","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-02-19T23:37:01Z","title_canon_sha256":"7d204d85b25a402d087eb001eef9ba2fa2316f4f8c9d92b2e0fcd8648ea7f040"},"schema_version":"1.0","source":{"id":"1202.4196","kind":"arxiv","version":1}},"canonical_sha256":"3e2666821712ed263fb4f092d6c0f90c1d27d65a6dade9c642b60408db5518fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e2666821712ed263fb4f092d6c0f90c1d27d65a6dade9c642b60408db5518fe","first_computed_at":"2026-05-17T23:51:44.869150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:44.869150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/yUy1T/unsLWyPZDaOSf9sM3KgqPAsN9YdcKGQj7r9heD1eQah5HmFbtVeJqgrTp8vLGAOhA3u+MqdpfXN7eCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:44.869613Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b217097341bf4567da1184572d35f95918ac17975563e757f13df56ddc868c1a","sha256:bc1fa131a22c6a2c602a8b35e8157ca0bcfe4dd7398430f2c5193a0b36506d8c"],"state_sha256":"fd819d120fa49a857a7a71d0f6b1a73038ef69eec43eb7df2d88ea50bfe23a36"}