{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:QALOWUE7YDL7O5SAMET465OJKD","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":"1adc99e9fefd66a4518b2e136b3720fa2929f7d213bd910a2bea563054427800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-20T19:51:11Z","title_canon_sha256":"4005a98a1a2ad1d038901572c40008652b3057d283452ef8bfb748ff666d99ab"},"schema_version":"1.0","source":{"id":"1601.05389","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05389","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05389v2","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05389","created_at":"2026-05-18T00:55:28Z"},{"alias_kind":"pith_short_12","alias_value":"QALOWUE7YDL7","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"QALOWUE7YDL7O5SA","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"QALOWUE7","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:bdf896402f40cf85ceeac383b69bfda8953c750b1452ba03794a7cd20de05816","target":"graph","created_at":"2026-05-18T00:55:28Z","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":"We present new lower bounds for the size of perfect and separating hash families ensuring their existence. Such new bounds are based on the algorithmic Cluster expansion improved version of the Lov\\'asz Local Lemma, which also implies that the Moser-Tardos algorithm finds such hash families in polynomial time.","authors_text":"Aldo Procacci, Remy Sanchis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-20T19:51:11Z","title":"Perfect and separating Hash families: new bounds via the algorithmic cluster expansion local lemma"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05389","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:c65d388469236186c7278e7a04d0703d44b14f8c690dd9b06596cfd2568b3f03","target":"record","created_at":"2026-05-18T00:55:28Z","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":"1adc99e9fefd66a4518b2e136b3720fa2929f7d213bd910a2bea563054427800","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-20T19:51:11Z","title_canon_sha256":"4005a98a1a2ad1d038901572c40008652b3057d283452ef8bfb748ff666d99ab"},"schema_version":"1.0","source":{"id":"1601.05389","kind":"arxiv","version":2}},"canonical_sha256":"8016eb509fc0d7f776406127cf75c950fecdbc9db6684fdcde3c9e2700ff5876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8016eb509fc0d7f776406127cf75c950fecdbc9db6684fdcde3c9e2700ff5876","first_computed_at":"2026-05-18T00:55:28.603957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:28.603957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kca5KyQz3Dn+5b/ooShJO9CfhVG1GUBl92BO9DP+bQw3ykSqKSwun+mg+O67dCJyQ+/6LAP+fkrYB3xuuUs3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:28.604621Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05389","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c65d388469236186c7278e7a04d0703d44b14f8c690dd9b06596cfd2568b3f03","sha256:bdf896402f40cf85ceeac383b69bfda8953c750b1452ba03794a7cd20de05816"],"state_sha256":"bc925781466631b7b9faaf2f09d759e1fbaea01eadb6ca67e98535b6ca530d2a"}