{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:367NX75HJ7QQAXDVFAU4IPXBVK","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":"ca84bd099483f623e2f3caedc55a9d749928a0b783a51ab306c1330f1adabafc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-13T09:41:52Z","title_canon_sha256":"c5eff82e84cde2b623e4b1b983fb18e15daa789812959516c39ef8b6e4ba22dc"},"schema_version":"1.0","source":{"id":"1105.2669","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2669","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2669v1","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2669","created_at":"2026-05-18T04:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"367NX75HJ7QQ","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"367NX75HJ7QQAXDV","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"367NX75H","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:2ef1f1ee2bc30ae922ac1f965ab6d11f24bab02f7c5942907a7dd1cda482cd10","target":"graph","created_at":"2026-05-18T04:22:09Z","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":"It is well-known that many famous pooling designs are constructed from mathematical structures by the \"containment matrix\" method. In this paper, we propose another method and obtain a family of pooling designs with surprisingly high degree of error correction based on a finite set. Given the numbers of items and pools, the error-tolerant property of our designs is much better than that of Macula's designs when the size of the set is large enough.","authors_text":"Jun Guo, Kaishun Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-13T09:41:52Z","title":"A construction of pooling designs with surprisingly high degree of error correction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2669","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":"sha256:72e34529e0ff0428c7b30cca710ad4bf6cdc647ddae2f8a6b38f3f16dd23ff8e","target":"record","created_at":"2026-05-18T04:22:09Z","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":"ca84bd099483f623e2f3caedc55a9d749928a0b783a51ab306c1330f1adabafc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-13T09:41:52Z","title_canon_sha256":"c5eff82e84cde2b623e4b1b983fb18e15daa789812959516c39ef8b6e4ba22dc"},"schema_version":"1.0","source":{"id":"1105.2669","kind":"arxiv","version":1}},"canonical_sha256":"dfbedbffa74fe1005c752829c43ee1aaa707c3556dcc529067be7df58f172783","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfbedbffa74fe1005c752829c43ee1aaa707c3556dcc529067be7df58f172783","first_computed_at":"2026-05-18T04:22:09.850793Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:09.850793Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"krH3yo4Gb5Vi8SRzlM5hohPjh+3YoDwheztu6dTs0lOIB9Awh9ULWqn30lQ3f88xtbi7xjscbC/kjBky+YIGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:09.851249Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2669","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72e34529e0ff0428c7b30cca710ad4bf6cdc647ddae2f8a6b38f3f16dd23ff8e","sha256:2ef1f1ee2bc30ae922ac1f965ab6d11f24bab02f7c5942907a7dd1cda482cd10"],"state_sha256":"5ac0a96d719637aea07b73d901083e56b51539aaa3fd794c6bef402009cc45c4"}