{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1994:CW7AXTHAGAZCCH4XZCQDBYSFOX","short_pith_number":"pith:CW7AXTHA","canonical_record":{"source":{"id":"math/9412222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1994-12-04T00:00:00Z","cross_cats_sorted":["q-bio"],"title_canon_sha256":"f35c750806d8729598cb276853be589683d83ec72cba388105406451cd910d8e","abstract_canon_sha256":"91c7c5ebff3e1de8c027ed56213084afd134256c61a0d2f6c1e491bf7bdcf15f"},"schema_version":"1.0"},"canonical_sha256":"15be0bcce03032211f97c8a030e24575cf825d9f72039a2405a61ed385641dfc","source":{"kind":"arxiv","id":"math/9412222","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9412222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9412222v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9412222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"CW7AXTHAGAZC","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CW7AXTHAGAZCCH4X","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CW7AXTHA","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1994:CW7AXTHAGAZCCH4XZCQDBYSFOX","target":"record","payload":{"canonical_record":{"source":{"id":"math/9412222","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"1994-12-04T00:00:00Z","cross_cats_sorted":["q-bio"],"title_canon_sha256":"f35c750806d8729598cb276853be589683d83ec72cba388105406451cd910d8e","abstract_canon_sha256":"91c7c5ebff3e1de8c027ed56213084afd134256c61a0d2f6c1e491bf7bdcf15f"},"schema_version":"1.0"},"canonical_sha256":"15be0bcce03032211f97c8a030e24575cf825d9f72039a2405a61ed385641dfc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.735042Z","signature_b64":"Cvefo2okeglVz5oarchKT8L9eL03C1hQcBhgLYILp0KQUKujk36uBsNYxafcR1J2ZkB2cDyx0pboBILguIANDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"15be0bcce03032211f97c8a030e24575cf825d9f72039a2405a61ed385641dfc","last_reissued_at":"2026-05-18T01:05:50.734474Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.734474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9412222","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jx3uI3/1POFwVXM1O5huON21F058nJXAelULUBaZuwge/S6LGR3Qw8bfe+dhU7snhuJUzWyDNsmeFLnM6gbBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:35:36.130074Z"},"content_sha256":"57dfa407fa7c5f24cae4aee7f38f736d82ebccad45d6d76e97bc917edb50a909","schema_version":"1.0","event_id":"sha256:57dfa407fa7c5f24cae4aee7f38f736d82ebccad45d6d76e97bc917edb50a909"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1994:CW7AXTHAGAZCCH4XZCQDBYSFOX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient pooling designs for library screening","license":"","headline":"","cross_cats":["q-bio"],"primary_cat":"math.CO","authors_text":"Craig C. Whittaker, David C. Torney, David J. Balding, D. C. Bruce, Emanuel Knill, N. A. Doggett, R. L. Stallings, William J. Bruno, W. W. Sawhill","submitted_at":"1994-12-04T00:00:00Z","abstract_excerpt":"We describe efficient methods for screening clone libraries, based on pooling schemes which we call ``random $k$-sets designs''. In these designs, the pools in which any clone occurs are equally likely to be any possible selection of $k$ from the $v$ pools. The values of $k$ and $v$ can be chosen to optimize desirable properties. Random $k$-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412222","kind":"arxiv","version":1},"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":"2026-05-18T01:05:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/72xegrWP0koflMKyB0AJvRL14xQdfiDO7KFlQi6P2smYkUe2dkdtXEKf68zwnrMeVhUCROzqi9EhyUCP2JiDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T05:35:36.130753Z"},"content_sha256":"354803ff4763ba42202d1b12a3f5fbb9715dd0b3a61cfdcfb5705fae1bcef646","schema_version":"1.0","event_id":"sha256:354803ff4763ba42202d1b12a3f5fbb9715dd0b3a61cfdcfb5705fae1bcef646"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/bundle.json","state_url":"https://pith.science/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/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":"2026-05-20T05:35:36Z","links":{"resolver":"https://pith.science/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX","bundle":"https://pith.science/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/bundle.json","state":"https://pith.science/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CW7AXTHAGAZCCH4XZCQDBYSFOX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1994:CW7AXTHAGAZCCH4XZCQDBYSFOX","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":"91c7c5ebff3e1de8c027ed56213084afd134256c61a0d2f6c1e491bf7bdcf15f","cross_cats_sorted":["q-bio"],"license":"","primary_cat":"math.CO","submitted_at":"1994-12-04T00:00:00Z","title_canon_sha256":"f35c750806d8729598cb276853be589683d83ec72cba388105406451cd910d8e"},"schema_version":"1.0","source":{"id":"math/9412222","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9412222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"arxiv_version","alias_value":"math/9412222v1","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9412222","created_at":"2026-05-18T01:05:50Z"},{"alias_kind":"pith_short_12","alias_value":"CW7AXTHAGAZC","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"CW7AXTHAGAZCCH4X","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"CW7AXTHA","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:354803ff4763ba42202d1b12a3f5fbb9715dd0b3a61cfdcfb5705fae1bcef646","target":"graph","created_at":"2026-05-18T01:05:50Z","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 describe efficient methods for screening clone libraries, based on pooling schemes which we call ``random $k$-sets designs''. In these designs, the pools in which any clone occurs are equally likely to be any possible selection of $k$ from the $v$ pools. The values of $k$ and $v$ can be chosen to optimize desirable properties. Random $k$-sets designs have substantial advantages over alternative pooling schemes: they are efficient, flexible, easy to specify, require fewer pools, and have error-correcting and error-detecting capabilities. In addition, screening can often be achieved in only o","authors_text":"Craig C. Whittaker, David C. Torney, David J. Balding, D. C. Bruce, Emanuel Knill, N. A. Doggett, R. L. Stallings, William J. Bruno, W. W. Sawhill","cross_cats":["q-bio"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"1994-12-04T00:00:00Z","title":"Efficient pooling designs for library screening"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412222","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":"sha256:57dfa407fa7c5f24cae4aee7f38f736d82ebccad45d6d76e97bc917edb50a909","target":"record","created_at":"2026-05-18T01:05:50Z","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":"91c7c5ebff3e1de8c027ed56213084afd134256c61a0d2f6c1e491bf7bdcf15f","cross_cats_sorted":["q-bio"],"license":"","primary_cat":"math.CO","submitted_at":"1994-12-04T00:00:00Z","title_canon_sha256":"f35c750806d8729598cb276853be589683d83ec72cba388105406451cd910d8e"},"schema_version":"1.0","source":{"id":"math/9412222","kind":"arxiv","version":1}},"canonical_sha256":"15be0bcce03032211f97c8a030e24575cf825d9f72039a2405a61ed385641dfc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"15be0bcce03032211f97c8a030e24575cf825d9f72039a2405a61ed385641dfc","first_computed_at":"2026-05-18T01:05:50.734474Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:50.734474Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Cvefo2okeglVz5oarchKT8L9eL03C1hQcBhgLYILp0KQUKujk36uBsNYxafcR1J2ZkB2cDyx0pboBILguIANDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:50.735042Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9412222","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57dfa407fa7c5f24cae4aee7f38f736d82ebccad45d6d76e97bc917edb50a909","sha256:354803ff4763ba42202d1b12a3f5fbb9715dd0b3a61cfdcfb5705fae1bcef646"],"state_sha256":"40d0d072469bb9fe5b683986345c209e9635a8e2c037f7d5cd0b5e774fed484d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AKext1YlgJ8nUGKqpzoypn+KAxl1Fea0zRWf7FzEu3Q/bgynD8AEfArsNDh/i3Vm1W9+Z8zE8R9LiiTBPQk6Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T05:35:36.134264Z","bundle_sha256":"d55c6c00b55d0770a2fd3f2080b86aa8927ca07cd2a39f07d5e27474847ef209"}}