{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:QESP7DCFRTE5HKMAPX7IDJHQPM","short_pith_number":"pith:QESP7DCF","canonical_record":{"source":{"id":"1703.05398","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-15T21:54:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3972b248cf499d307c36a7aa333b8a49b0de48bd64104d72593a090a546cd773","abstract_canon_sha256":"f77f49166be116f04ddd4e40450843d700cdb19b2c7ed932700dca58c49058fc"},"schema_version":"1.0"},"canonical_sha256":"8124ff8c458cc9d3a9807dfe81a4f07b30025c79d60743572e9654fbf1b438f7","source":{"kind":"arxiv","id":"1703.05398","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05398","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05398v3","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05398","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"QESP7DCFRTE5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QESP7DCFRTE5HKMA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QESP7DCF","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:QESP7DCFRTE5HKMAPX7IDJHQPM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.05398","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-15T21:54:38Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"3972b248cf499d307c36a7aa333b8a49b0de48bd64104d72593a090a546cd773","abstract_canon_sha256":"f77f49166be116f04ddd4e40450843d700cdb19b2c7ed932700dca58c49058fc"},"schema_version":"1.0"},"canonical_sha256":"8124ff8c458cc9d3a9807dfe81a4f07b30025c79d60743572e9654fbf1b438f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:05.802936Z","signature_b64":"ybzGapXP3w0lkznfx45T7NfelGtsTW+OwUq9VQgYsRdsJG2oXnw+wVg9vjsOeXcOriP4WJz3r9y3FD+uqHaqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8124ff8c458cc9d3a9807dfe81a4f07b30025c79d60743572e9654fbf1b438f7","last_reissued_at":"2026-05-18T00:25:05.802580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:05.802580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.05398","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VhmNu21AHiqqlLhuXzHlm3JKS9+S30QH3qiJHPZA7TAemlLskXL0H7H4aQQodf87pj+cEVdwf8j2ksQu4bNABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:22:54.184628Z"},"content_sha256":"daea62682ee2c22ed812fd3d3bd1ca602e1afae6f4379616977dcb1d766cbcf0","schema_version":"1.0","event_id":"sha256:daea62682ee2c22ed812fd3d3bd1ca602e1afae6f4379616977dcb1d766cbcf0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:QESP7DCFRTE5HKMAPX7IDJHQPM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Smart elements in combinatorial group testing problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"D\\'aniel Gerbner, M\\'at\\'e Vizer","submitted_at":"2017-03-15T21:54:38Z","abstract_excerpt":"In combinatorial group testing problems Questioner needs to find a special element $x \\in [n]$ by testing subsets of $[n]$. Tapolcai et al. introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one. Using classical results of extremal set theory we prove that if $\\mathcal{F}_n \\subset 2^{[n]}$ solves the non-adaptive version of this problem and has minimal cardinality, then $$\\lim_{n \\rightarrow \\infty} \\frac{|\\mathcal{F}_n|}{\\log_2 n} = \\log_{(3/2)}2.$$ This improves results by Tapolcai et al.\n  We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05398","kind":"arxiv","version":3},"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":"2026-05-18T00:25:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NQY2O555DvXhMRFOCtuTqs4xGOyGDi09SCBFWbNF+Ra59CS/svVY8qbMi8NyxVyuf8QVXvtMdS55ToqXoAV7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:22:54.185074Z"},"content_sha256":"2500a644072174825167b9e676f16f56abdb21952222613eb2bca6ae39422272","schema_version":"1.0","event_id":"sha256:2500a644072174825167b9e676f16f56abdb21952222613eb2bca6ae39422272"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/bundle.json","state_url":"https://pith.science/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/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":"2026-05-30T11:22:54Z","links":{"resolver":"https://pith.science/pith/QESP7DCFRTE5HKMAPX7IDJHQPM","bundle":"https://pith.science/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/bundle.json","state":"https://pith.science/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QESP7DCFRTE5HKMAPX7IDJHQPM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:QESP7DCFRTE5HKMAPX7IDJHQPM","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":"f77f49166be116f04ddd4e40450843d700cdb19b2c7ed932700dca58c49058fc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-15T21:54:38Z","title_canon_sha256":"3972b248cf499d307c36a7aa333b8a49b0de48bd64104d72593a090a546cd773"},"schema_version":"1.0","source":{"id":"1703.05398","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.05398","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"arxiv_version","alias_value":"1703.05398v3","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.05398","created_at":"2026-05-18T00:25:05Z"},{"alias_kind":"pith_short_12","alias_value":"QESP7DCFRTE5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"QESP7DCFRTE5HKMA","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"QESP7DCF","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:2500a644072174825167b9e676f16f56abdb21952222613eb2bca6ae39422272","target":"graph","created_at":"2026-05-18T00:25:05Z","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 combinatorial group testing problems Questioner needs to find a special element $x \\in [n]$ by testing subsets of $[n]$. Tapolcai et al. introduced a new model, where each element knows the answer for those queries that contain it and each element should be able to identify the special one. Using classical results of extremal set theory we prove that if $\\mathcal{F}_n \\subset 2^{[n]}$ solves the non-adaptive version of this problem and has minimal cardinality, then $$\\lim_{n \\rightarrow \\infty} \\frac{|\\mathcal{F}_n|}{\\log_2 n} = \\log_{(3/2)}2.$$ This improves results by Tapolcai et al.\n  We","authors_text":"D\\'aniel Gerbner, M\\'at\\'e Vizer","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-15T21:54:38Z","title":"Smart elements in combinatorial group testing problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05398","kind":"arxiv","version":3},"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:daea62682ee2c22ed812fd3d3bd1ca602e1afae6f4379616977dcb1d766cbcf0","target":"record","created_at":"2026-05-18T00:25:05Z","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":"f77f49166be116f04ddd4e40450843d700cdb19b2c7ed932700dca58c49058fc","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-03-15T21:54:38Z","title_canon_sha256":"3972b248cf499d307c36a7aa333b8a49b0de48bd64104d72593a090a546cd773"},"schema_version":"1.0","source":{"id":"1703.05398","kind":"arxiv","version":3}},"canonical_sha256":"8124ff8c458cc9d3a9807dfe81a4f07b30025c79d60743572e9654fbf1b438f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8124ff8c458cc9d3a9807dfe81a4f07b30025c79d60743572e9654fbf1b438f7","first_computed_at":"2026-05-18T00:25:05.802580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:05.802580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ybzGapXP3w0lkznfx45T7NfelGtsTW+OwUq9VQgYsRdsJG2oXnw+wVg9vjsOeXcOriP4WJz3r9y3FD+uqHaqBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:05.802936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.05398","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:daea62682ee2c22ed812fd3d3bd1ca602e1afae6f4379616977dcb1d766cbcf0","sha256:2500a644072174825167b9e676f16f56abdb21952222613eb2bca6ae39422272"],"state_sha256":"0aeef21e72d9c96153898d823c6adec9babedc302805104fd5772f03e34400a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IoVe4WyRpBIiizzNqfRPhJPY+bUPREwb633U1b3FKvycJm4UEgWdxoA4qKYVgCFeq21m69OdjzZrA91sxOY7Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:22:54.189030Z","bundle_sha256":"a0655609aeae98f1e3fab6573ed17694c7a5af3298bd033c3b40678e91454c83"}}