{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:NLCTXATKJQYQJM2MVT3L2IYJKJ","short_pith_number":"pith:NLCTXATK","schema_version":"1.0","canonical_sha256":"6ac53b826a4c3104b34cacf6bd230952586e76ccc7adf0c57d6093855494024b","source":{"kind":"arxiv","id":"1901.02283","version":1},"attestation_state":"computed","paper":{"title":"Improved encoding and decoding for non-adaptive threshold group testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Isao Echizen, Mahdi Cheraghchi, Minoru Kuribayashi, Thach V. Bui","submitted_at":"2019-01-08T12:34:31Z","abstract_excerpt":"The goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our objective is to identify defective items in sublinear time the number of items, e.g., $\\mathrm{poly}(d, \\ln{n}),$ by using the number of tests as low as possible. In this paper, we reduce the number of tests to $O \\left( h \\times \\frac{d^2 \\ln^2{n}}{\\mathsf{W}^2(d \\ln{n})} \\right)$ and the decoding time to $O \\left( \\mathrm{dec}_0 \\times h \\right),$ where $\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1901.02283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2019-01-08T12:34:31Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f4ef6a00ad52df16673a3b4aa0d3cf239828c607275e35092e91a73776a65cd7","abstract_canon_sha256":"d170af67616e065d8dd3fa58373026268b630bf7c24b8df4d247f17537ebeadb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:43.648870Z","signature_b64":"1n7YZKlBb6RKedfizABqTwbU3ekH8uP985HxBBNRVBQP2Q1XZGdEbaahgcq8E7RMJNpEZwD/6nixaTO3mC36Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ac53b826a4c3104b34cacf6bd230952586e76ccc7adf0c57d6093855494024b","last_reissued_at":"2026-05-17T23:56:43.648470Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:43.648470Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved encoding and decoding for non-adaptive threshold group testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Isao Echizen, Mahdi Cheraghchi, Minoru Kuribayashi, Thach V. Bui","submitted_at":"2019-01-08T12:34:31Z","abstract_excerpt":"The goal of threshold group testing is to identify up to $d$ defective items among a population of $n$ items, where $d$ is usually much smaller than $n$. A test is positive if it has at least $u$ defective items and negative otherwise. Our objective is to identify defective items in sublinear time the number of items, e.g., $\\mathrm{poly}(d, \\ln{n}),$ by using the number of tests as low as possible. In this paper, we reduce the number of tests to $O \\left( h \\times \\frac{d^2 \\ln^2{n}}{\\mathsf{W}^2(d \\ln{n})} \\right)$ and the decoding time to $O \\left( \\mathrm{dec}_0 \\times h \\right),$ where $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02283","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1901.02283","created_at":"2026-05-17T23:56:43.648530+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.02283v1","created_at":"2026-05-17T23:56:43.648530+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.02283","created_at":"2026-05-17T23:56:43.648530+00:00"},{"alias_kind":"pith_short_12","alias_value":"NLCTXATKJQYQ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"NLCTXATKJQYQJM2M","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"NLCTXATK","created_at":"2026-05-18T12:33:24.271573+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ","json":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ.json","graph_json":"https://pith.science/api/pith-number/NLCTXATKJQYQJM2MVT3L2IYJKJ/graph.json","events_json":"https://pith.science/api/pith-number/NLCTXATKJQYQJM2MVT3L2IYJKJ/events.json","paper":"https://pith.science/paper/NLCTXATK"},"agent_actions":{"view_html":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ","download_json":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ.json","view_paper":"https://pith.science/paper/NLCTXATK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.02283&json=true","fetch_graph":"https://pith.science/api/pith-number/NLCTXATKJQYQJM2MVT3L2IYJKJ/graph.json","fetch_events":"https://pith.science/api/pith-number/NLCTXATKJQYQJM2MVT3L2IYJKJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ/action/storage_attestation","attest_author":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ/action/author_attestation","sign_citation":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ/action/citation_signature","submit_replication":"https://pith.science/pith/NLCTXATKJQYQJM2MVT3L2IYJKJ/action/replication_record"}},"created_at":"2026-05-17T23:56:43.648530+00:00","updated_at":"2026-05-17T23:56:43.648530+00:00"}