{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WUZ6RXFIAEIBBNE5UWKNPDL2OA","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":"e195f0dbc1cdae4cbb4417e5ea1bf35c23b4ca22718d131e0c17702a99c688a5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-11T05:46:17Z","title_canon_sha256":"51337606db137b3ad1099f7ca6f86d583dfa20181efc03bf56e53314c44c971f"},"schema_version":"1.0","source":{"id":"1804.03819","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.03819","created_at":"2026-07-05T00:29:35Z"},{"alias_kind":"arxiv_version","alias_value":"1804.03819v4","created_at":"2026-07-05T00:29:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03819","created_at":"2026-07-05T00:29:35Z"},{"alias_kind":"pith_short_12","alias_value":"WUZ6RXFIAEIB","created_at":"2026-07-05T00:29:35Z"},{"alias_kind":"pith_short_16","alias_value":"WUZ6RXFIAEIBBNE5","created_at":"2026-07-05T00:29:35Z"},{"alias_kind":"pith_short_8","alias_value":"WUZ6RXFI","created_at":"2026-07-05T00:29:35Z"}],"graph_snapshots":[{"event_id":"sha256:0455e50d9255b05881b9a634f572f6f445dc83387eec5958a52708dffb3634d6","target":"graph","created_at":"2026-07-05T00:29:35Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1804.03819/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The task of non-adaptive group testing is to identify up to $d$ defective items from $N$ items, where a test is positive if it contains at least one defective item, and negative otherwise. If there are $t$ tests, they can be represented as a $t \\times N$ measurement matrix. We have answered the question of whether there exists a scheme such that a larger measurement matrix, built from a given $t\\times N$ measurement matrix, can be used to identify up to $d$ defective items in time $O(t \\log_2{N})$. In the meantime, a $t \\times N$ nonrandom measurement matrix with $t = O \\left(\\frac{d^2 \\log_2^","authors_text":"Isao Echizen, Minoru Kuribayashi, Roghayyeh Haghvirdinezhad, Tetsuya Kojima, Thach V. Bui","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-11T05:46:17Z","title":"Efficient (nonrandom) construction and decoding for non-adaptive group testing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03819","kind":"arxiv","version":4},"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:c0f02370e99a6d304e33d9ee0909324812f8bff02b337d9c5c02dcf29ffb8fd7","target":"record","created_at":"2026-07-05T00:29:35Z","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":"e195f0dbc1cdae4cbb4417e5ea1bf35c23b4ca22718d131e0c17702a99c688a5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-04-11T05:46:17Z","title_canon_sha256":"51337606db137b3ad1099f7ca6f86d583dfa20181efc03bf56e53314c44c971f"},"schema_version":"1.0","source":{"id":"1804.03819","kind":"arxiv","version":4}},"canonical_sha256":"b533e8dca8011010b49da594d78d7a702f5668ea28131fcecebcd4afdfb577d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b533e8dca8011010b49da594d78d7a702f5668ea28131fcecebcd4afdfb577d0","first_computed_at":"2026-07-05T00:29:35.466332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:29:35.466332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f5qR7ezk6j4XGAr8cuh+FENdP47q60JNTg7gQzVwMNlCSd+Cj5Vhb6Kr92Oc3R6wwS7pIjsvE/nbWq6kEGlcCA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:29:35.466907Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.03819","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0f02370e99a6d304e33d9ee0909324812f8bff02b337d9c5c02dcf29ffb8fd7","sha256:0455e50d9255b05881b9a634f572f6f445dc83387eec5958a52708dffb3634d6"],"state_sha256":"fd082d5d467f1fa6a5b79365b89897b8353c3bd17dbf8d01ca42edf143d2ae2a"}