{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:XXKNPMHG6R2JPMMOLMJMJXERUB","short_pith_number":"pith:XXKNPMHG","canonical_record":{"source":{"id":"2411.03839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2024-11-06T11:22:40Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"38290d30b5bb2ad80f73afdd92aed171fd2b81408db06f451e5e299d78f50935","abstract_canon_sha256":"2161583d39af875ee186bed7b1171f2dc24c42f6e1b30bfe452e562bcd9ac3b4"},"schema_version":"1.0"},"canonical_sha256":"bdd4d7b0e6f47497b18e5b12c4dc91a06468085aa3d2ef286214defdd3766324","source":{"kind":"arxiv","id":"2411.03839","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.03839","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.03839v2","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03839","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"XXKNPMHG6R2J","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_16","alias_value":"XXKNPMHG6R2JPMMO","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_8","alias_value":"XXKNPMHG","created_at":"2026-07-05T09:35:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:XXKNPMHG6R2JPMMOLMJMJXERUB","target":"record","payload":{"canonical_record":{"source":{"id":"2411.03839","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2024-11-06T11:22:40Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"38290d30b5bb2ad80f73afdd92aed171fd2b81408db06f451e5e299d78f50935","abstract_canon_sha256":"2161583d39af875ee186bed7b1171f2dc24c42f6e1b30bfe452e562bcd9ac3b4"},"schema_version":"1.0"},"canonical_sha256":"bdd4d7b0e6f47497b18e5b12c4dc91a06468085aa3d2ef286214defdd3766324","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:14.324643Z","signature_b64":"+KLgO7pFPlott9keYNEk6g+K2CxwsheXoIMHrUqoAZln347Yzr0A4pnMTbVeMN2sRzRE0mEqCA5UMXb0TQ3IBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bdd4d7b0e6f47497b18e5b12c4dc91a06468085aa3d2ef286214defdd3766324","last_reissued_at":"2026-07-05T09:35:14.324099Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:14.324099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.03839","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B0MmTSMxxYRLiCt31gysXeZdXaj/pPkCFrjRqpafuiz4ZEtkBUz4ZiXnHE3nKk9E9cmAgcu78To2Ax4CBCBaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:13:48.448945Z"},"content_sha256":"f0ab167b3c7ed930d5dae82568d6888d243751302214a43e3ed0cd53861d697c","schema_version":"1.0","event_id":"sha256:f0ab167b3c7ed930d5dae82568d6888d243751302214a43e3ed0cd53861d697c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:XXKNPMHG6R2JPMMOLMJMJXERUB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noisy Linear Group Testing: Exact Thresholds and Efficient Algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"cs.DM","authors_text":"Haodong Zhu, Lena Krieg, Lukas Hintze, Olga Scheftelowitsch","submitted_at":"2024-11-06T11:22:40Z","abstract_excerpt":"In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\\alpha$, independent of all other items. In the (over-)idealized noiseless setting, tests are positive exactly if any of the tested items are defective. We study a more realistic model in which observed test results are subject to noise, i.e., tests can display false positive or false negative results with constant positive probabilities. We determine precise constants $c$ such that $cn\\log"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03839","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.03839/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:35:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sujHizqjwRoMZ4XGmgC1zwMCtgGk//c6TgU8ScAPzBDhCN4AplhtE26ZZ87cb3UtZoG9KJSFc9KJg7zecPCECQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T14:13:48.449334Z"},"content_sha256":"32a1b329fbc9d08378cc9c0abe7d4b03ebf2bfdf5d1fea057c67abe4a5846652","schema_version":"1.0","event_id":"sha256:32a1b329fbc9d08378cc9c0abe7d4b03ebf2bfdf5d1fea057c67abe4a5846652"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/bundle.json","state_url":"https://pith.science/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/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":"2026-07-07T14:13:48Z","links":{"resolver":"https://pith.science/pith/XXKNPMHG6R2JPMMOLMJMJXERUB","bundle":"https://pith.science/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/bundle.json","state":"https://pith.science/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XXKNPMHG6R2JPMMOLMJMJXERUB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:XXKNPMHG6R2JPMMOLMJMJXERUB","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":"2161583d39af875ee186bed7b1171f2dc24c42f6e1b30bfe452e562bcd9ac3b4","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2024-11-06T11:22:40Z","title_canon_sha256":"38290d30b5bb2ad80f73afdd92aed171fd2b81408db06f451e5e299d78f50935"},"schema_version":"1.0","source":{"id":"2411.03839","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.03839","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"arxiv_version","alias_value":"2411.03839v2","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.03839","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_12","alias_value":"XXKNPMHG6R2J","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_16","alias_value":"XXKNPMHG6R2JPMMO","created_at":"2026-07-05T09:35:14Z"},{"alias_kind":"pith_short_8","alias_value":"XXKNPMHG","created_at":"2026-07-05T09:35:14Z"}],"graph_snapshots":[{"event_id":"sha256:32a1b329fbc9d08378cc9c0abe7d4b03ebf2bfdf5d1fea057c67abe4a5846652","target":"graph","created_at":"2026-07-05T09:35:14Z","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/2411.03839/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\\alpha$, independent of all other items. In the (over-)idealized noiseless setting, tests are positive exactly if any of the tested items are defective. We study a more realistic model in which observed test results are subject to noise, i.e., tests can display false positive or false negative results with constant positive probabilities. We determine precise constants $c$ such that $cn\\log","authors_text":"Haodong Zhu, Lena Krieg, Lukas Hintze, Olga Scheftelowitsch","cross_cats":["cs.IT","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2024-11-06T11:22:40Z","title":"Noisy Linear Group Testing: Exact Thresholds and Efficient Algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.03839","kind":"arxiv","version":2},"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:f0ab167b3c7ed930d5dae82568d6888d243751302214a43e3ed0cd53861d697c","target":"record","created_at":"2026-07-05T09:35:14Z","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":"2161583d39af875ee186bed7b1171f2dc24c42f6e1b30bfe452e562bcd9ac3b4","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2024-11-06T11:22:40Z","title_canon_sha256":"38290d30b5bb2ad80f73afdd92aed171fd2b81408db06f451e5e299d78f50935"},"schema_version":"1.0","source":{"id":"2411.03839","kind":"arxiv","version":2}},"canonical_sha256":"bdd4d7b0e6f47497b18e5b12c4dc91a06468085aa3d2ef286214defdd3766324","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bdd4d7b0e6f47497b18e5b12c4dc91a06468085aa3d2ef286214defdd3766324","first_computed_at":"2026-07-05T09:35:14.324099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:14.324099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+KLgO7pFPlott9keYNEk6g+K2CxwsheXoIMHrUqoAZln347Yzr0A4pnMTbVeMN2sRzRE0mEqCA5UMXb0TQ3IBg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:14.324643Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.03839","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f0ab167b3c7ed930d5dae82568d6888d243751302214a43e3ed0cd53861d697c","sha256:32a1b329fbc9d08378cc9c0abe7d4b03ebf2bfdf5d1fea057c67abe4a5846652"],"state_sha256":"87f50ea0d3ef2bdc06d05a2a99eb5535bcf0b11eb8635ff2d7f2765859691cf3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YRSqUQs2lqDFTZhE2G5RGmFJBRWsgQsRxGsZPig6lNnWiR+tSL7hUKbhudZSR7cK8PFdLq+xbYg25BSZm3eSBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T14:13:48.451232Z","bundle_sha256":"4ca002d3c39250efc6fbd142c126ad2f80b79ee3cc37a7504b29b4b8ebeae640"}}