{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TS64F4BMQ27JEGBGY4MDFN5NUU","short_pith_number":"pith:TS64F4BM","canonical_record":{"source":{"id":"1612.09388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-30T04:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"4c9686e4fe1b5526fed6e3b1ecfcb37830d829565d3478b34161f01dd14e689b","abstract_canon_sha256":"dc8e8297b64ab2252790a1f732f22dd19eb35c5bacbf3602f800f54c9952dab4"},"schema_version":"1.0"},"canonical_sha256":"9cbdc2f02c86be921826c71832b7ada5113ea089328adc8a527b2483867bd57f","source":{"kind":"arxiv","id":"1612.09388","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09388","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09388v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09388","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"TS64F4BMQ27J","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TS64F4BMQ27JEGBG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TS64F4BM","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TS64F4BMQ27JEGBGY4MDFN5NUU","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09388","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-30T04:50:26Z","cross_cats_sorted":[],"title_canon_sha256":"4c9686e4fe1b5526fed6e3b1ecfcb37830d829565d3478b34161f01dd14e689b","abstract_canon_sha256":"dc8e8297b64ab2252790a1f732f22dd19eb35c5bacbf3602f800f54c9952dab4"},"schema_version":"1.0"},"canonical_sha256":"9cbdc2f02c86be921826c71832b7ada5113ea089328adc8a527b2483867bd57f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:41.639209Z","signature_b64":"rStTzTMq+Co3DX7oTyzEHRDLzKOh1MjcFbcXQ6qbEXx9x0gqd5mesroK15/wD/1uIeo8M36aqLhwqiQflgzuAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9cbdc2f02c86be921826c71832b7ada5113ea089328adc8a527b2483867bd57f","last_reissued_at":"2026-05-18T00:53:41.638851Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:41.638851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09388","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rZql/yj5OdbiAWjHiMcOQfY3T1tOPDYud2Xrpk7Fq/Bqn8NfsD7nan+rfvBHi/Y9cZ2clWBMWAN14HL8zLEBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:23:34.765920Z"},"content_sha256":"19bb496858f4bf1b34d72134205d11523c5a61180dbd5a36cb7c8618eeeed29e","schema_version":"1.0","event_id":"sha256:19bb496858f4bf1b34d72134205d11523c5a61180dbd5a36cb7c8618eeeed29e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TS64F4BMQ27JEGBGY4MDFN5NUU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Set membership with non-adaptive bit probes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Jaikumar Radhakrishnan, Mohit Garg","submitted_at":"2016-12-30T04:50:26Z","abstract_excerpt":"We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form \"Is x in S?\" by non-adaptively probing the bit vector at t places. Let s_N(m,n,t) be the minimum number of bits of storage needed for such a scheme. In this work, we show existence of non-adaptive and adaptive schemes for a range of t that improves an upper bound of Buhrman, Miltersen, Radhakrishnan and Srinivasan (2002) on s_N(m,n,t). For three non-adaptive probes,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09388","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KnsG9pH1nkC9LHaAOoLq5onQ87LVO5C1h9/esjucfz4i3rE7IL6oZIgIGGewEkCGhoRkeMApGejVgJGB0YsKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T08:23:34.766609Z"},"content_sha256":"b2a467ebcea012ceb741b5cd09b3c61644a5f34ef72f7bddfe1b3ba502adbaad","schema_version":"1.0","event_id":"sha256:b2a467ebcea012ceb741b5cd09b3c61644a5f34ef72f7bddfe1b3ba502adbaad"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/bundle.json","state_url":"https://pith.science/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/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":"2026-06-07T08:23:34Z","links":{"resolver":"https://pith.science/pith/TS64F4BMQ27JEGBGY4MDFN5NUU","bundle":"https://pith.science/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/bundle.json","state":"https://pith.science/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TS64F4BMQ27JEGBGY4MDFN5NUU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TS64F4BMQ27JEGBGY4MDFN5NUU","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":"dc8e8297b64ab2252790a1f732f22dd19eb35c5bacbf3602f800f54c9952dab4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-30T04:50:26Z","title_canon_sha256":"4c9686e4fe1b5526fed6e3b1ecfcb37830d829565d3478b34161f01dd14e689b"},"schema_version":"1.0","source":{"id":"1612.09388","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09388","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09388v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09388","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"TS64F4BMQ27J","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TS64F4BMQ27JEGBG","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TS64F4BM","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:b2a467ebcea012ceb741b5cd09b3c61644a5f34ef72f7bddfe1b3ba502adbaad","target":"graph","created_at":"2026-05-18T00:53:41Z","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 consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form \"Is x in S?\" by non-adaptively probing the bit vector at t places. Let s_N(m,n,t) be the minimum number of bits of storage needed for such a scheme. In this work, we show existence of non-adaptive and adaptive schemes for a range of t that improves an upper bound of Buhrman, Miltersen, Radhakrishnan and Srinivasan (2002) on s_N(m,n,t). For three non-adaptive probes,","authors_text":"Jaikumar Radhakrishnan, Mohit Garg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-30T04:50:26Z","title":"Set membership with non-adaptive bit probes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09388","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":"sha256:19bb496858f4bf1b34d72134205d11523c5a61180dbd5a36cb7c8618eeeed29e","target":"record","created_at":"2026-05-18T00:53:41Z","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":"dc8e8297b64ab2252790a1f732f22dd19eb35c5bacbf3602f800f54c9952dab4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-12-30T04:50:26Z","title_canon_sha256":"4c9686e4fe1b5526fed6e3b1ecfcb37830d829565d3478b34161f01dd14e689b"},"schema_version":"1.0","source":{"id":"1612.09388","kind":"arxiv","version":1}},"canonical_sha256":"9cbdc2f02c86be921826c71832b7ada5113ea089328adc8a527b2483867bd57f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9cbdc2f02c86be921826c71832b7ada5113ea089328adc8a527b2483867bd57f","first_computed_at":"2026-05-18T00:53:41.638851Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:41.638851Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rStTzTMq+Co3DX7oTyzEHRDLzKOh1MjcFbcXQ6qbEXx9x0gqd5mesroK15/wD/1uIeo8M36aqLhwqiQflgzuAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:41.639209Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19bb496858f4bf1b34d72134205d11523c5a61180dbd5a36cb7c8618eeeed29e","sha256:b2a467ebcea012ceb741b5cd09b3c61644a5f34ef72f7bddfe1b3ba502adbaad"],"state_sha256":"f5f42aec3a2dd2f7ab19467eb622c5f8a8f31dc098ff18303f4ebb26f65b8587"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QwBZGARvuioiGYsTeVy48wZB1eEyEhtBaGpwkuISPrN1cOtLdvf8rxWAtc5IKuWgZ9TyuwaLegWU6xyOa+HyAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T08:23:34.770438Z","bundle_sha256":"278ffe2276f1abdff4a5a2644a9853db23bcc59e19dd3b5ce1b6d29b3aa22114"}}