{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PZA5MCPJTZ4BDUUKMWABOV5Z3C","short_pith_number":"pith:PZA5MCPJ","canonical_record":{"source":{"id":"1402.4073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-02-17T17:22:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"14939e2600313a85d5b811e2746cc271fcc7480e0ff96223c7aea9d79ad585de","abstract_canon_sha256":"e0ff15d9cbbf49862bf3978ab8d8d3a973cf47daa944f9804d2bf5b4f12a6372"},"schema_version":"1.0"},"canonical_sha256":"7e41d609e99e7811d28a65801757b9d882b97b33dd43d19c7a4c3633129cb7be","source":{"kind":"arxiv","id":"1402.4073","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4073","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4073v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4073","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"PZA5MCPJTZ4B","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PZA5MCPJTZ4BDUUK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PZA5MCPJ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PZA5MCPJTZ4BDUUKMWABOV5Z3C","target":"record","payload":{"canonical_record":{"source":{"id":"1402.4073","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-02-17T17:22:05Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"14939e2600313a85d5b811e2746cc271fcc7480e0ff96223c7aea9d79ad585de","abstract_canon_sha256":"e0ff15d9cbbf49862bf3978ab8d8d3a973cf47daa944f9804d2bf5b4f12a6372"},"schema_version":"1.0"},"canonical_sha256":"7e41d609e99e7811d28a65801757b9d882b97b33dd43d19c7a4c3633129cb7be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:55.765974Z","signature_b64":"emPys7d14B5c8++bawapEeCQMYAfqseQkTuMahVVlppZ1ZAPzu4zkxN5jMoNbf11REBbEsFEAKmysDVlFZ55Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e41d609e99e7811d28a65801757b9d882b97b33dd43d19c7a4c3633129cb7be","last_reissued_at":"2026-05-18T00:58:55.765459Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:55.765459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.4073","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":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N5E334ypszhWqoalhU0gCEltzIPutPD5+PVi/33G4sT6pBu2apcHBmt7P2p5NN9G6zfdK6Zw2bzdkdiFRowWDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:30:25.839122Z"},"content_sha256":"e30d2fc905b461a5c6c88c4dd25fed2bcaa4f8ee13ae1d4c56de0668ac1c1561","schema_version":"1.0","event_id":"sha256:e30d2fc905b461a5c6c88c4dd25fed2bcaa4f8ee13ae1d4c56de0668ac1c1561"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PZA5MCPJTZ4BDUUKMWABOV5Z3C","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Threshold and Symmetric Functions over Bitmaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DB","authors_text":"Daniel Lemire, Owen Kaser","submitted_at":"2014-02-17T17:22:05Z","abstract_excerpt":"Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the application of bitmap indexes to more advanced queries. We want to extend the applicability of bitmap indexes. As a starting point, we consider symmetric Boolean queries (e.g., threshold functions). For example, we might consider stores as sets of products, and ask for products that are on sale in 2 to 10 stores. Such symmetric Boolean queries generalize interse"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4073","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":""},"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":"2026-05-18T00:58:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Zh/gvno2KZYnDehnleX88BcDLYedzWAKsSShVMJKj/hbnF+aofhU0C/siQil4C5tlRG8qrSbp5ZwrCbTcRQsBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T09:30:25.839612Z"},"content_sha256":"56301e26e757e5aae9c6425695248e5b0225a092439a2977044ba39f6a863ade","schema_version":"1.0","event_id":"sha256:56301e26e757e5aae9c6425695248e5b0225a092439a2977044ba39f6a863ade"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/bundle.json","state_url":"https://pith.science/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/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":"2026-05-27T09:30:25Z","links":{"resolver":"https://pith.science/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C","bundle":"https://pith.science/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/bundle.json","state":"https://pith.science/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZA5MCPJTZ4BDUUKMWABOV5Z3C/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PZA5MCPJTZ4BDUUKMWABOV5Z3C","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":"e0ff15d9cbbf49862bf3978ab8d8d3a973cf47daa944f9804d2bf5b4f12a6372","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-02-17T17:22:05Z","title_canon_sha256":"14939e2600313a85d5b811e2746cc271fcc7480e0ff96223c7aea9d79ad585de"},"schema_version":"1.0","source":{"id":"1402.4073","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4073","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4073v2","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4073","created_at":"2026-05-18T00:58:55Z"},{"alias_kind":"pith_short_12","alias_value":"PZA5MCPJTZ4B","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PZA5MCPJTZ4BDUUK","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PZA5MCPJ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:56301e26e757e5aae9c6425695248e5b0225a092439a2977044ba39f6a863ade","target":"graph","created_at":"2026-05-18T00:58:55Z","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":"Bitmap indexes are routinely used to speed up simple aggregate queries in databases. Set operations such as intersections, unions and complements can be represented as logical operations (AND, OR, NOT). However, less is known about the application of bitmap indexes to more advanced queries. We want to extend the applicability of bitmap indexes. As a starting point, we consider symmetric Boolean queries (e.g., threshold functions). For example, we might consider stores as sets of products, and ask for products that are on sale in 2 to 10 stores. Such symmetric Boolean queries generalize interse","authors_text":"Daniel Lemire, Owen Kaser","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-02-17T17:22:05Z","title":"Threshold and Symmetric Functions over Bitmaps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4073","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:e30d2fc905b461a5c6c88c4dd25fed2bcaa4f8ee13ae1d4c56de0668ac1c1561","target":"record","created_at":"2026-05-18T00:58:55Z","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":"e0ff15d9cbbf49862bf3978ab8d8d3a973cf47daa944f9804d2bf5b4f12a6372","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DB","submitted_at":"2014-02-17T17:22:05Z","title_canon_sha256":"14939e2600313a85d5b811e2746cc271fcc7480e0ff96223c7aea9d79ad585de"},"schema_version":"1.0","source":{"id":"1402.4073","kind":"arxiv","version":2}},"canonical_sha256":"7e41d609e99e7811d28a65801757b9d882b97b33dd43d19c7a4c3633129cb7be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e41d609e99e7811d28a65801757b9d882b97b33dd43d19c7a4c3633129cb7be","first_computed_at":"2026-05-18T00:58:55.765459Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:55.765459Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"emPys7d14B5c8++bawapEeCQMYAfqseQkTuMahVVlppZ1ZAPzu4zkxN5jMoNbf11REBbEsFEAKmysDVlFZ55Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:55.765974Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4073","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e30d2fc905b461a5c6c88c4dd25fed2bcaa4f8ee13ae1d4c56de0668ac1c1561","sha256:56301e26e757e5aae9c6425695248e5b0225a092439a2977044ba39f6a863ade"],"state_sha256":"a03e7d5595d22d398728936981c2ad48ea2e1f0a70819fa0c9669a2ab50879a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+b8+LOcOAe/p0VpB2uDmENLbSwjsSmU84iKfOs3dN8e15mobhWmm8YJxS5mUZPcypoehRj7R2iFE1stU8xTAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T09:30:25.842888Z","bundle_sha256":"8c575c98d78cd0014c3760a6e80cc568ccce414ab1876c45ebff3b7ccc513b96"}}