{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:I37RRBVF3HBE54G4DZEQUAQT5A","short_pith_number":"pith:I37RRBVF","schema_version":"1.0","canonical_sha256":"46ff1886a5d9c24ef0dc1e490a0213e8191858cfd1d411f0cdc6791877f39db4","source":{"kind":"arxiv","id":"1111.2621","version":2},"attestation_state":"computed","paper":{"title":"Optimal Lower and Upper Bounds for Representing Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Gonzalo Navarro","submitted_at":"2011-11-10T21:51:27Z","abstract_excerpt":"Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article we prove a strong lower bound for $rank$, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, operations $access$ and $select$ can be solved in constant or almost-constant tim"},"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":"1111.2621","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2011-11-10T21:51:27Z","cross_cats_sorted":[],"title_canon_sha256":"ca09e477c23946e5ea9bb59a0d2e2030c54cd8e40a3686e10c2007485b4f8ec8","abstract_canon_sha256":"cc6efd16ff226a1bb52c92ea566767771b97729c8c6292ef55a685d6cdf64734"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:18.928995Z","signature_b64":"gz4oxvg8M4yTtFfWnpm6gMnW621Uy7uXhozhh3z0IR24ik5HGpi5165PHs/NoCl5gtmk44lgdMxLhs/7PSYAAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46ff1886a5d9c24ef0dc1e490a0213e8191858cfd1d411f0cdc6791877f39db4","last_reissued_at":"2026-05-18T03:15:18.928167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:18.928167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Lower and Upper Bounds for Representing Sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Djamal Belazzougui, Gonzalo Navarro","submitted_at":"2011-11-10T21:51:27Z","abstract_excerpt":"Sequence representations supporting queries $access$, $select$ and $rank$ are at the core of many data structures. There is a considerable gap between the various upper bounds and the few lower bounds known for such representations, and how they relate to the space used. In this article we prove a strong lower bound for $rank$, which holds for rather permissive assumptions on the space used, and give matching upper bounds that require only a compressed representation of the sequence. Within this compressed space, operations $access$ and $select$ can be solved in constant or almost-constant tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2621","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.2621","created_at":"2026-05-18T03:15:18.928301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.2621v2","created_at":"2026-05-18T03:15:18.928301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2621","created_at":"2026-05-18T03:15:18.928301+00:00"},{"alias_kind":"pith_short_12","alias_value":"I37RRBVF3HBE","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_16","alias_value":"I37RRBVF3HBE54G4","created_at":"2026-05-18T12:26:30.835961+00:00"},{"alias_kind":"pith_short_8","alias_value":"I37RRBVF","created_at":"2026-05-18T12:26:30.835961+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/I37RRBVF3HBE54G4DZEQUAQT5A","json":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A.json","graph_json":"https://pith.science/api/pith-number/I37RRBVF3HBE54G4DZEQUAQT5A/graph.json","events_json":"https://pith.science/api/pith-number/I37RRBVF3HBE54G4DZEQUAQT5A/events.json","paper":"https://pith.science/paper/I37RRBVF"},"agent_actions":{"view_html":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A","download_json":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A.json","view_paper":"https://pith.science/paper/I37RRBVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.2621&json=true","fetch_graph":"https://pith.science/api/pith-number/I37RRBVF3HBE54G4DZEQUAQT5A/graph.json","fetch_events":"https://pith.science/api/pith-number/I37RRBVF3HBE54G4DZEQUAQT5A/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A/action/timestamp_anchor","attest_storage":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A/action/storage_attestation","attest_author":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A/action/author_attestation","sign_citation":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A/action/citation_signature","submit_replication":"https://pith.science/pith/I37RRBVF3HBE54G4DZEQUAQT5A/action/replication_record"}},"created_at":"2026-05-18T03:15:18.928301+00:00","updated_at":"2026-05-18T03:15:18.928301+00:00"}