{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:RYLETVIOKA2KI25U7PZYXLNW3F","short_pith_number":"pith:RYLETVIO","schema_version":"1.0","canonical_sha256":"8e1649d50e5034a46bb4fbf38badb6d978399ab57b486c3d42bfaaa464d8bef6","source":{"kind":"arxiv","id":"1903.02533","version":1},"attestation_state":"computed","paper":{"title":"Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. Ian Munro, Sebastian Wild","submitted_at":"2019-03-06T18:13:33Z","abstract_excerpt":"The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been unknown whether such a data structure can be made adaptive to the reduced entropy of random inputs (Davoodi et al. 2014). We construct a succinct data structure with the optimal $1.736n+o(n)$ bits of space on average for random RMQ instances, settling this open problem.\n  Our solution relies on a compressed data structure for binary trees that is of indepen"},"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":"1903.02533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-03-06T18:13:33Z","cross_cats_sorted":[],"title_canon_sha256":"8bcfa7c86c04df00f7bc03b28c5cd83b07bab24c62b5ac7b771eded8c8b48d97","abstract_canon_sha256":"0cdd7d0bca95c370b9bfef852513b648564b0771240a85144c5a5b0b480dcfd7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:55.130228Z","signature_b64":"/CGIXh/bIrMkVgh3hq7mkF9DH4j5UtcP563cwaPqrQNI+chLAruZ9vtXaH/afKZn2QIZR8H493dqPhemYwFIDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e1649d50e5034a46bb4fbf38badb6d978399ab57b486c3d42bfaaa464d8bef6","last_reissued_at":"2026-05-17T23:51:55.129733Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:55.129733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Entropy Trees and Range-Minimum Queries In Optimal Average-Case Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"J. Ian Munro, Sebastian Wild","submitted_at":"2019-03-06T18:13:33Z","abstract_excerpt":"The range-minimum query (RMQ) problem is a fundamental data structuring task with numerous applications. Despite the fact that succinct solutions with worst-case optimal $2n+o(n)$ bits of space and constant query time are known, it has been unknown whether such a data structure can be made adaptive to the reduced entropy of random inputs (Davoodi et al. 2014). We construct a succinct data structure with the optimal $1.736n+o(n)$ bits of space on average for random RMQ instances, settling this open problem.\n  Our solution relies on a compressed data structure for binary trees that is of indepen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02533","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.02533","created_at":"2026-05-17T23:51:55.129825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.02533v1","created_at":"2026-05-17T23:51:55.129825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.02533","created_at":"2026-05-17T23:51:55.129825+00:00"},{"alias_kind":"pith_short_12","alias_value":"RYLETVIOKA2K","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"RYLETVIOKA2KI25U","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"RYLETVIO","created_at":"2026-05-18T12:33:27.125529+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/RYLETVIOKA2KI25U7PZYXLNW3F","json":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F.json","graph_json":"https://pith.science/api/pith-number/RYLETVIOKA2KI25U7PZYXLNW3F/graph.json","events_json":"https://pith.science/api/pith-number/RYLETVIOKA2KI25U7PZYXLNW3F/events.json","paper":"https://pith.science/paper/RYLETVIO"},"agent_actions":{"view_html":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F","download_json":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F.json","view_paper":"https://pith.science/paper/RYLETVIO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.02533&json=true","fetch_graph":"https://pith.science/api/pith-number/RYLETVIOKA2KI25U7PZYXLNW3F/graph.json","fetch_events":"https://pith.science/api/pith-number/RYLETVIOKA2KI25U7PZYXLNW3F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F/action/storage_attestation","attest_author":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F/action/author_attestation","sign_citation":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F/action/citation_signature","submit_replication":"https://pith.science/pith/RYLETVIOKA2KI25U7PZYXLNW3F/action/replication_record"}},"created_at":"2026-05-17T23:51:55.129825+00:00","updated_at":"2026-05-17T23:51:55.129825+00:00"}