{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:FRAP6WLWILMGBUYKTXM7N5VXE5","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":"02c6da5377bca4ba1a755f712bc7d9871cb6931cdfbe24d8ec44481c762f31fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-14T18:47:01Z","title_canon_sha256":"de5f7c52b56054c9395342c625b4208f539f00a21a3ac57e79686d9af3ac6722"},"schema_version":"1.0","source":{"id":"1606.04495","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.04495","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"arxiv_version","alias_value":"1606.04495v1","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.04495","created_at":"2026-05-18T01:12:25Z"},{"alias_kind":"pith_short_12","alias_value":"FRAP6WLWILMG","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_16","alias_value":"FRAP6WLWILMGBUYK","created_at":"2026-05-18T12:30:15Z"},{"alias_kind":"pith_short_8","alias_value":"FRAP6WLW","created_at":"2026-05-18T12:30:15Z"}],"graph_snapshots":[{"event_id":"sha256:08b612aab01fc9081049ce666a65f81ed4dbd0bde8244005fcfc31c143447f58","target":"graph","created_at":"2026-05-18T01:12:25Z","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":"Karpinski and Nekrich (2008) introduced the problem of parameterized range majority, which asks us to preprocess a string of length $n$ such that, given the endpoints of a range, one can quickly find all the distinct elements whose relative frequencies in that range are more than a threshold $\\tau$. Subsequent authors have reduced their time and space bounds such that, when $\\tau$ is fixed at preprocessing time, we need either $O(n \\log (1 / \\tau))$ space and optimal $O(1 / \\tau)$ query time or linear space and $O((1 / \\tau) \\log \\log \\sigma)$ query time, where $\\sigma$ is the alphabet size. I","authors_text":"Djamal Belazzougui, Gonzalo Navarro, J. Ian Munro, Travis Gagie, Yakov Nekrich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-14T18:47:01Z","title":"Range Majorities and Minorities in Arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.04495","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":"sha256:90409a5f31920a75a096378eebcd3a26c3c9eca612226b0a4c34602e729b8a3f","target":"record","created_at":"2026-05-18T01:12:25Z","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":"02c6da5377bca4ba1a755f712bc7d9871cb6931cdfbe24d8ec44481c762f31fb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-06-14T18:47:01Z","title_canon_sha256":"de5f7c52b56054c9395342c625b4208f539f00a21a3ac57e79686d9af3ac6722"},"schema_version":"1.0","source":{"id":"1606.04495","kind":"arxiv","version":1}},"canonical_sha256":"2c40ff597642d860d30a9dd9f6f6b7275403e06954948f63c0b602422446c78b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c40ff597642d860d30a9dd9f6f6b7275403e06954948f63c0b602422446c78b","first_computed_at":"2026-05-18T01:12:25.526676Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:25.526676Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QVfcWmw8K1SqdaXq9jV8gxsGZtQ2Eg0wL9RrBixA/TJVYHImrrM3RCrt/OMVpwEzS3YCmg3GcsaZMkSnclRHDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:25.527003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.04495","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90409a5f31920a75a096378eebcd3a26c3c9eca612226b0a4c34602e729b8a3f","sha256:08b612aab01fc9081049ce666a65f81ed4dbd0bde8244005fcfc31c143447f58"],"state_sha256":"314b770bb582fe3b2b1a2e4e6cb73806c18451ed2ffe538cf493cc14a51d7842"}