{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VYCW7Y5IKB6TRNKBQAKGDVGVLN","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":"bd54a9ba4c65fea298662bfcab4929bb49c340d4b66d7b7e48ee617452f126e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T19:00:45Z","title_canon_sha256":"2f669b25b5ae8645a29a8aed035329e65c6c5144cec6db727d7894e8337c48f5"},"schema_version":"1.0","source":{"id":"1807.03827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.03827","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"arxiv_version","alias_value":"1807.03827v1","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03827","created_at":"2026-05-18T00:10:58Z"},{"alias_kind":"pith_short_12","alias_value":"VYCW7Y5IKB6T","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VYCW7Y5IKB6TRNKB","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VYCW7Y5I","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:2eed375a40af89d5a0919427f8c415cdde4337b30a4758ab1725c3113f4b6d86","target":"graph","created_at":"2026-05-18T00:10:58Z","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":"Given an array A of $n$ elements, we wish to support queries for the most frequent and least frequent element in a subrange $[l, r]$ of $A$. We also wish to support updates that change a particular element at index $i$ or insert/ delete an element at index $i$. For the range mode problem, our data structure supports all operations in $O(n^{2/3})$ deterministic time using only $O(n)$ space. This improves two results by Chan et al. \\cite{C14}: a linear space data structure supporting update and query operations in $\\tilde{O}(n^{3/4})$ time and an $O(n^{4/3})$ space data structure supporting upda","authors_text":"Bryce Sandlund, Hicham El-Zein, J. Ian Munro, Meng He","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T19:00:45Z","title":"Improved Time and Space Bounds for Dynamic Range Mode"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03827","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":"sha256:8ef88c32cdf64ae6b37cb986bd316693db84f84aadb6f1f280729e78186b79a6","target":"record","created_at":"2026-05-18T00:10:58Z","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":"bd54a9ba4c65fea298662bfcab4929bb49c340d4b66d7b7e48ee617452f126e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-10T19:00:45Z","title_canon_sha256":"2f669b25b5ae8645a29a8aed035329e65c6c5144cec6db727d7894e8337c48f5"},"schema_version":"1.0","source":{"id":"1807.03827","kind":"arxiv","version":1}},"canonical_sha256":"ae056fe3a8507d38b541801461d4d55b74ceccaf138418cbbe1f8b297316b632","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae056fe3a8507d38b541801461d4d55b74ceccaf138418cbbe1f8b297316b632","first_computed_at":"2026-05-18T00:10:58.948442Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:58.948442Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"75u72sf68UU2M+f/iESjue68MOPYXvPyR2dYTuVLniQ7lUEcS0rXq6fzOdepk2pts1/RvtHDd1J+ofT4Gq+rDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:58.949268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.03827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ef88c32cdf64ae6b37cb986bd316693db84f84aadb6f1f280729e78186b79a6","sha256:2eed375a40af89d5a0919427f8c415cdde4337b30a4758ab1725c3113f4b6d86"],"state_sha256":"5f271b59c71450154354835e1871498f5a9d583430dfd02eca96d7bce997bd3a"}