{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:G6GRIXMWGZS73RRP323DBMTKKP","short_pith_number":"pith:G6GRIXMW","schema_version":"1.0","canonical_sha256":"378d145d963665fdc62fdeb630b26a53dced1c61f71dc6c47151c57769f41838","source":{"kind":"arxiv","id":"1309.7724","version":4},"attestation_state":"computed","paper":{"title":"The Dynamic Longest Increasing Subsequence Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alex Chen, Nathan Pinsker, Timothy Chu","submitted_at":"2013-09-30T05:24:37Z","abstract_excerpt":"In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\\log n)$ worst-case time and supports inserts anywhere in the sequence in $O \\left(r\\log{n/r}\\right)$ worst-case time (where $r$ is the length of the longest increasing subsequence). The same data structure with a minor modification supports $O(\\log n)$ worst-case time insertions if the insertions are performed at the end of the sequence. The data structure presented ca"},"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":"1309.7724","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-09-30T05:24:37Z","cross_cats_sorted":[],"title_canon_sha256":"e70ee1013c7f996002748f55a5f3d33176d2d527c06a0bd5ef767636c1c0efb2","abstract_canon_sha256":"efc35280b927230bbde21db28971080b4782ae7e31d1bef7bc0402f8281df374"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:37.023256Z","signature_b64":"zX4JIeFbp72XtTqdFhHJZaKvqnp0tPH2xMUcilc/a9Ow5BsCJDhwyNoHGy1LCYsN41MUem0q2vjwU9CExDwTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"378d145d963665fdc62fdeb630b26a53dced1c61f71dc6c47151c57769f41838","last_reissued_at":"2026-05-18T03:04:37.022523Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:37.022523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Dynamic Longest Increasing Subsequence Problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Alex Chen, Nathan Pinsker, Timothy Chu","submitted_at":"2013-09-30T05:24:37Z","abstract_excerpt":"In this paper, we construct a data structure to efficiently compute the longest increasing subsequence of a sequence subject to dynamic updates. Our data structure supports a query for the longest increasing subsequence in $O(r+\\log n)$ worst-case time and supports inserts anywhere in the sequence in $O \\left(r\\log{n/r}\\right)$ worst-case time (where $r$ is the length of the longest increasing subsequence). The same data structure with a minor modification supports $O(\\log n)$ worst-case time insertions if the insertions are performed at the end of the sequence. The data structure presented ca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.7724","kind":"arxiv","version":4},"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":"1309.7724","created_at":"2026-05-18T03:04:37.022655+00:00"},{"alias_kind":"arxiv_version","alias_value":"1309.7724v4","created_at":"2026-05-18T03:04:37.022655+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.7724","created_at":"2026-05-18T03:04:37.022655+00:00"},{"alias_kind":"pith_short_12","alias_value":"G6GRIXMWGZS7","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"G6GRIXMWGZS73RRP","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"G6GRIXMW","created_at":"2026-05-18T12:27:45.050594+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/G6GRIXMWGZS73RRP323DBMTKKP","json":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP.json","graph_json":"https://pith.science/api/pith-number/G6GRIXMWGZS73RRP323DBMTKKP/graph.json","events_json":"https://pith.science/api/pith-number/G6GRIXMWGZS73RRP323DBMTKKP/events.json","paper":"https://pith.science/paper/G6GRIXMW"},"agent_actions":{"view_html":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP","download_json":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP.json","view_paper":"https://pith.science/paper/G6GRIXMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1309.7724&json=true","fetch_graph":"https://pith.science/api/pith-number/G6GRIXMWGZS73RRP323DBMTKKP/graph.json","fetch_events":"https://pith.science/api/pith-number/G6GRIXMWGZS73RRP323DBMTKKP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP/action/storage_attestation","attest_author":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP/action/author_attestation","sign_citation":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP/action/citation_signature","submit_replication":"https://pith.science/pith/G6GRIXMWGZS73RRP323DBMTKKP/action/replication_record"}},"created_at":"2026-05-18T03:04:37.022655+00:00","updated_at":"2026-05-18T03:04:37.022655+00:00"}