{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MWR6HGVEMZSXNZRVCBP2ONPX2N","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":"5e619f22d5582a6cb017a19738d85ff27cdb4077c438c9afd77240bbe144bc69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-22T12:54:30Z","title_canon_sha256":"2fefcea47af2fbc64b2efd21341db20f7d72534bb56ee4a3d7a47b7d498654d3"},"schema_version":"1.0","source":{"id":"1607.06660","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.06660","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"arxiv_version","alias_value":"1607.06660v1","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.06660","created_at":"2026-05-18T01:10:39Z"},{"alias_kind":"pith_short_12","alias_value":"MWR6HGVEMZSX","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MWR6HGVEMZSXNZRV","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MWR6HGVE","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:a1c03d39f32effff03a1a774517c402a3615897e9933fc29d6284456186b77c8","target":"graph","created_at":"2026-05-18T01:10:39Z","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":"In this paper we address the longest common extension (LCE) problem: to compute the length $\\ell$ of the longest common prefix between any two suffixes of $T\\in \\Sigma^n$ with $ \\Sigma = \\{0, \\ldots \\sigma-1\\} $. We present two fast and space-efficient solutions based on (Karp-Rabin) \\textit{fingerprinting} and \\textit{sampling}. Our first data structure exploits properties of Mersenne prime numbers when used as moduli of the Karp-Rabin hash function and takes $n\\lceil \\log_2\\sigma\\rceil$ bits of space. Our second structure works with any prime modulus and takes $n\\lceil \\log_2\\sigma\\rceil + n","authors_text":"Alberto Policriti, Nicola Prezza","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-22T12:54:30Z","title":"Fast Longest Common Extensions in Small Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.06660","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":"sha256:3c849dd48cf89d3dcdbb6aff5e19206318ac9ad95fd6c27141007f6dab74f8e8","target":"record","created_at":"2026-05-18T01:10:39Z","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":"5e619f22d5582a6cb017a19738d85ff27cdb4077c438c9afd77240bbe144bc69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-07-22T12:54:30Z","title_canon_sha256":"2fefcea47af2fbc64b2efd21341db20f7d72534bb56ee4a3d7a47b7d498654d3"},"schema_version":"1.0","source":{"id":"1607.06660","kind":"arxiv","version":1}},"canonical_sha256":"65a3e39aa4666576e635105fa735f7d341da6052e22ffe5caa391e191ed5c6f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"65a3e39aa4666576e635105fa735f7d341da6052e22ffe5caa391e191ed5c6f3","first_computed_at":"2026-05-18T01:10:39.342806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:39.342806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZZ56ibchkXPlvqCAiH12n/5i5C+J3FQFBUqruJ+gbvIlXv24u3RssvSX6Nh45+fZdrh3up2gc4cOmuhAjYyBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:39.343408Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.06660","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3c849dd48cf89d3dcdbb6aff5e19206318ac9ad95fd6c27141007f6dab74f8e8","sha256:a1c03d39f32effff03a1a774517c402a3615897e9933fc29d6284456186b77c8"],"state_sha256":"6e988adaa7271e6c0a13d796f9d7643e7eb12f13f300adeb8bd06030fc9c7751"}