{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EOTJ4IXHIG3C7TSI4LO6PN25ST","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":"b75739982149fe5d96447d0cb1e50a4783754163e933444cf44e67cbf4bdac96","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-20T15:29:35Z","title_canon_sha256":"3ee298623909a04b2bd92620d07871ccf194de9eb69519da09c0cb4fe34e22b1"},"schema_version":"1.0","source":{"id":"1504.05086","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05086","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05086v1","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05086","created_at":"2026-05-18T02:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"EOTJ4IXHIG3C","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EOTJ4IXHIG3C7TSI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EOTJ4IXH","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:0e3eaecf3e43596d772771caf03647c9cee61625c2a31f98a9305f0edf225cac","target":"graph","created_at":"2026-05-18T02:18:22Z","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":"The Korkine-Zolotareff (KZ) reduction has been used in communications and cryptography. In this paper, we modify a very recent KZ reduction algorithm proposed by Zhang et al., resulting in a new algorithm, which can be much faster and more numerically reliable, especially when the basis matrix is ill conditioned.","authors_text":"Jinming Wen, Xiao-Wen Chang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-20T15:29:35Z","title":"A Modified KZ Reduction Algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05086","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":"sha256:8d1b5cfa6a9a7df88c5855d97b05cffe7c38bbb907668601663894cfb4917cd8","target":"record","created_at":"2026-05-18T02:18:22Z","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":"b75739982149fe5d96447d0cb1e50a4783754163e933444cf44e67cbf4bdac96","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-20T15:29:35Z","title_canon_sha256":"3ee298623909a04b2bd92620d07871ccf194de9eb69519da09c0cb4fe34e22b1"},"schema_version":"1.0","source":{"id":"1504.05086","kind":"arxiv","version":1}},"canonical_sha256":"23a69e22e741b62fce48e2dde7b75d94d9e9f524e5188e9518eba2f81a4bed4f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"23a69e22e741b62fce48e2dde7b75d94d9e9f524e5188e9518eba2f81a4bed4f","first_computed_at":"2026-05-18T02:18:22.673335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:22.673335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RdHj+fFAdwh7x+GXtikjfHjczMUdYXuKt9obF9GcF3HRtkclXglO18QVEzagNMijQ6Pe0J20P3SEeK7di99zDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:22.674058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05086","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d1b5cfa6a9a7df88c5855d97b05cffe7c38bbb907668601663894cfb4917cd8","sha256:0e3eaecf3e43596d772771caf03647c9cee61625c2a31f98a9305f0edf225cac"],"state_sha256":"4f6051565877bedd3caecaedea19ee7a5c4543078a98b547f4e4834e7cab3244"}