{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:APLNV4HOBQ4X222TPYE6LRGW3B","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":"c155940b213fa63f13aab62b3e70b6906248339d92c80e837d95cb979a67adbb","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-12-13T23:41:21Z","title_canon_sha256":"e4c002e5b7783a42ec042e72ddfcd1e600f71d448c6e194b30bb1a0ea50fd5a6"},"schema_version":"1.0","source":{"id":"1512.04138","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04138","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04138v5","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04138","created_at":"2026-05-17T23:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"APLNV4HOBQ4X","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"APLNV4HOBQ4X222T","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"APLNV4HO","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:164bb0ef21cbcede7d93373bdb2e9557d888c7080351a1f70526790a5badf31e","target":"graph","created_at":"2026-05-17T23:55:34Z","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":"We show the first dimension-preserving search-to-decision reductions for approximate SVP and CVP. In particular, for any $\\gamma \\leq 1 + O(\\log n/n)$, we obtain an efficient dimension-preserving reduction from $\\gamma^{O(n/\\log n)}$-SVP to $\\gamma$-GapSVP and an efficient dimension-preserving reduction from $\\gamma^{O(n)}$-CVP to $\\gamma$-GapCVP. These results generalize the known equivalences of the search and decision versions of these problems in the exact case when $\\gamma = 1$. For SVP, we actually obtain something slightly stronger than a search-to-decision reduction---we reduce $\\gamma","authors_text":"Noah Stephens-Davidowitz","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-12-13T23:41:21Z","title":"Search-to-Decision Reductions for Lattice Problems with Approximation Factors (Slightly) Greater Than One"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04138","kind":"arxiv","version":5},"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":"sha256:4ce1229344d793190fc0804fe3130aa45317f97244720bd4d4659426e23ea91f","target":"record","created_at":"2026-05-17T23:55:34Z","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":"c155940b213fa63f13aab62b3e70b6906248339d92c80e837d95cb979a67adbb","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2015-12-13T23:41:21Z","title_canon_sha256":"e4c002e5b7783a42ec042e72ddfcd1e600f71d448c6e194b30bb1a0ea50fd5a6"},"schema_version":"1.0","source":{"id":"1512.04138","kind":"arxiv","version":5}},"canonical_sha256":"03d6daf0ee0c397d6b537e09e5c4d6d84cab8fc0989ad1901ae7b55734475936","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03d6daf0ee0c397d6b537e09e5c4d6d84cab8fc0989ad1901ae7b55734475936","first_computed_at":"2026-05-17T23:55:34.914751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:34.914751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"e8LB2H3SEAKlV8meGByUoZyhFet4fTUjUsZZiwXU/S2mQqle9uWfCdUvcR/eePSmUhYv3CZ7XOsNkynL3teUDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:34.915371Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04138","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ce1229344d793190fc0804fe3130aa45317f97244720bd4d4659426e23ea91f","sha256:164bb0ef21cbcede7d93373bdb2e9557d888c7080351a1f70526790a5badf31e"],"state_sha256":"62209dd5310344363d6938d256481514ac55f88299a3c1f8153cdde48e138a61"}