{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:AG2IMIXGSHWGWEAH3MDKEFTXEC","short_pith_number":"pith:AG2IMIXG","schema_version":"1.0","canonical_sha256":"01b48622e691ec6b1007db06a2167720b9a099749b0ead704433e7c6a569ee02","source":{"kind":"arxiv","id":"1102.2936","version":3},"attestation_state":"computed","paper":{"title":"Decoding by Embedding: Correct Decoding Radius and DMT Optimality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cong Ling, Damien Stehle, Laura Luzzi","submitted_at":"2011-02-15T00:20:12Z","abstract_excerpt":"The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's \\emph{embedding technique} is a powerful technique for solving the approximate CVP, yet its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a \\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary analyses of the embedding technique: We establish a reduction from BD"},"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":"1102.2936","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2011-02-15T00:20:12Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"db848187782503266a809bf4dfcabc4b25d39503d090b743a741b2f36c6739da","abstract_canon_sha256":"d2df12b6ee5d3415e723b7505017a8d50dd1de907ca1c97cc1089f0aeaefd210"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:43.637871Z","signature_b64":"0KeERdByHpSFlZzVuzWAusjxU+HcO1d8RseaohGpL5LtP76WNkeTAW2/l7yT+zO01RPTCmGoPXkQylRPpoBABQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"01b48622e691ec6b1007db06a2167720b9a099749b0ead704433e7c6a569ee02","last_reissued_at":"2026-05-18T00:58:43.637201Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:43.637201Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Decoding by Embedding: Correct Decoding Radius and DMT Optimality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cong Ling, Damien Stehle, Laura Luzzi","submitted_at":"2011-02-15T00:20:12Z","abstract_excerpt":"The closest vector problem (CVP) and shortest (nonzero) vector problem (SVP) are the core algorithmic problems on Euclidean lattices. They are central to the applications of lattices in many problems of communications and cryptography. Kannan's \\emph{embedding technique} is a powerful technique for solving the approximate CVP, yet its remarkable practical performance is not well understood. In this paper, the embedding technique is analyzed from a \\emph{bounded distance decoding} (BDD) viewpoint. We present two complementary analyses of the embedding technique: We establish a reduction from BD"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2936","kind":"arxiv","version":3},"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":"1102.2936","created_at":"2026-05-18T00:58:43.637330+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.2936v3","created_at":"2026-05-18T00:58:43.637330+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2936","created_at":"2026-05-18T00:58:43.637330+00:00"},{"alias_kind":"pith_short_12","alias_value":"AG2IMIXGSHWG","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"AG2IMIXGSHWGWEAH","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"AG2IMIXG","created_at":"2026-05-18T12:26:24.575870+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/AG2IMIXGSHWGWEAH3MDKEFTXEC","json":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC.json","graph_json":"https://pith.science/api/pith-number/AG2IMIXGSHWGWEAH3MDKEFTXEC/graph.json","events_json":"https://pith.science/api/pith-number/AG2IMIXGSHWGWEAH3MDKEFTXEC/events.json","paper":"https://pith.science/paper/AG2IMIXG"},"agent_actions":{"view_html":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC","download_json":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC.json","view_paper":"https://pith.science/paper/AG2IMIXG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.2936&json=true","fetch_graph":"https://pith.science/api/pith-number/AG2IMIXGSHWGWEAH3MDKEFTXEC/graph.json","fetch_events":"https://pith.science/api/pith-number/AG2IMIXGSHWGWEAH3MDKEFTXEC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC/action/storage_attestation","attest_author":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC/action/author_attestation","sign_citation":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC/action/citation_signature","submit_replication":"https://pith.science/pith/AG2IMIXGSHWGWEAH3MDKEFTXEC/action/replication_record"}},"created_at":"2026-05-18T00:58:43.637330+00:00","updated_at":"2026-05-18T00:58:43.637330+00:00"}