{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2ZNYIPVLHWDVQXWPOQ2YB6HS53","short_pith_number":"pith:2ZNYIPVL","canonical_record":{"source":{"id":"1006.1666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-08T21:12:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0ea7dfd96ba348eceecbc2b32f7bb773f94ebb25e9a0e9993012d89471390d6a","abstract_canon_sha256":"5a45ccd0345ccb10aa7f2bd4abc6304c702184c92fb5ea54fffbafd7a3eb2149"},"schema_version":"1.0"},"canonical_sha256":"d65b843eab3d87585ecf743580f8f2eef5ed6c5422f04ac98820bc4a53fc1f5d","source":{"kind":"arxiv","id":"1006.1666","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1666","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1666v2","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1666","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"2ZNYIPVLHWDV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZNYIPVLHWDVQXWP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZNYIPVL","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2ZNYIPVLHWDVQXWPOQ2YB6HS53","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1666","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-08T21:12:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"0ea7dfd96ba348eceecbc2b32f7bb773f94ebb25e9a0e9993012d89471390d6a","abstract_canon_sha256":"5a45ccd0345ccb10aa7f2bd4abc6304c702184c92fb5ea54fffbafd7a3eb2149"},"schema_version":"1.0"},"canonical_sha256":"d65b843eab3d87585ecf743580f8f2eef5ed6c5422f04ac98820bc4a53fc1f5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:12.139807Z","signature_b64":"6UanMZ7obWoyeApeWitHu3fk90BlNbU5WoSyfeWPFocWK6PjdcYyQhHUzGR4XapHSEemu3+acq/s/BlK1P6wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d65b843eab3d87585ecf743580f8f2eef5ed6c5422f04ac98820bc4a53fc1f5d","last_reissued_at":"2026-05-18T01:29:12.139088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:12.139088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1666","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4o4irJw6nUNV5NjZXwKS57KoH9RUQyEkpnrMayH7ob8bp/5cF12/ZPJ5yqYqCqrscEtAlDz/K/heTUSCD+5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:21:43.956176Z"},"content_sha256":"36ed539a4a7705203e0c4bceee6a3b3f5bd940925e1d4d5165b4a745b7225327","schema_version":"1.0","event_id":"sha256:36ed539a4a7705203e0c4bceee6a3b3f5bd940925e1d4d5165b4a745b7225327"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2ZNYIPVLHWDVQXWPOQ2YB6HS53","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Proximity Factors of Lattice Reduction-Aided Decoding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Cong Ling","submitted_at":"2010-06-08T21:12:07Z","abstract_excerpt":"Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this aim, the proximity factors are defined to measure the worst-case losses in distances relative to closest point search (in an infinite lattice). Upper bounds on the proximity factors are derived, which are functions of the dimension $n$ of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis red"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1666","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"argBQ1HmmbaBg9lWlhsWmlehht5g7i9mScmgsAmXt/kBdgK/tDgrcItlOomMtW3IwTbQyWv7JJPLV8HGC743Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T21:21:43.956552Z"},"content_sha256":"0a69130c9d4bce4cc979eb763f85721595680f15496b8797aaa460095a172242","schema_version":"1.0","event_id":"sha256:0a69130c9d4bce4cc979eb763f85721595680f15496b8797aaa460095a172242"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/bundle.json","state_url":"https://pith.science/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T21:21:43Z","links":{"resolver":"https://pith.science/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53","bundle":"https://pith.science/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/bundle.json","state":"https://pith.science/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2ZNYIPVLHWDVQXWPOQ2YB6HS53/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2ZNYIPVLHWDVQXWPOQ2YB6HS53","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":"5a45ccd0345ccb10aa7f2bd4abc6304c702184c92fb5ea54fffbafd7a3eb2149","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-08T21:12:07Z","title_canon_sha256":"0ea7dfd96ba348eceecbc2b32f7bb773f94ebb25e9a0e9993012d89471390d6a"},"schema_version":"1.0","source":{"id":"1006.1666","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1666","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1666v2","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1666","created_at":"2026-05-18T01:29:12Z"},{"alias_kind":"pith_short_12","alias_value":"2ZNYIPVLHWDV","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2ZNYIPVLHWDVQXWP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2ZNYIPVL","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:0a69130c9d4bce4cc979eb763f85721595680f15496b8797aaa460095a172242","target":"graph","created_at":"2026-05-18T01:29:12Z","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":"Lattice reduction-aided decoding features reduced decoding complexity and near-optimum performance in multi-input multi-output communications. In this paper, a quantitative analysis of lattice reduction-aided decoding is presented. To this aim, the proximity factors are defined to measure the worst-case losses in distances relative to closest point search (in an infinite lattice). Upper bounds on the proximity factors are derived, which are functions of the dimension $n$ of the lattice alone. The study is then extended to the dual-basis reduction. It is found that the bounds for dual basis red","authors_text":"Cong Ling","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-08T21:12:07Z","title":"On the Proximity Factors of Lattice Reduction-Aided Decoding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1666","kind":"arxiv","version":2},"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":"sha256:36ed539a4a7705203e0c4bceee6a3b3f5bd940925e1d4d5165b4a745b7225327","target":"record","created_at":"2026-05-18T01:29:12Z","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":"5a45ccd0345ccb10aa7f2bd4abc6304c702184c92fb5ea54fffbafd7a3eb2149","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-06-08T21:12:07Z","title_canon_sha256":"0ea7dfd96ba348eceecbc2b32f7bb773f94ebb25e9a0e9993012d89471390d6a"},"schema_version":"1.0","source":{"id":"1006.1666","kind":"arxiv","version":2}},"canonical_sha256":"d65b843eab3d87585ecf743580f8f2eef5ed6c5422f04ac98820bc4a53fc1f5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d65b843eab3d87585ecf743580f8f2eef5ed6c5422f04ac98820bc4a53fc1f5d","first_computed_at":"2026-05-18T01:29:12.139088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:12.139088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6UanMZ7obWoyeApeWitHu3fk90BlNbU5WoSyfeWPFocWK6PjdcYyQhHUzGR4XapHSEemu3+acq/s/BlK1P6wAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:12.139807Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1666","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:36ed539a4a7705203e0c4bceee6a3b3f5bd940925e1d4d5165b4a745b7225327","sha256:0a69130c9d4bce4cc979eb763f85721595680f15496b8797aaa460095a172242"],"state_sha256":"34a15afb73583f5d31093b75f782c2379f149c4af85efd1c22384dadc6a67ff1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+Lzbwd0B1jh8VUidiPjhw9LBaj6BcJMxTg57JZK3cpoInuXokcwhrQ83QrhdYyEVPQ1mgysOyo6jCXlCK7lxCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T21:21:43.958566Z","bundle_sha256":"054bc4e5fdb4f5788fb3adebc3146c203ed9f7fda3a9fb07598c6aa5b92c9c80"}}