{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NDOBS3CCYBJAJJ3TR23IGCJ3SW","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":"a0c8c8626052f73a1dea5b134103405ce95f545df2f19ad7f96939d260cb72e8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-20T21:59:01Z","title_canon_sha256":"8f85bb760d057de58bf35ecc6620a9608b9cc53480e9a628e37934d8d0fc95f3"},"schema_version":"1.0","source":{"id":"1610.06618","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06618","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06618v3","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06618","created_at":"2026-05-18T00:01:39Z"},{"alias_kind":"pith_short_12","alias_value":"NDOBS3CCYBJA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NDOBS3CCYBJAJJ3T","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NDOBS3CC","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:2a50796147463be20df7cd0ddbc47261d6a126bd046ca504c211d4965b3a9908","target":"graph","created_at":"2026-05-18T00:01:39Z","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 many applications including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an $n$-dimensional lattice to get an optimal integer coefficient matrix $\\A^\\star\\in \\mathbb{Z}^{n\\times n}$. In this paper, we first propose an efficient optimal SMP algorithm with an $\\bigO(n^2)$ memory complexity. The main idea behind the new algorithm is it first initializes with a suitable suboptimal solution, which is then updated, via a novel algorithm with only $\\bigO(n^2)$ flops in each updating, until $\\A^{\\star}$ is ","authors_text":"Jinming Wen, Lanping Li, Wai Ho Mow, Xiaohu Tang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-20T21:59:01Z","title":"An Efficient Optimal Algorithm for the Successive Minima Problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06618","kind":"arxiv","version":3},"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":"sha256:049bd6d37acde985e5410b9f05b46d57d6a0bfcc30d86e342e2f921a0c244ce1","target":"record","created_at":"2026-05-18T00:01:39Z","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":"a0c8c8626052f73a1dea5b134103405ce95f545df2f19ad7f96939d260cb72e8","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-10-20T21:59:01Z","title_canon_sha256":"8f85bb760d057de58bf35ecc6620a9608b9cc53480e9a628e37934d8d0fc95f3"},"schema_version":"1.0","source":{"id":"1610.06618","kind":"arxiv","version":3}},"canonical_sha256":"68dc196c42c05204a7738eb683093b959ebe0dfb2a428c5f0266aa05a9fce4db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68dc196c42c05204a7738eb683093b959ebe0dfb2a428c5f0266aa05a9fce4db","first_computed_at":"2026-05-18T00:01:39.291733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:39.291733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSnYPsMLUIVNvw6Fxu+zcwo0BSAlDEqZwpgOOVv/Z3tIiGSZcCBUsxWG2K2CLKc69fusOql0bEdKESVkz9A0AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:39.292177Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06618","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:049bd6d37acde985e5410b9f05b46d57d6a0bfcc30d86e342e2f921a0c244ce1","sha256:2a50796147463be20df7cd0ddbc47261d6a126bd046ca504c211d4965b3a9908"],"state_sha256":"a324656d36724f9a01d17ee8bd149b76b9bcf640e24b19a3bb090737bdd465a7"}