{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TNQR26KSSXARQMDI7XICKXKDGI","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":"0d706ce152dd879e86dc1bd2d6071c30575debfcc550ca33e7cc4adc727e2272","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-25T14:43:17Z","title_canon_sha256":"a916ed080c12da14fa73f7b8f3244e77d6ef6d65cbf7bcb3d2fc989f1e9daa1c"},"schema_version":"1.0","source":{"id":"1608.07179","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.07179","created_at":"2026-05-18T01:06:28Z"},{"alias_kind":"arxiv_version","alias_value":"1608.07179v1","created_at":"2026-05-18T01:06:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.07179","created_at":"2026-05-18T01:06:28Z"},{"alias_kind":"pith_short_12","alias_value":"TNQR26KSSXAR","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TNQR26KSSXARQMDI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TNQR26KS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:21762bb7ceb6dd64795b8e3de2823610be1fb2280a7016026f6fb7b8c236ebd5","target":"graph","created_at":"2026-05-18T01:06:28Z","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":"A sampling-based optimization method for quadratic functions is proposed. Our method approximately solves the following $n$-dimensional quadratic minimization problem in constant time, which is independent of $n$: $z^*=\\min_{\\mathbf{v} \\in \\mathbb{R}^n}\\langle\\mathbf{v}, A \\mathbf{v}\\rangle + n\\langle\\mathbf{v}, \\mathrm{diag}(\\mathbf{d})\\mathbf{v}\\rangle + n\\langle\\mathbf{b}, \\mathbf{v}\\rangle$, where $A \\in \\mathbb{R}^{n \\times n}$ is a matrix and $\\mathbf{d},\\mathbf{b} \\in \\mathbb{R}^n$ are vectors. Our theoretical analysis specifies the number of samples $k(\\delta, \\epsilon)$ such that the ","authors_text":"Kohei Hayashi, Yuichi Yoshida","cross_cats":["cs.DS","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-25T14:43:17Z","title":"Minimizing Quadratic Functions in Constant Time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07179","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":"sha256:0b88ef6cb61176c5a7d1f7456cf20a4a4e748c1e51b30b40dd5608fd95e5aca4","target":"record","created_at":"2026-05-18T01:06:28Z","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":"0d706ce152dd879e86dc1bd2d6071c30575debfcc550ca33e7cc4adc727e2272","cross_cats_sorted":["cs.DS","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-08-25T14:43:17Z","title_canon_sha256":"a916ed080c12da14fa73f7b8f3244e77d6ef6d65cbf7bcb3d2fc989f1e9daa1c"},"schema_version":"1.0","source":{"id":"1608.07179","kind":"arxiv","version":1}},"canonical_sha256":"9b611d795295c1183068fdd0255d4332144ac94a7a52e15055a2d603f18daf67","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b611d795295c1183068fdd0255d4332144ac94a7a52e15055a2d603f18daf67","first_computed_at":"2026-05-18T01:06:28.326649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:28.326649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"w35cdx0wTNFWNW58WFYjL4sjfAI+hHUN5lFvnIV8qtjJHfGF6XO0yHqf8Oeq229xIhBrp3x2X6Ds4OvYXwMxDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:28.327260Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.07179","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b88ef6cb61176c5a7d1f7456cf20a4a4e748c1e51b30b40dd5608fd95e5aca4","sha256:21762bb7ceb6dd64795b8e3de2823610be1fb2280a7016026f6fb7b8c236ebd5"],"state_sha256":"a1812b72f5b8cc49fee9fc6e31175d78340050ef31858313785b6f79305a20eb"}