{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:VJ7TI2BICWWZXWSWDBI5QKKHVJ","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":"a87e19b316fc24e4f3fa9cadfb8924aaacc7ffbebb5ebf455ea92157ada1dc8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-01T23:15:59Z","title_canon_sha256":"1d925a785dc73b1fc6a6db2fc127742060d6ad81a9557ccfb581c6188c331de1"},"schema_version":"1.0","source":{"id":"1605.00320","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.00320","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"arxiv_version","alias_value":"1605.00320v1","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.00320","created_at":"2026-05-18T01:15:56Z"},{"alias_kind":"pith_short_12","alias_value":"VJ7TI2BICWWZ","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_16","alias_value":"VJ7TI2BICWWZXWSW","created_at":"2026-05-18T12:30:48Z"},{"alias_kind":"pith_short_8","alias_value":"VJ7TI2BI","created_at":"2026-05-18T12:30:48Z"}],"graph_snapshots":[{"event_id":"sha256:1baf736ea627f229e593602a111ff65d95a4c61f59d4f723123de6784ce3e97a","target":"graph","created_at":"2026-05-18T01:15:56Z","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":"Nesterov's accelerated gradient method for minimizing a smooth strongly convex function $f$ is known to reduce $f(\\x_k)-f(\\x^*)$ by a factor of $\\eps\\in(0,1)$ after $k\\ge O(\\sqrt{L/\\ell}\\log(1/\\eps))$ iterations, where $\\ell,L$ are the two parameters of smooth strong convexity. Furthermore, it is known that this is the best possible complexity in the function-gradient oracle model of computation. The method of linear conjugate gradients (CG) also satisfies the same complexity bound in the special case of strongly convex quadratic functions, but in this special case it is faster than the accele","authors_text":"Sahar Karimi, Stephen A. Vavasis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-01T23:15:59Z","title":"A unified convergence bound for conjugate gradient and accelerated gradient"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00320","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":"sha256:7894b99f73d26928f6986848bdf28ea5e197db3bb293d354d2485b1e20465196","target":"record","created_at":"2026-05-18T01:15:56Z","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":"a87e19b316fc24e4f3fa9cadfb8924aaacc7ffbebb5ebf455ea92157ada1dc8f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-05-01T23:15:59Z","title_canon_sha256":"1d925a785dc73b1fc6a6db2fc127742060d6ad81a9557ccfb581c6188c331de1"},"schema_version":"1.0","source":{"id":"1605.00320","kind":"arxiv","version":1}},"canonical_sha256":"aa7f34682815ad9bda561851d82947aa5b653689e0265aa81308d985b7ac0942","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa7f34682815ad9bda561851d82947aa5b653689e0265aa81308d985b7ac0942","first_computed_at":"2026-05-18T01:15:56.178434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:15:56.178434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LpPMoncAgAVD3+FiVlvzmnvX7mP9ObaKVMAJ9LHeJKd8AWKXbLfaDyqKuHsI4WfBcm1CLz7vc++GtShoFQqCAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:15:56.179210Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.00320","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7894b99f73d26928f6986848bdf28ea5e197db3bb293d354d2485b1e20465196","sha256:1baf736ea627f229e593602a111ff65d95a4c61f59d4f723123de6784ce3e97a"],"state_sha256":"204af10f2a8d16d6702a2086af43d63af71a60a4d01d14a352be44921d2b58f7"}