{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:MHHKQLEPUCDXWCZSVJQ5HLDQEU","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":"53d37cf4b0cd19eea4d7ba7735e968d15099f82549f72e4bd98dc886d489fd8d","cross_cats_sorted":["cs.CC","cs.DS","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T22:39:35Z","title_canon_sha256":"5d0fd9f6144f2d20560ebd9ff25077fbb84630d364b90772d109f44455bcb749"},"schema_version":"1.0","source":{"id":"1906.11985","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11985","created_at":"2026-07-05T05:45:02Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11985v3","created_at":"2026-07-05T05:45:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11985","created_at":"2026-07-05T05:45:02Z"},{"alias_kind":"pith_short_12","alias_value":"MHHKQLEPUCDX","created_at":"2026-07-05T05:45:02Z"},{"alias_kind":"pith_short_16","alias_value":"MHHKQLEPUCDXWCZS","created_at":"2026-07-05T05:45:02Z"},{"alias_kind":"pith_short_8","alias_value":"MHHKQLEP","created_at":"2026-07-05T05:45:02Z"}],"graph_snapshots":[{"event_id":"sha256:4950826ba35a3b99f5782030f402ecefaa483c8a84315685a95c166ac0668eec","target":"graph","created_at":"2026-07-05T05:45:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1906.11985/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we provide near-optimal accelerated first-order methods for minimizing a broad class of smooth nonconvex functions that are strictly unimodal on all lines through a minimizer. This function class, which we call the class of smooth quasar-convex functions, is parameterized by a constant $\\gamma \\in (0,1]$, where $\\gamma = 1$ encompasses the classes of smooth convex and star-convex functions, and smaller values of $\\gamma$ indicate that the function can be \"more nonconvex.\" We develop a variant of accelerated gradient descent that computes an $\\epsilon$-approximate minimizer of a ","authors_text":"Aaron Sidford, Nimit S. Sohoni, Oliver Hinder","cross_cats":["cs.CC","cs.DS","cs.LG","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T22:39:35Z","title":"Near-Optimal Methods for Minimizing Star-Convex Functions and Beyond"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11985","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":"sha256:043c6c685c278d7dfb5716bd6455390a13b666677fca766d22e0bb80b9a55dd4","target":"record","created_at":"2026-07-05T05:45:02Z","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":"53d37cf4b0cd19eea4d7ba7735e968d15099f82549f72e4bd98dc886d489fd8d","cross_cats_sorted":["cs.CC","cs.DS","cs.LG","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2019-06-27T22:39:35Z","title_canon_sha256":"5d0fd9f6144f2d20560ebd9ff25077fbb84630d364b90772d109f44455bcb749"},"schema_version":"1.0","source":{"id":"1906.11985","kind":"arxiv","version":3}},"canonical_sha256":"61cea82c8fa0877b0b32aa61d3ac70250a2d727459b9dce00272ecedcbd3705e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"61cea82c8fa0877b0b32aa61d3ac70250a2d727459b9dce00272ecedcbd3705e","first_computed_at":"2026-07-05T05:45:02.067088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:45:02.067088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Mj8cIT25yfje4GoB3abkUZbsu96nG3taM8GOuyS44OWmKr+NBRWmSGFJRWVU7TlmPYtxBroltyKP9iFFnrrKAg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:45:02.067684Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11985","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:043c6c685c278d7dfb5716bd6455390a13b666677fca766d22e0bb80b9a55dd4","sha256:4950826ba35a3b99f5782030f402ecefaa483c8a84315685a95c166ac0668eec"],"state_sha256":"bda6a48d6506cf31878adad3cc0964f0eefeaa37eb710cb3da4c77db1401550a"}