{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:S24JTVYT4XVAF7UUPH3TXF2CMN","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":"741fdee1a78adeeece8df235d001f5c9471b95a0ac53ce43f2f1e95176932563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-06-10T08:34:59Z","title_canon_sha256":"76f2e0421237fbe1a236c94c2febc5759eb8187696693ee779494c48a93fccd9"},"schema_version":"1.0","source":{"id":"2406.06100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2406.06100","created_at":"2026-07-05T10:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"2406.06100v2","created_at":"2026-07-05T10:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2406.06100","created_at":"2026-07-05T10:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"S24JTVYT4XVA","created_at":"2026-07-05T10:56:33Z"},{"alias_kind":"pith_short_16","alias_value":"S24JTVYT4XVAF7UU","created_at":"2026-07-05T10:56:33Z"},{"alias_kind":"pith_short_8","alias_value":"S24JTVYT","created_at":"2026-07-05T10:56:33Z"}],"graph_snapshots":[{"event_id":"sha256:5cbd8314af8d5fd610b01bfcb6c9914e33f7c260d8c7d957f4cf0ba99f7477ba","target":"graph","created_at":"2026-07-05T10:56:33Z","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/2406.06100/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"First-order optimization methods for nonconvex functions with Lipschitz continuous gradient and Hessian have been extensively studied. State-of-the-art methods for finding an $\\varepsilon$-stationary point within $O(\\varepsilon^{-{7/4}})$ or $\\tilde{O}(\\varepsilon^{-{7/4}})$ gradient evaluations are based on Nesterov's accelerated gradient descent (AGD) or Polyak's heavy-ball (HB) method. However, these algorithms employ additional mechanisms, such as restart schemes and negative curvature exploitation, which complicate their behavior and make it challenging to apply them to more advanced sett","authors_text":"Akiko Takeda, Kaito Okamura, Naoki Marumo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-06-10T08:34:59Z","title":"Heavy-ball Differential Equation Achieves $O(\\varepsilon^{-7/4})$ Convergence for Nonconvex Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2406.06100","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:ff8e309e90d425c330e1a8be8288676c565a293435d4047dd66911bda5be1062","target":"record","created_at":"2026-07-05T10:56:33Z","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":"741fdee1a78adeeece8df235d001f5c9471b95a0ac53ce43f2f1e95176932563","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-06-10T08:34:59Z","title_canon_sha256":"76f2e0421237fbe1a236c94c2febc5759eb8187696693ee779494c48a93fccd9"},"schema_version":"1.0","source":{"id":"2406.06100","kind":"arxiv","version":2}},"canonical_sha256":"96b899d713e5ea02fe9479f73b97426351fad539b0ee6c80e01127192499e852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96b899d713e5ea02fe9479f73b97426351fad539b0ee6c80e01127192499e852","first_computed_at":"2026-07-05T10:56:33.408783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:56:33.408783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oTfw1MPN1iziPFvHBgJQ7LeJahmBuc5yobd2hv0gN7ZAiLiuIV2rwJ66YJjmGsfjCNJppcBuf/ieEgq6600fBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:56:33.409270Z","signed_message":"canonical_sha256_bytes"},"source_id":"2406.06100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ff8e309e90d425c330e1a8be8288676c565a293435d4047dd66911bda5be1062","sha256:5cbd8314af8d5fd610b01bfcb6c9914e33f7c260d8c7d957f4cf0ba99f7477ba"],"state_sha256":"f86d830d908d463b78b437b3f3d744350d43157c7b413e683c38bbd9255a5309"}