{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:IR2O7ZGKFBQVIFZ73VX74RGA27","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":"d13837c2a45118cf0b12775704f6a35c3bfd9791bcd4c073e1668a1d937dda28","cross_cats_sorted":["cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2022-11-03T06:50:19Z","title_canon_sha256":"2bb68081b7709f586bac3c4c37b29a42d94b1e8ebf6db8c120560265b61d5bec"},"schema_version":"1.0","source":{"id":"2211.01610","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2211.01610","created_at":"2026-07-05T05:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"2211.01610v1","created_at":"2026-07-05T05:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.01610","created_at":"2026-07-05T05:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"IR2O7ZGKFBQV","created_at":"2026-07-05T05:12:58Z"},{"alias_kind":"pith_short_16","alias_value":"IR2O7ZGKFBQVIFZ7","created_at":"2026-07-05T05:12:58Z"},{"alias_kind":"pith_short_8","alias_value":"IR2O7ZGK","created_at":"2026-07-05T05:12:58Z"}],"graph_snapshots":[{"event_id":"sha256:93b9933a5501478be40f9c2a0995eeeeeeff12cbe970586259df845051eee9f0","target":"graph","created_at":"2026-07-05T05:12:58Z","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/2211.01610/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For first-order smooth optimization, the research on the acceleration phenomenon has a long-time history. Until recently, the mechanism leading to acceleration was not successfully uncovered by the gradient correction term and its equivalent implicit-velocity form. Furthermore, based on the high-resolution differential equation framework with the corresponding emerging techniques, phase-space representation and Lyapunov function, the squared gradient norm of Nesterov's accelerated gradient descent (\\texttt{NAG}) method at an inverse cubic rate is discovered. However, this result cannot be dire","authors_text":"Bin Shi, Bowen Li, Ya-Xiang Yuan","cross_cats":["cs.LG","math.ST","stat.ML","stat.TH"],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2022-11-03T06:50:19Z","title":"Proximal Subgradient Norm Minimization of ISTA and FISTA"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.01610","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":"sha256:856d8c0db3b8729a77daa8a4b82e7e52c0ea053113e4db08e1b881f2f339c624","target":"record","created_at":"2026-07-05T05:12:58Z","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":"d13837c2a45118cf0b12775704f6a35c3bfd9791bcd4c073e1668a1d937dda28","cross_cats_sorted":["cs.LG","math.ST","stat.ML","stat.TH"],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.OC","submitted_at":"2022-11-03T06:50:19Z","title_canon_sha256":"2bb68081b7709f586bac3c4c37b29a42d94b1e8ebf6db8c120560265b61d5bec"},"schema_version":"1.0","source":{"id":"2211.01610","kind":"arxiv","version":1}},"canonical_sha256":"4474efe4ca286154173fdd6ffe44c0d7e0393c3abbfd2afcf6969d8bdbf94ecf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4474efe4ca286154173fdd6ffe44c0d7e0393c3abbfd2afcf6969d8bdbf94ecf","first_computed_at":"2026-07-05T05:12:58.096699Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:12:58.096699Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sSgdiAe/QAj/v8mrUOmJZjdgNzZHWuoAHsFaNIQXh4zsVHzpN4VBhaPtcMce/yLGXfx3LgXToXp5pjq4tAT9Cg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:12:58.097087Z","signed_message":"canonical_sha256_bytes"},"source_id":"2211.01610","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:856d8c0db3b8729a77daa8a4b82e7e52c0ea053113e4db08e1b881f2f339c624","sha256:93b9933a5501478be40f9c2a0995eeeeeeff12cbe970586259df845051eee9f0"],"state_sha256":"26329e0aa5ec300f5739de71976a3cc55f30b5eff1ad86d52a509e8b21e50c31"}