{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:COM6LOX4U2IRPLZJHQR4QYZKNU","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":"5f6a65418d76ecdb5e56f0c3cbe14098615eec014f3925ca046fad290f41d9c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-03T16:36:18Z","title_canon_sha256":"22ff2839e1d1483e625cee0a5b0944ebe3b5b7a0fe44c28f7de4a49672570677"},"schema_version":"1.0","source":{"id":"1609.00842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00842","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00842v1","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00842","created_at":"2026-05-18T01:06:19Z"},{"alias_kind":"pith_short_12","alias_value":"COM6LOX4U2IR","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"COM6LOX4U2IRPLZJ","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"COM6LOX4","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:26177bafab4a4e55aa47352d622c7a08629ede704abcd112af03fb5e32dcdfea","target":"graph","created_at":"2026-05-18T01:06:19Z","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":"We prove that the bundle method for nonsmooth optimization achieves solution accuracy $\\varepsilon$ in at most $\\mathcal{O}\\big(\\ln(1/\\varepsilon)/\\varepsilon\\big)$ iterations, if the function is strongly convex. The result is true for the versions of the method with multiple cuts and with cut aggregation.","authors_text":"Andrzej Ruszczynski, Yu Du","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-03T16:36:18Z","title":"Rate of Convergence of the Bundle Method"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00842","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":"sha256:7079742bdc17135a2a151ac3ee1cafa26e6c996de6f4ced5544d13f61f90646d","target":"record","created_at":"2026-05-18T01:06:19Z","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":"5f6a65418d76ecdb5e56f0c3cbe14098615eec014f3925ca046fad290f41d9c6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-09-03T16:36:18Z","title_canon_sha256":"22ff2839e1d1483e625cee0a5b0944ebe3b5b7a0fe44c28f7de4a49672570677"},"schema_version":"1.0","source":{"id":"1609.00842","kind":"arxiv","version":1}},"canonical_sha256":"1399e5bafca69117af293c23c8632a6d31269121b4e67a35162ec37d456027d0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1399e5bafca69117af293c23c8632a6d31269121b4e67a35162ec37d456027d0","first_computed_at":"2026-05-18T01:06:19.802141Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:19.802141Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SA60ZyhoREdfIBjKFOJx26SWPfk/6zTfWaXciiFszUprnRTD9wwiXJu2bEZ1z70+5z5MPM8vi8EkZPEOxQ0yBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:19.802689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7079742bdc17135a2a151ac3ee1cafa26e6c996de6f4ced5544d13f61f90646d","sha256:26177bafab4a4e55aa47352d622c7a08629ede704abcd112af03fb5e32dcdfea"],"state_sha256":"ae2c928c9a014423e138a24307b457fdde5a96a527bc9e7439f86a44a6c1713b"}