{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:TWO2ILHP4UHA2KG2GQ74PDGCAZ","short_pith_number":"pith:TWO2ILHP","canonical_record":{"source":{"id":"2409.16047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-24T12:51:13Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"4936dc32643e1922b05a3ef8a71a10423235434b2c6a2d4429b201e9879901ed","abstract_canon_sha256":"db126a66f2606ae0267d0d4874911ab837d103afd4b94f58702a63909a1f929f"},"schema_version":"1.0"},"canonical_sha256":"9d9da42cefe50e0d28da343fc78cc206540c058fd1f2b224774d0c810c36669c","source":{"kind":"arxiv","id":"2409.16047","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16047","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16047v1","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16047","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_12","alias_value":"TWO2ILHP4UHA","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_16","alias_value":"TWO2ILHP4UHA2KG2","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_8","alias_value":"TWO2ILHP","created_at":"2026-07-05T09:11:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:TWO2ILHP4UHA2KG2GQ74PDGCAZ","target":"record","payload":{"canonical_record":{"source":{"id":"2409.16047","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-24T12:51:13Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"4936dc32643e1922b05a3ef8a71a10423235434b2c6a2d4429b201e9879901ed","abstract_canon_sha256":"db126a66f2606ae0267d0d4874911ab837d103afd4b94f58702a63909a1f929f"},"schema_version":"1.0"},"canonical_sha256":"9d9da42cefe50e0d28da343fc78cc206540c058fd1f2b224774d0c810c36669c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:11:04.164877Z","signature_b64":"yQEhV0ICjk9cGTqdZKProX3z9Z7bn1HibCNOkI1mF/I1zZ/u5rer38EqnbaLJwt5QldYEM4LxlyIxNpRsw+CDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d9da42cefe50e0d28da343fc78cc206540c058fd1f2b224774d0c810c36669c","last_reissued_at":"2026-07-05T09:11:04.164380Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:11:04.164380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.16047","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:11:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SerjMDlzkONL9jCtA/WjPP6YL6s9CVxbyqAFF/Ofz1RJYsc5RZ/RPOyGqDCTimVpyP9ZfFl4bwT2oR/jq5UBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:24:29.945648Z"},"content_sha256":"6225bcc0aae88c241f0315dfc1a702ea56ec0feed593b60a93a502e927c6b309","schema_version":"1.0","event_id":"sha256:6225bcc0aae88c241f0315dfc1a702ea56ec0feed593b60a93a502e927c6b309"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:TWO2ILHP4UHA2KG2GQ74PDGCAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Examples of slow convergence for adaptive regularization optimization methods are not isolated","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Philippe L. Toint","submitted_at":"2024-09-24T12:51:13Z","abstract_excerpt":"The adaptive regularization algorithm for unconstrained nonconvex optimization was shown in Nesterov and Polyak (2006) and Cartis, Gould and Toint (2011) to require, under standard assumptions, at most $\\mathcal{O}(\\epsilon^{3/(3-q)})$ evaluations of the objective function and its derivatives of degrees one and two to produce an $\\epsilon$-approximate critical point of order $q\\in\\{1,2\\}$. This bound was shown to be sharp for $q \\in\\{1,2\\}$. This note revisits these results and shows that the example for which slow convergence is exhibited is not isolated, but that this behaviour occurs for a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16047","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.16047/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:11:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjmxTg2khxFOa9YS7CE2gO84SBYdgxwr00MKzYE3W5lZxuJsEeNvCOKswpB0CAlVcrzOANdnYMLLIoFQQuLfAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T23:24:29.946169Z"},"content_sha256":"ce0b0a61c299bf16f511b8ee78cf828fa7afcbceb23995b9c4c47ff6d2dc3659","schema_version":"1.0","event_id":"sha256:ce0b0a61c299bf16f511b8ee78cf828fa7afcbceb23995b9c4c47ff6d2dc3659"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/bundle.json","state_url":"https://pith.science/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T23:24:29Z","links":{"resolver":"https://pith.science/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ","bundle":"https://pith.science/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/bundle.json","state":"https://pith.science/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TWO2ILHP4UHA2KG2GQ74PDGCAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:TWO2ILHP4UHA2KG2GQ74PDGCAZ","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":"db126a66f2606ae0267d0d4874911ab837d103afd4b94f58702a63909a1f929f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-24T12:51:13Z","title_canon_sha256":"4936dc32643e1922b05a3ef8a71a10423235434b2c6a2d4429b201e9879901ed"},"schema_version":"1.0","source":{"id":"2409.16047","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16047","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16047v1","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16047","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_12","alias_value":"TWO2ILHP4UHA","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_16","alias_value":"TWO2ILHP4UHA2KG2","created_at":"2026-07-05T09:11:04Z"},{"alias_kind":"pith_short_8","alias_value":"TWO2ILHP","created_at":"2026-07-05T09:11:04Z"}],"graph_snapshots":[{"event_id":"sha256:ce0b0a61c299bf16f511b8ee78cf828fa7afcbceb23995b9c4c47ff6d2dc3659","target":"graph","created_at":"2026-07-05T09:11:04Z","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/2409.16047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The adaptive regularization algorithm for unconstrained nonconvex optimization was shown in Nesterov and Polyak (2006) and Cartis, Gould and Toint (2011) to require, under standard assumptions, at most $\\mathcal{O}(\\epsilon^{3/(3-q)})$ evaluations of the objective function and its derivatives of degrees one and two to produce an $\\epsilon$-approximate critical point of order $q\\in\\{1,2\\}$. This bound was shown to be sharp for $q \\in\\{1,2\\}$. This note revisits these results and shows that the example for which slow convergence is exhibited is not isolated, but that this behaviour occurs for a ","authors_text":"Philippe L. Toint","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-24T12:51:13Z","title":"Examples of slow convergence for adaptive regularization optimization methods are not isolated"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16047","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":"sha256:6225bcc0aae88c241f0315dfc1a702ea56ec0feed593b60a93a502e927c6b309","target":"record","created_at":"2026-07-05T09:11:04Z","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":"db126a66f2606ae0267d0d4874911ab837d103afd4b94f58702a63909a1f929f","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2024-09-24T12:51:13Z","title_canon_sha256":"4936dc32643e1922b05a3ef8a71a10423235434b2c6a2d4429b201e9879901ed"},"schema_version":"1.0","source":{"id":"2409.16047","kind":"arxiv","version":1}},"canonical_sha256":"9d9da42cefe50e0d28da343fc78cc206540c058fd1f2b224774d0c810c36669c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9d9da42cefe50e0d28da343fc78cc206540c058fd1f2b224774d0c810c36669c","first_computed_at":"2026-07-05T09:11:04.164380Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:11:04.164380Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yQEhV0ICjk9cGTqdZKProX3z9Z7bn1HibCNOkI1mF/I1zZ/u5rer38EqnbaLJwt5QldYEM4LxlyIxNpRsw+CDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:11:04.164877Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.16047","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6225bcc0aae88c241f0315dfc1a702ea56ec0feed593b60a93a502e927c6b309","sha256:ce0b0a61c299bf16f511b8ee78cf828fa7afcbceb23995b9c4c47ff6d2dc3659"],"state_sha256":"92f1eaec8384217d9406b4b740ac4c69cdf18798c0b032a46f763adadfe6e098"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/S47yeQ2hrlVjJX3OJQY3y6nFHxB67fHrBOp13ubj/klZ1Qo3rbOqkMeFmWB0Nc9aS0xzTZ5hSTSsuCSaf5sBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T23:24:29.951432Z","bundle_sha256":"2b52a9685810912bde5de399cb6da85f79e18273c46e9dd05230757bd2b77735"}}