{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:4JWMPV33L4SH4LODTA2I6HX7EX","short_pith_number":"pith:4JWMPV33","canonical_record":{"source":{"id":"2502.08532","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T16:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"82a3303c8b525f26bbf827f8497f21f5f5c451d381b2ba67e7e5cf7a8f38151b","abstract_canon_sha256":"1823e07ca58b5b69e206bbf95e3e187ed1fd4a83447952f86e7e2b7730744514"},"schema_version":"1.0"},"canonical_sha256":"e26cc7d77b5f247e2dc398348f1eff25e385e628cfd3ad8d9d30e8a11a41b5fd","source":{"kind":"arxiv","id":"2502.08532","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08532","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08532v2","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08532","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_12","alias_value":"4JWMPV33L4SH","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_16","alias_value":"4JWMPV33L4SH4LOD","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_8","alias_value":"4JWMPV33","created_at":"2026-07-05T11:22:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:4JWMPV33L4SH4LODTA2I6HX7EX","target":"record","payload":{"canonical_record":{"source":{"id":"2502.08532","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T16:12:17Z","cross_cats_sorted":[],"title_canon_sha256":"82a3303c8b525f26bbf827f8497f21f5f5c451d381b2ba67e7e5cf7a8f38151b","abstract_canon_sha256":"1823e07ca58b5b69e206bbf95e3e187ed1fd4a83447952f86e7e2b7730744514"},"schema_version":"1.0"},"canonical_sha256":"e26cc7d77b5f247e2dc398348f1eff25e385e628cfd3ad8d9d30e8a11a41b5fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:36.620010Z","signature_b64":"8Gn5yjMHHgRkZRFrZglY0J8iyP96uWaNuAjDgp17Me7Je0+S6yGcqh3hLtM50F0wvFdvRecnMfMyl6iERZ+KDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26cc7d77b5f247e2dc398348f1eff25e385e628cfd3ad8d9d30e8a11a41b5fd","last_reissued_at":"2026-07-05T11:22:36.619503Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:36.619503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.08532","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1n4B6Gy/GFpJK4cS0M1o1uWItq1gwgvNX2OZDc1MJJGOh+Ut5J7kf7eaV6YFOW5TDm/Ie2s9Uyf/IXEY3q5IDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:56:13.071833Z"},"content_sha256":"b25e523dec1be668d227f2e8d8ed575082de8f3f581abde32199b377ea00a036","schema_version":"1.0","event_id":"sha256:b25e523dec1be668d227f2e8d8ed575082de8f3f581abde32199b377ea00a036"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:4JWMPV33L4SH4LODTA2I6HX7EX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Emanuel Laude, Jan Quan, Konstantinos Oikonomidis, Panagiotis Patrinos","submitted_at":"2025-02-12T16:12:17Z","abstract_excerpt":"We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of $(L_0,L_1)$-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08532","kind":"arxiv","version":2},"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/2502.08532/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":"2026-07-05T11:22:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ESowu0pdKsZCTd5gXDMh1ZrPDKdY0GLsT6kEzaV6B8MIC5yo+CwxBeCENJwq+rrwrV5TiPvOwzzFfQ86ccPSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T16:56:13.072435Z"},"content_sha256":"f70d6d59f8378fe96cdb08f4b9f4bb47c94eec0239dcfb240da3c260a2384afb","schema_version":"1.0","event_id":"sha256:f70d6d59f8378fe96cdb08f4b9f4bb47c94eec0239dcfb240da3c260a2384afb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4JWMPV33L4SH4LODTA2I6HX7EX/bundle.json","state_url":"https://pith.science/pith/4JWMPV33L4SH4LODTA2I6HX7EX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4JWMPV33L4SH4LODTA2I6HX7EX/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":"2026-08-08T16:56:13Z","links":{"resolver":"https://pith.science/pith/4JWMPV33L4SH4LODTA2I6HX7EX","bundle":"https://pith.science/pith/4JWMPV33L4SH4LODTA2I6HX7EX/bundle.json","state":"https://pith.science/pith/4JWMPV33L4SH4LODTA2I6HX7EX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4JWMPV33L4SH4LODTA2I6HX7EX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:4JWMPV33L4SH4LODTA2I6HX7EX","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":"1823e07ca58b5b69e206bbf95e3e187ed1fd4a83447952f86e7e2b7730744514","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T16:12:17Z","title_canon_sha256":"82a3303c8b525f26bbf827f8497f21f5f5c451d381b2ba67e7e5cf7a8f38151b"},"schema_version":"1.0","source":{"id":"2502.08532","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.08532","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"arxiv_version","alias_value":"2502.08532v2","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.08532","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_12","alias_value":"4JWMPV33L4SH","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_16","alias_value":"4JWMPV33L4SH4LOD","created_at":"2026-07-05T11:22:36Z"},{"alias_kind":"pith_short_8","alias_value":"4JWMPV33","created_at":"2026-07-05T11:22:36Z"}],"graph_snapshots":[{"event_id":"sha256:f70d6d59f8378fe96cdb08f4b9f4bb47c94eec0239dcfb240da3c260a2384afb","target":"graph","created_at":"2026-07-05T11:22:36Z","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/2502.08532/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and provide sufficient first- and second-order conditions. Notably, our framework encapsulates algorithms associated with the gradient clipping method and brings out novel insights for the class of $(L_0,L_1)$-smooth functions that has received widespread interest recently, thus allowing us to extend beyond already established methods. We investigate the convergence o","authors_text":"Emanuel Laude, Jan Quan, Konstantinos Oikonomidis, Panagiotis Patrinos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T16:12:17Z","title":"Nonlinearly Preconditioned Gradient Methods under Generalized Smoothness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.08532","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:b25e523dec1be668d227f2e8d8ed575082de8f3f581abde32199b377ea00a036","target":"record","created_at":"2026-07-05T11:22:36Z","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":"1823e07ca58b5b69e206bbf95e3e187ed1fd4a83447952f86e7e2b7730744514","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.OC","submitted_at":"2025-02-12T16:12:17Z","title_canon_sha256":"82a3303c8b525f26bbf827f8497f21f5f5c451d381b2ba67e7e5cf7a8f38151b"},"schema_version":"1.0","source":{"id":"2502.08532","kind":"arxiv","version":2}},"canonical_sha256":"e26cc7d77b5f247e2dc398348f1eff25e385e628cfd3ad8d9d30e8a11a41b5fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e26cc7d77b5f247e2dc398348f1eff25e385e628cfd3ad8d9d30e8a11a41b5fd","first_computed_at":"2026-07-05T11:22:36.619503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:22:36.619503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8Gn5yjMHHgRkZRFrZglY0J8iyP96uWaNuAjDgp17Me7Je0+S6yGcqh3hLtM50F0wvFdvRecnMfMyl6iERZ+KDg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:22:36.620010Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.08532","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b25e523dec1be668d227f2e8d8ed575082de8f3f581abde32199b377ea00a036","sha256:f70d6d59f8378fe96cdb08f4b9f4bb47c94eec0239dcfb240da3c260a2384afb"],"state_sha256":"bb2bbf4d7476e81b77a41e90e0ef7c4192ca195b62cd5dfeebd35c746a4e0e5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nIoGi+YOWjxQdBsOGqDnH6M6lTRxJ45Sk5jAAEP42wp25Znb0d98UY1LzonH9D0jTldT5wv8nwvfVxEeVnAJAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T16:56:13.077455Z","bundle_sha256":"224e4e1474e10a09d600125b140df20dd677d2da4d8b57e64336225038a91da5"}}