{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:KBI3YJ4JGJFCOQFEAKIX25JET6","short_pith_number":"pith:KBI3YJ4J","canonical_record":{"source":{"id":"2002.03213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-08T18:10:20Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"94a4e8c70eda39c496e30739e08827c247b86c182cbac1202dde9a00b762506f","abstract_canon_sha256":"92b043ebf7283e86da08a23e55283c50c2af3d7abb0175c6dfd0813bc09cab9b"},"schema_version":"1.0"},"canonical_sha256":"5051bc2789324a2740a402917d75249fa552e7a07b46120dfae2977050868712","source":{"kind":"arxiv","id":"2002.03213","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.03213","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"2002.03213v2","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.03213","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"KBI3YJ4JGJFC","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"KBI3YJ4JGJFCOQFE","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"KBI3YJ4J","created_at":"2026-07-05T02:39:00Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:KBI3YJ4JGJFCOQFEAKIX25JET6","target":"record","payload":{"canonical_record":{"source":{"id":"2002.03213","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-08T18:10:20Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"94a4e8c70eda39c496e30739e08827c247b86c182cbac1202dde9a00b762506f","abstract_canon_sha256":"92b043ebf7283e86da08a23e55283c50c2af3d7abb0175c6dfd0813bc09cab9b"},"schema_version":"1.0"},"canonical_sha256":"5051bc2789324a2740a402917d75249fa552e7a07b46120dfae2977050868712","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:39:00.419129Z","signature_b64":"SZy+SYvl684p/+gEsgSI9WwhasjuLSZwDZ3pBRm43vvy3PW1trvtJO2ADnKa839UVILI8C7ItKkjSHYNHaRUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5051bc2789324a2740a402917d75249fa552e7a07b46120dfae2977050868712","last_reissued_at":"2026-07-05T02:39:00.418718Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:39:00.418718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2002.03213","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":"2026-07-05T02:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kvNLYKobu/P+3J7one3JjUADzX3743cBMvhrLthHEAqQIFePLqzHcAkg/yCbknix6XMxBSG4WidD6f3rgMWpAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T04:08:59.736763Z"},"content_sha256":"d0335bda8760ba9b528768d16a3a4b18cc8c8637e8ed377d203cd360a4c8f4ce","schema_version":"1.0","event_id":"sha256:d0335bda8760ba9b528768d16a3a4b18cc8c8637e8ed377d203cd360a4c8f4ce"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:KBI3YJ4JGJFCOQFEAKIX25JET6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Curvature of Feasible Sets in Offline and Online Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DS","authors_text":"Marco Molinaro","submitted_at":"2020-02-08T18:10:20Z","abstract_excerpt":"It is known that the curvature of the feasible set in convex optimization allows for algorithms with better convergence rates, and there has been renewed interest in this topic both for offline as well as online problems. In this paper, leveraging results on geometry and convex analysis, we further our understanding of the role of curvature in optimization:\n  - We first show the equivalence of two notions of curvature, namely strong convexity and gauge bodies, proving a conjecture of Abernethy et al. As a consequence, this show that the Frank-Wolfe-type method of Wang and Abernethy has acceler"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.03213","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/2002.03213/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":"2026-07-05T02:39:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NRIvu2jpSmJSjJNwZDgQcPsVvhNE18negDN41/I94UaR3M5ORDX60RY0YhX8ip/ckl3PUp4RiiwZMjRFlQpMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-22T04:08:59.737592Z"},"content_sha256":"930fa5199af30d7f36ffbc2d7580ffffefbf452cbd2c7e0adce918f3238c638a","schema_version":"1.0","event_id":"sha256:930fa5199af30d7f36ffbc2d7580ffffefbf452cbd2c7e0adce918f3238c638a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/bundle.json","state_url":"https://pith.science/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/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":"2026-08-22T04:08:59Z","links":{"resolver":"https://pith.science/pith/KBI3YJ4JGJFCOQFEAKIX25JET6","bundle":"https://pith.science/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/bundle.json","state":"https://pith.science/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBI3YJ4JGJFCOQFEAKIX25JET6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:KBI3YJ4JGJFCOQFEAKIX25JET6","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":"92b043ebf7283e86da08a23e55283c50c2af3d7abb0175c6dfd0813bc09cab9b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-08T18:10:20Z","title_canon_sha256":"94a4e8c70eda39c496e30739e08827c247b86c182cbac1202dde9a00b762506f"},"schema_version":"1.0","source":{"id":"2002.03213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2002.03213","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"arxiv_version","alias_value":"2002.03213v2","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2002.03213","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_12","alias_value":"KBI3YJ4JGJFC","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_16","alias_value":"KBI3YJ4JGJFCOQFE","created_at":"2026-07-05T02:39:00Z"},{"alias_kind":"pith_short_8","alias_value":"KBI3YJ4J","created_at":"2026-07-05T02:39:00Z"}],"graph_snapshots":[{"event_id":"sha256:930fa5199af30d7f36ffbc2d7580ffffefbf452cbd2c7e0adce918f3238c638a","target":"graph","created_at":"2026-07-05T02:39:00Z","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/2002.03213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"It is known that the curvature of the feasible set in convex optimization allows for algorithms with better convergence rates, and there has been renewed interest in this topic both for offline as well as online problems. In this paper, leveraging results on geometry and convex analysis, we further our understanding of the role of curvature in optimization:\n  - We first show the equivalence of two notions of curvature, namely strong convexity and gauge bodies, proving a conjecture of Abernethy et al. As a consequence, this show that the Frank-Wolfe-type method of Wang and Abernethy has acceler","authors_text":"Marco Molinaro","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-08T18:10:20Z","title":"Curvature of Feasible Sets in Offline and Online Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2002.03213","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:d0335bda8760ba9b528768d16a3a4b18cc8c8637e8ed377d203cd360a4c8f4ce","target":"record","created_at":"2026-07-05T02:39:00Z","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":"92b043ebf7283e86da08a23e55283c50c2af3d7abb0175c6dfd0813bc09cab9b","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2020-02-08T18:10:20Z","title_canon_sha256":"94a4e8c70eda39c496e30739e08827c247b86c182cbac1202dde9a00b762506f"},"schema_version":"1.0","source":{"id":"2002.03213","kind":"arxiv","version":2}},"canonical_sha256":"5051bc2789324a2740a402917d75249fa552e7a07b46120dfae2977050868712","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5051bc2789324a2740a402917d75249fa552e7a07b46120dfae2977050868712","first_computed_at":"2026-07-05T02:39:00.418718Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:39:00.418718Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SZy+SYvl684p/+gEsgSI9WwhasjuLSZwDZ3pBRm43vvy3PW1trvtJO2ADnKa839UVILI8C7ItKkjSHYNHaRUCg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:39:00.419129Z","signed_message":"canonical_sha256_bytes"},"source_id":"2002.03213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0335bda8760ba9b528768d16a3a4b18cc8c8637e8ed377d203cd360a4c8f4ce","sha256:930fa5199af30d7f36ffbc2d7580ffffefbf452cbd2c7e0adce918f3238c638a"],"state_sha256":"ae70202d7938e5a82ad55772e3f623a8d17871d318f9c6b0d6736d8d4be90dc4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xGPQgWxRUOoRLM7y8dJekOSsM3d+ZY9dMw4qm2OqiBDG8osAu6HO73e4STL4ohlEtagfi7/QmLo9P46q2pr4Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-22T04:08:59.750606Z","bundle_sha256":"602ab8bc7aedd3ca8c5cd3ab246bb1de6a46e9ac94e9bb533acd8c3ee9585193"}}