{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:U2YLLAZ5QGA4LPV75UF6KOXX7R","short_pith_number":"pith:U2YLLAZ5","schema_version":"1.0","canonical_sha256":"a6b0b5833d8181c5bebfed0be53af7fc743f7caa16dc3893b68e9a9c015d6d45","source":{"kind":"arxiv","id":"2102.05134","version":2},"attestation_state":"computed","paper":{"title":"Local and Global Uniform Convexity Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Alexandre d'Aspremont, Sebastian Pokutta, Thomas Kerdreux","submitted_at":"2021-02-09T21:09:53Z","abstract_excerpt":"We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \\textit{scaling inequalities} used in analysing the convergence of optimization methods. In particular, we establish local versions of these conditions to provide sharper insights on a recent body of complexity results in learning theory, online learning, or offline optimization, which rely on the strong convexity of the feasible set. While they have a significant impact on complexity, these strong convexity or u"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2102.05134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2021-02-09T21:09:53Z","cross_cats_sorted":["cs.LG"],"title_canon_sha256":"2f3b8c38ca867cc506ed092727221ae72cc0d2e5b514fe209d82140fba73a88b","abstract_canon_sha256":"7183716ddd1c188e6ac69472df0fb79cf299469d20df4abf707d9c233495f74e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:16:17.728592Z","signature_b64":"LYHRl3oqZglHsxDfQ+nPnKkSxE8ipvsBnnXZPVXKCfP+68SKx0ujhkZwkNYaIFwVBPWvcPkCpzIOIljDytWxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6b0b5833d8181c5bebfed0be53af7fc743f7caa16dc3893b68e9a9c015d6d45","last_reissued_at":"2026-07-05T02:16:17.728116Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:16:17.728116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local and Global Uniform Convexity Conditions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG"],"primary_cat":"math.OC","authors_text":"Alexandre d'Aspremont, Sebastian Pokutta, Thomas Kerdreux","submitted_at":"2021-02-09T21:09:53Z","abstract_excerpt":"We review various characterizations of uniform convexity and smoothness on norm balls in finite-dimensional spaces and connect results stemming from the geometry of Banach spaces with \\textit{scaling inequalities} used in analysing the convergence of optimization methods. In particular, we establish local versions of these conditions to provide sharper insights on a recent body of complexity results in learning theory, online learning, or offline optimization, which rely on the strong convexity of the feasible set. While they have a significant impact on complexity, these strong convexity or u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2102.05134","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/2102.05134/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2102.05134","created_at":"2026-07-05T02:16:17.728185+00:00"},{"alias_kind":"arxiv_version","alias_value":"2102.05134v2","created_at":"2026-07-05T02:16:17.728185+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2102.05134","created_at":"2026-07-05T02:16:17.728185+00:00"},{"alias_kind":"pith_short_12","alias_value":"U2YLLAZ5QGA4","created_at":"2026-07-05T02:16:17.728185+00:00"},{"alias_kind":"pith_short_16","alias_value":"U2YLLAZ5QGA4LPV7","created_at":"2026-07-05T02:16:17.728185+00:00"},{"alias_kind":"pith_short_8","alias_value":"U2YLLAZ5","created_at":"2026-07-05T02:16:17.728185+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2601.20443","citing_title":"Adaptive Conditional Gradient Sliding: Projection-Free and Line-Search-Free Acceleration","ref_index":2019,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R","json":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R.json","graph_json":"https://pith.science/api/pith-number/U2YLLAZ5QGA4LPV75UF6KOXX7R/graph.json","events_json":"https://pith.science/api/pith-number/U2YLLAZ5QGA4LPV75UF6KOXX7R/events.json","paper":"https://pith.science/paper/U2YLLAZ5"},"agent_actions":{"view_html":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R","download_json":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R.json","view_paper":"https://pith.science/paper/U2YLLAZ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2102.05134&json=true","fetch_graph":"https://pith.science/api/pith-number/U2YLLAZ5QGA4LPV75UF6KOXX7R/graph.json","fetch_events":"https://pith.science/api/pith-number/U2YLLAZ5QGA4LPV75UF6KOXX7R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R/action/storage_attestation","attest_author":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R/action/author_attestation","sign_citation":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R/action/citation_signature","submit_replication":"https://pith.science/pith/U2YLLAZ5QGA4LPV75UF6KOXX7R/action/replication_record"}},"created_at":"2026-07-05T02:16:17.728185+00:00","updated_at":"2026-07-05T02:16:17.728185+00:00"}