{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:ARGMFHHCBBBVOPU6MEVFZ5FIE6","short_pith_number":"pith:ARGMFHHC","schema_version":"1.0","canonical_sha256":"044cc29ce20843573e9e612a5cf4a827b084e340a5e39e4c3d648ce0682cf332","source":{"kind":"arxiv","id":"2607.13335","version":1},"attestation_state":"computed","paper":{"title":"Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Phillip Kerger","submitted_at":"2026-07-14T23:45:21Z","abstract_excerpt":"We study the deterministic query complexity of minimizing a convex Lipschitz function over a $d$-dimensional Euclidean ball using only exact function values. At accuracy $\\Theta(d^{-1/2})$, the previously applicable lower bound was $\\Omega(d)$, inherited from the stronger full first-order oracle, while an upper bound from Protasov's value-only method requires $O(d^2\\log^2 d)$ evaluations. By providing a lower bound of $\\Omega(\\,\\frac{d^2}{\\log(d+1)})$ on the oracle complexity in this setting, we thereby close this gap dating back to 1996, up to polylogarithmic factors. Furthermore, we are able"},"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":"2607.13335","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OC","submitted_at":"2026-07-14T23:45:21Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"94316ebb390d4fc00af34899582909181c45a7ca17a7136be4b63e26803dffc9","abstract_canon_sha256":"3b180fa3b9e83ad58a320a042eb487ba52de66d094307b20575422d129662d97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T00:22:12.912353Z","signature_b64":"ZgukNaYY553exHHpLyJPms1NG/i4MZre2I8cZgsF/FdPK//6/tTWb0iN2xJ/WrgAQLKT9tMqGM2Qww33Ek5kDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"044cc29ce20843573e9e612a5cf4a827b084e340a5e39e4c3d648ce0682cf332","last_reissued_at":"2026-07-16T00:22:12.911489Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T00:22:12.911489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closing the Oracle-Complexity Gap in Derivative-Free Convex Optimization: A Near-Quadratic Lower Bound from Exact Function Values","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.OC","authors_text":"Phillip Kerger","submitted_at":"2026-07-14T23:45:21Z","abstract_excerpt":"We study the deterministic query complexity of minimizing a convex Lipschitz function over a $d$-dimensional Euclidean ball using only exact function values. At accuracy $\\Theta(d^{-1/2})$, the previously applicable lower bound was $\\Omega(d)$, inherited from the stronger full first-order oracle, while an upper bound from Protasov's value-only method requires $O(d^2\\log^2 d)$ evaluations. By providing a lower bound of $\\Omega(\\,\\frac{d^2}{\\log(d+1)})$ on the oracle complexity in this setting, we thereby close this gap dating back to 1996, up to polylogarithmic factors. Furthermore, we are able"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.13335","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/2607.13335/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":"2607.13335","created_at":"2026-07-16T00:22:12.911934+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.13335v1","created_at":"2026-07-16T00:22:12.911934+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.13335","created_at":"2026-07-16T00:22:12.911934+00:00"},{"alias_kind":"pith_short_12","alias_value":"ARGMFHHCBBBV","created_at":"2026-07-16T00:22:12.911934+00:00"},{"alias_kind":"pith_short_16","alias_value":"ARGMFHHCBBBVOPU6","created_at":"2026-07-16T00:22:12.911934+00:00"},{"alias_kind":"pith_short_8","alias_value":"ARGMFHHC","created_at":"2026-07-16T00:22:12.911934+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.07407","citing_title":"A Domain-Specific Harness for End-to-End Automation of Optimization Research","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6","json":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6.json","graph_json":"https://pith.science/api/pith-number/ARGMFHHCBBBVOPU6MEVFZ5FIE6/graph.json","events_json":"https://pith.science/api/pith-number/ARGMFHHCBBBVOPU6MEVFZ5FIE6/events.json","paper":"https://pith.science/paper/ARGMFHHC"},"agent_actions":{"view_html":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6","download_json":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6.json","view_paper":"https://pith.science/paper/ARGMFHHC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.13335&json=true","fetch_graph":"https://pith.science/api/pith-number/ARGMFHHCBBBVOPU6MEVFZ5FIE6/graph.json","fetch_events":"https://pith.science/api/pith-number/ARGMFHHCBBBVOPU6MEVFZ5FIE6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6/action/storage_attestation","attest_author":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6/action/author_attestation","sign_citation":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6/action/citation_signature","submit_replication":"https://pith.science/pith/ARGMFHHCBBBVOPU6MEVFZ5FIE6/action/replication_record"}},"created_at":"2026-07-16T00:22:12.911934+00:00","updated_at":"2026-07-16T00:22:12.911934+00:00"}