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We also derive the first Õ(ε^{-3}) oracle-complexity bounds for stochastic optimization with expectation constraints, improving upon the existing Õ(ε^{-4}) complexity.","weakest_assumption":"The central high-probability bound and complexity results rest on the validity and applicability of the newly introduced dimension-free vector-valued Freedman inequality in smooth normed spaces (including Banach spaces for mirror descent)."}},"verdict_id":"ee37f637-5b38-4af1-9385-ba7c7be68b7c"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2b6146f4cbc425252f5b797929e9216849c28cb292e4bfdfc5f65e9af2a1583f","target":"record","created_at":"2026-05-20T00:00:55Z","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":"a1ac0cb28bf02ba75c689f94a4ecd5aeb374185c767f227400b30536275fc0c5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-05-14T20:17:10Z","title_canon_sha256":"2f0048b8781c6330df2e1c46100031bd7ac63e506a8724e6e39310b2ee34a842"},"schema_version":"1.0","source":{"id":"2605.15388","kind":"arxiv","version":1}},"canonical_sha256":"da5d31131111f717242d95f01b15c797ec3a4b6474343c85cf6328b0053ca916","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da5d31131111f717242d95f01b15c797ec3a4b6474343c85cf6328b0053ca916","first_computed_at":"2026-05-20T00:00:55.978991Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:00:55.978991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gTbKkl/S+Eo8qe7hCrES+Na9m4MAiejK5wboBP2efj60UNaiwAvlr8HNL8UN2Y4Ma++Zsv16h+4MZeLCvvI0BA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:00:55.979828Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15388","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b6146f4cbc425252f5b797929e9216849c28cb292e4bfdfc5f65e9af2a1583f","sha256:af975d1ff810c36ecc66312576180822abbb957ba902226d0207c951ec9ad7b5"],"state_sha256":"8992a9817f03e640a0da8449f3d702199a5571f67f0bd7a384ff456a590ea09d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5EHFp6fVhcBThWx4zIKm+OjkMOimwj1qvq/ZMi0B3419Jhi9Z3DNP3dj7Z7+8LIvR6gwR0dVLxdIV79KwBchDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T23:35:11.067212Z","bundle_sha256":"d91811c9591078476055a94fe312377f06e472e592daa5da4baae1861df820e4"}}