{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6TU24P7OW43T6QXEHCCMXCDXTJ","short_pith_number":"pith:6TU24P7O","canonical_record":{"source":{"id":"2607.18652","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-21T02:44:33Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"f13188ac1c7d7a5b940066d59460e22bb2a2eff7390df9d1a66fbb1e9615f1cf","abstract_canon_sha256":"e857a282657573ba9e90cd643b8288c39050deba26663d72e205adde4d03eef7"},"schema_version":"1.0"},"canonical_sha256":"f4e9ae3feeb7373f42e43884cb88779a74cf55e11f30ad627631242d9ec8de42","source":{"kind":"arxiv","id":"2607.18652","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18652","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18652v1","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18652","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"6TU24P7OW43T","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_16","alias_value":"6TU24P7OW43T6QXE","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_8","alias_value":"6TU24P7O","created_at":"2026-07-22T00:22:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6TU24P7OW43T6QXEHCCMXCDXTJ","target":"record","payload":{"canonical_record":{"source":{"id":"2607.18652","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-21T02:44:33Z","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"title_canon_sha256":"f13188ac1c7d7a5b940066d59460e22bb2a2eff7390df9d1a66fbb1e9615f1cf","abstract_canon_sha256":"e857a282657573ba9e90cd643b8288c39050deba26663d72e205adde4d03eef7"},"schema_version":"1.0"},"canonical_sha256":"f4e9ae3feeb7373f42e43884cb88779a74cf55e11f30ad627631242d9ec8de42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T00:22:58.602482Z","signature_b64":"X8JAcLMUrbDHNbH4GTAN1RMkhyzu6OvnOIwLVr+mcIwqmO0gfvyPVxjj6wT2hd7o+DmWRObglzRD0xOG2625Dg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4e9ae3feeb7373f42e43884cb88779a74cf55e11f30ad627631242d9ec8de42","last_reissued_at":"2026-07-22T00:22:58.601658Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T00:22:58.601658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.18652","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-22T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OLpn4X/p1YCwK4iKiAhVQdVXP4jwNUaDn0iHljirp0u1xB2P7lVGdeUym1u9NY4JR9OpI7UmVCklApMYup/FBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:44.317608Z"},"content_sha256":"e35428620ab4a66c387bc4cc0206013bcf07001f0a660754ccc36a5643c7b5db","schema_version":"1.0","event_id":"sha256:e35428620ab4a66c387bc4cc0206013bcf07001f0a660754ccc36a5643c7b5db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6TU24P7OW43T6QXEHCCMXCDXTJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Price of Hidden Curvature: An $\\widetilde{\\Omega} (d^{5/4} \\sqrt{T})$ Lower Bound for Bandit Convex Optimization","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","cs.LG","math.IT"],"primary_cat":"stat.ML","authors_text":"Nived Rajaraman","submitted_at":"2026-07-21T02:44:33Z","abstract_excerpt":"We establish a $\\widetilde\\Omega(d^{5/4}\\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\\sqrt{T}$ for this problem, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits.\n  The hard class of convex functions we construct takes the following form in dimension $2d$: for an action $a = (a^1,a^2) \\in \\mathbb{B}^{2d}_2$, each function is the scaled soft maximum of a \"tube\", $r^{-1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18652","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/2607.18652/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":"2026-07-22T00:22:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p9WedxSTOkpWmpOj5h3Uw4o05VNpLa2ODfvdB5j9PUTD9/lhVuU6Y55v4qhi1bpVFs6vMta23iCOQqjE6QCCAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T07:48:44.318000Z"},"content_sha256":"fdddfd2352a5a774f5d4b999bddc1c17629a385c798e346f2d85eee40b038370","schema_version":"1.0","event_id":"sha256:fdddfd2352a5a774f5d4b999bddc1c17629a385c798e346f2d85eee40b038370"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/bundle.json","state_url":"https://pith.science/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/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":"2026-08-04T07:48:44Z","links":{"resolver":"https://pith.science/pith/6TU24P7OW43T6QXEHCCMXCDXTJ","bundle":"https://pith.science/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/bundle.json","state":"https://pith.science/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TU24P7OW43T6QXEHCCMXCDXTJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6TU24P7OW43T6QXEHCCMXCDXTJ","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":"e857a282657573ba9e90cd643b8288c39050deba26663d72e205adde4d03eef7","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-21T02:44:33Z","title_canon_sha256":"f13188ac1c7d7a5b940066d59460e22bb2a2eff7390df9d1a66fbb1e9615f1cf"},"schema_version":"1.0","source":{"id":"2607.18652","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.18652","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"arxiv_version","alias_value":"2607.18652v1","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.18652","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_12","alias_value":"6TU24P7OW43T","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_16","alias_value":"6TU24P7OW43T6QXE","created_at":"2026-07-22T00:22:58Z"},{"alias_kind":"pith_short_8","alias_value":"6TU24P7O","created_at":"2026-07-22T00:22:58Z"}],"graph_snapshots":[{"event_id":"sha256:fdddfd2352a5a774f5d4b999bddc1c17629a385c798e346f2d85eee40b038370","target":"graph","created_at":"2026-07-22T00:22:58Z","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/2607.18652/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We establish a $\\widetilde\\Omega(d^{5/4}\\sqrt T)$ lower bound on the minimax expected regret of stochastic bandit convex optimization of $1$-Lipschitz functions on the Euclidean ball. This presents the first nontrivial regret lower bound that grows faster than $d\\sqrt{T}$ for this problem, establishing that stochastic bandit convex optimization is fundamentally harder than linear bandits.\n  The hard class of convex functions we construct takes the following form in dimension $2d$: for an action $a = (a^1,a^2) \\in \\mathbb{B}^{2d}_2$, each function is the scaled soft maximum of a \"tube\", $r^{-1}","authors_text":"Nived Rajaraman","cross_cats":["cs.IT","cs.LG","math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-21T02:44:33Z","title":"The Price of Hidden Curvature: An $\\widetilde{\\Omega} (d^{5/4} \\sqrt{T})$ Lower Bound for Bandit Convex Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.18652","kind":"arxiv","version":1},"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:e35428620ab4a66c387bc4cc0206013bcf07001f0a660754ccc36a5643c7b5db","target":"record","created_at":"2026-07-22T00:22:58Z","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":"e857a282657573ba9e90cd643b8288c39050deba26663d72e205adde4d03eef7","cross_cats_sorted":["cs.IT","cs.LG","math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"stat.ML","submitted_at":"2026-07-21T02:44:33Z","title_canon_sha256":"f13188ac1c7d7a5b940066d59460e22bb2a2eff7390df9d1a66fbb1e9615f1cf"},"schema_version":"1.0","source":{"id":"2607.18652","kind":"arxiv","version":1}},"canonical_sha256":"f4e9ae3feeb7373f42e43884cb88779a74cf55e11f30ad627631242d9ec8de42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4e9ae3feeb7373f42e43884cb88779a74cf55e11f30ad627631242d9ec8de42","first_computed_at":"2026-07-22T00:22:58.601658Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T00:22:58.601658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X8JAcLMUrbDHNbH4GTAN1RMkhyzu6OvnOIwLVr+mcIwqmO0gfvyPVxjj6wT2hd7o+DmWRObglzRD0xOG2625Dg==","signature_status":"signed_v1","signed_at":"2026-07-22T00:22:58.602482Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.18652","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e35428620ab4a66c387bc4cc0206013bcf07001f0a660754ccc36a5643c7b5db","sha256:fdddfd2352a5a774f5d4b999bddc1c17629a385c798e346f2d85eee40b038370"],"state_sha256":"8e701f84137cbcc3af45236443ec656e50b136c0fc558901172e79df40514d8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUMgME4WKdnpT6tE6f5l32FqsqcyDNGZvZmszrYVUi78o0djszECWhGj3vR4vjKUlwtfZNPGB4zz+Ktx/AtFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T07:48:44.320703Z","bundle_sha256":"af616f02456a312e6e064ddee088f22fd7d24d7eb5416542e56fc977bc520215"}}