{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:RMUCJXOZIQO2M2QDSQNG6S3NBZ","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":"87ba13eb7c5f069961118eb1023fac5681956720b2d4ad1a23437c2e170e59aa","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T16:44:20Z","title_canon_sha256":"6923f3fd88ce96faa94e78ec4cde2225257600e33f70d8bea91b71223b1eeda0"},"schema_version":"1.0","source":{"id":"2507.20982","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2507.20982","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"arxiv_version","alias_value":"2507.20982v2","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.20982","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_12","alias_value":"RMUCJXOZIQO2","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_16","alias_value":"RMUCJXOZIQO2M2QD","created_at":"2026-05-20T00:05:30Z"},{"alias_kind":"pith_short_8","alias_value":"RMUCJXOZ","created_at":"2026-05-20T00:05:30Z"}],"graph_snapshots":[{"event_id":"sha256:03e2ced36cb561ee361020688578631bacd7046a50588d9ea3d7f948dc16387e","target":"graph","created_at":"2026-05-20T00:05:30Z","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/2507.20982/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a dimension-free Bernstein-type tail inequality for self-normalised martingales, where the normalisation uses the predictable quadratic variation and the radius depends on the information gain of the observed covariance. As applications, we provide ellipsoidal confidence sequences for logistic regression with adaptively chosen Hilbert-valued covariates, and give instance-adaptive regret bounds for Hilbert-armed logistic bandits.","authors_text":"Alex Ayoub, Amitis Shidani, Arya Akhavan, David Janz","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T16:44:20Z","title":"Bernstein-type dimension-free concentration for self-normalised martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.20982","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":"sha256:110b2619c3f94faf1460160a63c6ae6667586d8e1c72a7c5c5724327be55213c","target":"record","created_at":"2026-05-20T00:05:30Z","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":"87ba13eb7c5f069961118eb1023fac5681956720b2d4ad1a23437c2e170e59aa","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2025-07-28T16:44:20Z","title_canon_sha256":"6923f3fd88ce96faa94e78ec4cde2225257600e33f70d8bea91b71223b1eeda0"},"schema_version":"1.0","source":{"id":"2507.20982","kind":"arxiv","version":2}},"canonical_sha256":"8b2824ddd9441da66a03941a6f4b6d0e647315411c2cfd4d79aad555cb8e1a9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b2824ddd9441da66a03941a6f4b6d0e647315411c2cfd4d79aad555cb8e1a9a","first_computed_at":"2026-05-20T00:05:30.754102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:30.754102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Irok6oJDrJXZpzDRy2+TgwKdSll+naUCCO5Le82KFXRureENlo2CQ3vqc5enhi2z9kcQUiKL7our/rKfR07YCA==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:30.754959Z","signed_message":"canonical_sha256_bytes"},"source_id":"2507.20982","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:110b2619c3f94faf1460160a63c6ae6667586d8e1c72a7c5c5724327be55213c","sha256:03e2ced36cb561ee361020688578631bacd7046a50588d9ea3d7f948dc16387e"],"state_sha256":"27a5b6702058911db26366313cd48847e30b4a6da3b0f21641fa03c61d144ccd"}