{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QVCAZ3RPDD2YBNVN3VQOKNYMOR","short_pith_number":"pith:QVCAZ3RP","canonical_record":{"source":{"id":"2504.02818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-03T17:58:10Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"df79a2748619cd89aa92269812f6c97fe5bd9bf14145207d4d886d8edba85cf8","abstract_canon_sha256":"0db00a4d4a97a01382aee9d777dc1b42982e248e2f5485994c8ac65b1a69a616"},"schema_version":"1.0"},"canonical_sha256":"85440cee2f18f580b6addd60e5370c744802c704fa14b450f6843c9a68c9659b","source":{"kind":"arxiv","id":"2504.02818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02818","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02818v1","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02818","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"QVCAZ3RPDD2Y","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_16","alias_value":"QVCAZ3RPDD2YBNVN","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_8","alias_value":"QVCAZ3RP","created_at":"2026-07-05T10:44:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QVCAZ3RPDD2YBNVN3VQOKNYMOR","target":"record","payload":{"canonical_record":{"source":{"id":"2504.02818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-03T17:58:10Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"df79a2748619cd89aa92269812f6c97fe5bd9bf14145207d4d886d8edba85cf8","abstract_canon_sha256":"0db00a4d4a97a01382aee9d777dc1b42982e248e2f5485994c8ac65b1a69a616"},"schema_version":"1.0"},"canonical_sha256":"85440cee2f18f580b6addd60e5370c744802c704fa14b450f6843c9a68c9659b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:44:02.759531Z","signature_b64":"J7rx67AqV1YohEa7p/nSTdftKWR5aHOk0vCjkGOP1J11iscjyRY9VR7SD+A8LxpNh0MTCG5ZUuqzCHHeIkNKDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85440cee2f18f580b6addd60e5370c744802c704fa14b450f6843c9a68c9659b","last_reissued_at":"2026-07-05T10:44:02.759059Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:44:02.759059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2504.02818","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":"2026-07-05T10:44:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XvYU414oTP115SUc+pgwPv3Ji5vKIw/x6HkaY6gmbzoIR4+KsLLBNMzws9sR6EOR5eE5rRIjun4+YqcnlsZtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:27:02.427538Z"},"content_sha256":"879419b8811b9cefc201673ffe71a95f46081bad0303276d5729adcec222f938","schema_version":"1.0","event_id":"sha256:879419b8811b9cefc201673ffe71a95f46081bad0303276d5729adcec222f938"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QVCAZ3RPDD2YBNVN3VQOKNYMOR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal Log-Optimality for General Classes of e-processes and Sequential Hypothesis Tests","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Ian Waudby-Smith, Michael I. Jordan, Ricardo Sandoval","submitted_at":"2025-04-03T17:58:10Z","abstract_excerpt":"We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of two-sample and independence testing as special cases -- we show that any $e$-process satisfying a certain sublinear regret bound is adaptively, asymptotically, and almost surely log-optimal for a composite alternative. This is a strong notion of optimality that has not previously been established for the aforementioned problems and we provide explicit test supermart"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02818","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/2504.02818/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":"2026-07-05T10:44:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bB0JSPfhGrKqgcWv37S/gRX2tRBPHyi6KhJ7tTavwQ5A6aDdXP9XhnjrJIkDtYLJZiGp772SS9tXS9VH+KxwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:27:02.428040Z"},"content_sha256":"a7cf5233415fd9c85486c3de600751a1c3cf4a2524366cbeecefc7ce224da800","schema_version":"1.0","event_id":"sha256:a7cf5233415fd9c85486c3de600751a1c3cf4a2524366cbeecefc7ce224da800"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/bundle.json","state_url":"https://pith.science/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/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":"2026-08-09T15:27:02Z","links":{"resolver":"https://pith.science/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR","bundle":"https://pith.science/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/bundle.json","state":"https://pith.science/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVCAZ3RPDD2YBNVN3VQOKNYMOR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QVCAZ3RPDD2YBNVN3VQOKNYMOR","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":"0db00a4d4a97a01382aee9d777dc1b42982e248e2f5485994c8ac65b1a69a616","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-03T17:58:10Z","title_canon_sha256":"df79a2748619cd89aa92269812f6c97fe5bd9bf14145207d4d886d8edba85cf8"},"schema_version":"1.0","source":{"id":"2504.02818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.02818","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"arxiv_version","alias_value":"2504.02818v1","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.02818","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_12","alias_value":"QVCAZ3RPDD2Y","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_16","alias_value":"QVCAZ3RPDD2YBNVN","created_at":"2026-07-05T10:44:02Z"},{"alias_kind":"pith_short_8","alias_value":"QVCAZ3RP","created_at":"2026-07-05T10:44:02Z"}],"graph_snapshots":[{"event_id":"sha256:a7cf5233415fd9c85486c3de600751a1c3cf4a2524366cbeecefc7ce224da800","target":"graph","created_at":"2026-07-05T10:44:02Z","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/2504.02818/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the problem of sequential hypothesis testing by betting. For a general class of composite testing problems -- which include bounded mean testing, equal mean testing for bounded random tuples, and some key ingredients of two-sample and independence testing as special cases -- we show that any $e$-process satisfying a certain sublinear regret bound is adaptively, asymptotically, and almost surely log-optimal for a composite alternative. This is a strong notion of optimality that has not previously been established for the aforementioned problems and we provide explicit test supermart","authors_text":"Ian Waudby-Smith, Michael I. Jordan, Ricardo Sandoval","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-03T17:58:10Z","title":"Universal Log-Optimality for General Classes of e-processes and Sequential Hypothesis Tests"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.02818","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":"sha256:879419b8811b9cefc201673ffe71a95f46081bad0303276d5729adcec222f938","target":"record","created_at":"2026-07-05T10:44:02Z","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":"0db00a4d4a97a01382aee9d777dc1b42982e248e2f5485994c8ac65b1a69a616","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-04-03T17:58:10Z","title_canon_sha256":"df79a2748619cd89aa92269812f6c97fe5bd9bf14145207d4d886d8edba85cf8"},"schema_version":"1.0","source":{"id":"2504.02818","kind":"arxiv","version":1}},"canonical_sha256":"85440cee2f18f580b6addd60e5370c744802c704fa14b450f6843c9a68c9659b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85440cee2f18f580b6addd60e5370c744802c704fa14b450f6843c9a68c9659b","first_computed_at":"2026-07-05T10:44:02.759059Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:44:02.759059Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J7rx67AqV1YohEa7p/nSTdftKWR5aHOk0vCjkGOP1J11iscjyRY9VR7SD+A8LxpNh0MTCG5ZUuqzCHHeIkNKDA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:44:02.759531Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.02818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:879419b8811b9cefc201673ffe71a95f46081bad0303276d5729adcec222f938","sha256:a7cf5233415fd9c85486c3de600751a1c3cf4a2524366cbeecefc7ce224da800"],"state_sha256":"254661710b4bdc9fc12f533a998f26eed50fc7dd0e06bcebedcf2d4f4e4587ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQMw62n8bdtx6dOtWsr7U41Xq+NWFRk6KXmxDEAY9s0uWsmj6hO2nkihj44LKyg/ra6pEsx1/hwClY9HwO+FDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:27:02.431323Z","bundle_sha256":"3efb285a423bc5fe64b6295a9cc127a88d7d3e4b3889daecd2f4a201c509476e"}}