{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:PMOAI5WOPRVJ22CPJGLHTY2Z7Z","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":"79543dcec792b07cbb12a394a9445ccdd80065f3c38528ebcb917e1c7078aa85","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2002-06-06T23:15:07Z","title_canon_sha256":"99e5d836b6f8fd57af68be5dce26a09d38e1f845ef5e54b6515339a9ac3c817d"},"schema_version":"1.0","source":{"id":"math/0206062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0206062","created_at":"2026-07-04T14:36:15Z"},{"alias_kind":"arxiv_version","alias_value":"math/0206062v1","created_at":"2026-07-04T14:36:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0206062","created_at":"2026-07-04T14:36:15Z"},{"alias_kind":"pith_short_12","alias_value":"PMOAI5WOPRVJ","created_at":"2026-07-04T14:36:15Z"},{"alias_kind":"pith_short_16","alias_value":"PMOAI5WOPRVJ22CP","created_at":"2026-07-04T14:36:15Z"},{"alias_kind":"pith_short_8","alias_value":"PMOAI5WO","created_at":"2026-07-04T14:36:15Z"}],"graph_snapshots":[{"event_id":"sha256:4bbef6ab40391c116cc89f7a4b619002d11caae9b7128fb55500f6d391b14e4b","target":"graph","created_at":"2026-07-04T14:36:15Z","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/math/0206062/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $1\\le p<\\8$ and $(x_n)_{\\nen}$ be a sequence of positive elements in a non-commutative $L_p$ space and $(E_n)_{\\nen}$ be an increasing sequence of conditional expectations, then the $L_p$ norm of \\sum_n E_n(x_n) can be estimated by c_p times the $L_p$ norm of \\sum_n x_n. This inequality is due to Burkholder, Davis and Gundy in the commutative case. By duality, we obtain a version of Doob's maximal inequality for $1<p\\le \\8$.","authors_text":"M. Junge","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2002-06-06T23:15:07Z","title":"Doob's inequality for non-commutative martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0206062","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":"sha256:1fc9e76c157070507f69cddcf20d978557a9ec4598b8fe25f03b69b932ee016d","target":"record","created_at":"2026-07-04T14:36:15Z","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":"79543dcec792b07cbb12a394a9445ccdd80065f3c38528ebcb917e1c7078aa85","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2002-06-06T23:15:07Z","title_canon_sha256":"99e5d836b6f8fd57af68be5dce26a09d38e1f845ef5e54b6515339a9ac3c817d"},"schema_version":"1.0","source":{"id":"math/0206062","kind":"arxiv","version":1}},"canonical_sha256":"7b1c0476ce7c6a9d684f499679e359fe72c749a5dce22f41d1cb88beb0d0c825","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b1c0476ce7c6a9d684f499679e359fe72c749a5dce22f41d1cb88beb0d0c825","first_computed_at":"2026-07-04T14:36:15.198827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:36:15.198827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1YP4g9nJY1H4B//opyWEKnkZDUqTiEwEZINcCXI/IUs87+N5MI1ffKn8O5oHveY3wccPtcwLFTOgyuHJ/oCtAA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:36:15.199360Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0206062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fc9e76c157070507f69cddcf20d978557a9ec4598b8fe25f03b69b932ee016d","sha256:4bbef6ab40391c116cc89f7a4b619002d11caae9b7128fb55500f6d391b14e4b"],"state_sha256":"15f9468469bb094c0a85925382172be6a081f6536c137ca997161c5f18f31673"}