{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:A663KSTUIXKMXA5RMVYUTHOW3F","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":"ab1ffb5e5e4829ca0413e4e6e2e826317b1bd7c6cdf7b5e0d417ca1e03652144","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T01:42:28Z","title_canon_sha256":"891061b661bf712af8b6a62cf09122feb99f906e5792a6b81b52466157a273d2"},"schema_version":"1.0","source":{"id":"1612.04452","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.04452","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"arxiv_version","alias_value":"1612.04452v1","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.04452","created_at":"2026-05-18T00:54:59Z"},{"alias_kind":"pith_short_12","alias_value":"A663KSTUIXKM","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"A663KSTUIXKMXA5R","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"A663KSTU","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:283d6e557d5c21a908d2b79ad2d24fdf88e3c0d046fe3d30dd6168807d77c156","target":"graph","created_at":"2026-05-18T00:54:59Z","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"},"paper":{"abstract_excerpt":"In this paper we study Johnson-Schechtman inequalities for noncommutative martingales. More precisely, disjointification inequalities of noncommutative martingale difference sequences are proved in an arbitrary symmetric operator space $E(\\mathcal{M})$ of a finite von Neumann algebra $\\mathcal{M}$ without making any assumption on the Boyd indices of $E$. We show that we can obtain Johnson-Schechtman inequalities for arbitrary martingale difference sequences and that, in contrast with the classical case of independent random variables or the noncommutative case of freely independent random vari","authors_text":"Dejian Zhou, Dmitriy Zanin, Fedor Sukochev, Yong Jiao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T01:42:28Z","title":"Johnson-Schechtman inequalities for noncommutative martingales"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.04452","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":"sha256:2381cb5de6501d28566250c78e311d9849253045d9e9991db9ff344464c24446","target":"record","created_at":"2026-05-18T00:54:59Z","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":"ab1ffb5e5e4829ca0413e4e6e2e826317b1bd7c6cdf7b5e0d417ca1e03652144","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.PR","submitted_at":"2016-12-14T01:42:28Z","title_canon_sha256":"891061b661bf712af8b6a62cf09122feb99f906e5792a6b81b52466157a273d2"},"schema_version":"1.0","source":{"id":"1612.04452","kind":"arxiv","version":1}},"canonical_sha256":"07bdb54a7445d4cb83b16571499dd6d94c0f834d054a87c1c14059f27ef967ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"07bdb54a7445d4cb83b16571499dd6d94c0f834d054a87c1c14059f27ef967ae","first_computed_at":"2026-05-18T00:54:59.506863Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:59.506863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QEGKI6zwR+vdNFDcEJrrocHZKllFMMfJ3V4VfgmyKhaCIGkKERD0osk/ohZtOV243fkDzmTOVBKIyaKcoRdXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:59.507375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.04452","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2381cb5de6501d28566250c78e311d9849253045d9e9991db9ff344464c24446","sha256:283d6e557d5c21a908d2b79ad2d24fdf88e3c0d046fe3d30dd6168807d77c156"],"state_sha256":"0b874700ab8e50bec5e240bd3686ed10224bac449932976c18fbc5dfddb7c5d3"}