{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:INSJFG2EDHD3AJ5MLSARW4ENXG","short_pith_number":"pith:INSJFG2E","canonical_record":{"source":{"id":"1406.3220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-12T12:50:29Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"e63bc4c56bcdf7e966982f8ec643e0b60ceb4522518e2d1ce784bb0db88d9728","abstract_canon_sha256":"05f20e4791d868b93c6af415243541eec6d2d41565f7cdfaab2a0e62c1658aba"},"schema_version":"1.0"},"canonical_sha256":"4364929b4419c7b027ac5c811b708db9826086f112fe44197813f5c32db5c363","source":{"kind":"arxiv","id":"1406.3220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3220","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3220v2","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3220","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"INSJFG2EDHD3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"INSJFG2EDHD3AJ5M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"INSJFG2E","created_at":"2026-05-18T12:28:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:INSJFG2EDHD3AJ5MLSARW4ENXG","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-12T12:50:29Z","cross_cats_sorted":["math.FA","math.PR"],"title_canon_sha256":"e63bc4c56bcdf7e966982f8ec643e0b60ceb4522518e2d1ce784bb0db88d9728","abstract_canon_sha256":"05f20e4791d868b93c6af415243541eec6d2d41565f7cdfaab2a0e62c1658aba"},"schema_version":"1.0"},"canonical_sha256":"4364929b4419c7b027ac5c811b708db9826086f112fe44197813f5c32db5c363","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:55.527244Z","signature_b64":"txZinvqpdu/v3SAwNxWN8S+WTrpGF7R0FsT/ak9K/9cJgqBHusFumxi9F8KF68waP+0VT6zaw2ofTALvDRM3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4364929b4419c7b027ac5c811b708db9826086f112fe44197813f5c32db5c363","last_reissued_at":"2026-05-18T01:09:55.526641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:55.526641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3220","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ba4DAiA3FwIfP5hsc5xGGFsgAID2Hy9+RTGKlWRpZB2CC3oSM6bbyd5C99aBOVVz4wE2Y/KF8EJMFmk4LqdbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:08:01.541636Z"},"content_sha256":"40c2596e2296ab29a1b681649510d93a3002139624cd03442d7d45f268cdd77c","schema_version":"1.0","event_id":"sha256:40c2596e2296ab29a1b681649510d93a3002139624cd03442d7d45f268cdd77c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:INSJFG2EDHD3AJ5MLSARW4ENXG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inequalities for sums of random variables in noncommutative probability spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.OA","authors_text":"Ghadir Sadeghi, Mohammad Sal Moslehian","submitted_at":"2014-06-12T12:50:29Z","abstract_excerpt":"In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\\leq r\\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative Hoeffding inequality as follows: Let $(\\mathfrak{M}, \\tau)$ be a noncommutative probability space, $\\mathfrak{N}$ be a von Neumann subalgebra of $\\mathfrak{M}$ with the corresponding conditional expectation $\\mathcal{E}_{\\mathfrak{N}}$ and let subalgebras $\\mathfrak{N}\\subseteq\\mathfrak{A}_j\\subseteq\\mathfrak{M}\\,\\,(j=1, \\cdots, n)$ be successively independent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3220","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T01:09:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FUUROs46tvbXAZoP35LwCDaPwPHVX1kJF6Q+5TD4NaEQiDjMBQoZO3YQZ4t5M5o4qQv0JDiAE74nJVvcdMYmBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T19:08:01.542357Z"},"content_sha256":"8a9cdd7b3ff0b5c71fe414b6c2025d4b557c5e3f9c3a9590955cde6553723c4a","schema_version":"1.0","event_id":"sha256:8a9cdd7b3ff0b5c71fe414b6c2025d4b557c5e3f9c3a9590955cde6553723c4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/bundle.json","state_url":"https://pith.science/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/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":"2026-06-07T19:08:01Z","links":{"resolver":"https://pith.science/pith/INSJFG2EDHD3AJ5MLSARW4ENXG","bundle":"https://pith.science/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/bundle.json","state":"https://pith.science/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/INSJFG2EDHD3AJ5MLSARW4ENXG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:INSJFG2EDHD3AJ5MLSARW4ENXG","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":"05f20e4791d868b93c6af415243541eec6d2d41565f7cdfaab2a0e62c1658aba","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-12T12:50:29Z","title_canon_sha256":"e63bc4c56bcdf7e966982f8ec643e0b60ceb4522518e2d1ce784bb0db88d9728"},"schema_version":"1.0","source":{"id":"1406.3220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3220","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3220v2","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3220","created_at":"2026-05-18T01:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"INSJFG2EDHD3","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_16","alias_value":"INSJFG2EDHD3AJ5M","created_at":"2026-05-18T12:28:33Z"},{"alias_kind":"pith_short_8","alias_value":"INSJFG2E","created_at":"2026-05-18T12:28:33Z"}],"graph_snapshots":[{"event_id":"sha256:8a9cdd7b3ff0b5c71fe414b6c2025d4b557c5e3f9c3a9590955cde6553723c4a","target":"graph","created_at":"2026-05-18T01:09:55Z","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 establish an extension of a noncommutative Bennett inequality with a parameter $1\\leq r\\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative Hoeffding inequality as follows: Let $(\\mathfrak{M}, \\tau)$ be a noncommutative probability space, $\\mathfrak{N}$ be a von Neumann subalgebra of $\\mathfrak{M}$ with the corresponding conditional expectation $\\mathcal{E}_{\\mathfrak{N}}$ and let subalgebras $\\mathfrak{N}\\subseteq\\mathfrak{A}_j\\subseteq\\mathfrak{M}\\,\\,(j=1, \\cdots, n)$ be successively independent","authors_text":"Ghadir Sadeghi, Mohammad Sal Moslehian","cross_cats":["math.FA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-12T12:50:29Z","title":"Inequalities for sums of random variables in noncommutative probability spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3220","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":"sha256:40c2596e2296ab29a1b681649510d93a3002139624cd03442d7d45f268cdd77c","target":"record","created_at":"2026-05-18T01:09:55Z","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":"05f20e4791d868b93c6af415243541eec6d2d41565f7cdfaab2a0e62c1658aba","cross_cats_sorted":["math.FA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-06-12T12:50:29Z","title_canon_sha256":"e63bc4c56bcdf7e966982f8ec643e0b60ceb4522518e2d1ce784bb0db88d9728"},"schema_version":"1.0","source":{"id":"1406.3220","kind":"arxiv","version":2}},"canonical_sha256":"4364929b4419c7b027ac5c811b708db9826086f112fe44197813f5c32db5c363","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4364929b4419c7b027ac5c811b708db9826086f112fe44197813f5c32db5c363","first_computed_at":"2026-05-18T01:09:55.526641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:55.526641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"txZinvqpdu/v3SAwNxWN8S+WTrpGF7R0FsT/ak9K/9cJgqBHusFumxi9F8KF68waP+0VT6zaw2ofTALvDRM3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:55.527244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40c2596e2296ab29a1b681649510d93a3002139624cd03442d7d45f268cdd77c","sha256:8a9cdd7b3ff0b5c71fe414b6c2025d4b557c5e3f9c3a9590955cde6553723c4a"],"state_sha256":"02b8b1aec783ebd7966da2722150ecda460b2f8d1e989ebc3973df10b0605c95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zvqApHs0Vv/YGfBG8B1iOIT5xlIoL2cWintTgFus9dRM5aUrZpgkwak2iaEnObWLPG3DSx3XoxpPXvZzfaqjCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T19:08:01.545859Z","bundle_sha256":"3f74ab343efc3115afbabc727044b7324db708172a9f9bc5adc3c650c130c2cf"}}