{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:R5GSIJVH6SMQMBXE6Q2H4KSF4C","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":"9952f3379ed962e3831f31c6e2c426cdbe4eda96486cffb4b27bd1277adca90b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-01T19:27:29Z","title_canon_sha256":"90cf0515ff289dc2b81ec0ee8a0c852e430b8471cbb1123ce1a6b9ad600c3fbf"},"schema_version":"1.0","source":{"id":"1604.00851","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00851","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00851v1","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00851","created_at":"2026-05-18T01:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"R5GSIJVH6SMQ","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"R5GSIJVH6SMQMBXE","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"R5GSIJVH","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:3bcd4317c8775668e0b743808a4e1d966dbaaf821e07fad5c74380535b9b91a5","target":"graph","created_at":"2026-05-18T01:17:48Z","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":"It is known that, for a positive Dunford-Schwartz operator in a noncommutative $L^p-$space, $1\\leq p<\\infty$ or, more generally, in a noncommutative Orlicz space with order continuous norm, the corresponding ergodic averages converge bilaterally almost uniformly. We show that these averages converge bilaterally almost uniformly in each noncommutative symmetric space $E$ such that $\\mu_t(x) \\to 0$ as $t \\to 0$ for every $x \\in E$, where $\\mu_t(x)$ is a non-increasing rearrangement of $x$. In particular, these averages converge bilaterally almost uniformly in all noncommutative symmetric spaces ","authors_text":"Semyon Litvinov, Vladimir Chilin","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-01T19:27:29Z","title":"Individual ergodic theorems in noncommutative symmetric spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00851","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":"sha256:5083297abbcaf124aa4c9efe8ad42a9a606c12a34039e99d1b1b4cfdfc4ad93d","target":"record","created_at":"2026-05-18T01:17:48Z","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":"9952f3379ed962e3831f31c6e2c426cdbe4eda96486cffb4b27bd1277adca90b","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-04-01T19:27:29Z","title_canon_sha256":"90cf0515ff289dc2b81ec0ee8a0c852e430b8471cbb1123ce1a6b9ad600c3fbf"},"schema_version":"1.0","source":{"id":"1604.00851","kind":"arxiv","version":1}},"canonical_sha256":"8f4d2426a7f4990606e4f4347e2a45e081e88c099f0c6e212ef804201ca018dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f4d2426a7f4990606e4f4347e2a45e081e88c099f0c6e212ef804201ca018dd","first_computed_at":"2026-05-18T01:17:48.014276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:48.014276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"l+j06rUpK+mbm2TMpq/qlgacw/V4Vi6zCAkjZTRLtU7C6tMyt3LWEk1B2Xd+H7cjxpFXGslHOv+AVuMtDTf2CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:48.014879Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00851","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5083297abbcaf124aa4c9efe8ad42a9a606c12a34039e99d1b1b4cfdfc4ad93d","sha256:3bcd4317c8775668e0b743808a4e1d966dbaaf821e07fad5c74380535b9b91a5"],"state_sha256":"6108f3c1cb3ba6515fdc5428c91a773002507e31d42de71008e590352ede9e3d"}