{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:T3TZ6GEGEEC6ZRNRITYGSOOPHI","short_pith_number":"pith:T3TZ6GEG","canonical_record":{"source":{"id":"math/0505308","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2005-05-14T14:00:03Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"ce7ef97d248dd2a2ff0c083cf910a68a2aee7ae3e07f9240f538d5b14a80ec36","abstract_canon_sha256":"f94b0f59c6577491c9c0b6dc273f393461bde6e63ee27ede6053c768c5ad9c23"},"schema_version":"1.0"},"canonical_sha256":"9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7","source":{"kind":"arxiv","id":"math/0505308","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505308","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505308v2","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505308","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"T3TZ6GEGEEC6","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_16","alias_value":"T3TZ6GEGEEC6ZRNR","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_8","alias_value":"T3TZ6GEG","created_at":"2026-07-04T14:50:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:T3TZ6GEGEEC6ZRNRITYGSOOPHI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0505308","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2005-05-14T14:00:03Z","cross_cats_sorted":["math.DS","math.FA"],"title_canon_sha256":"ce7ef97d248dd2a2ff0c083cf910a68a2aee7ae3e07f9240f538d5b14a80ec36","abstract_canon_sha256":"f94b0f59c6577491c9c0b6dc273f393461bde6e63ee27ede6053c768c5ad9c23"},"schema_version":"1.0"},"canonical_sha256":"9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:50:13.549804Z","signature_b64":"nyeQ/u2duYpg+1z0tfSknMzWpKm+wqkwc7KLk+X2YHGgG7d7MTV5L99cyXhO/Z4Sm2tz4K8etgql7mIt5jpTDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7","last_reissued_at":"2026-07-04T14:50:13.549399Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:50:13.549399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0505308","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":"2026-07-04T14:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rPIYkHd5yc+Axp5u0ztB+tE2WeEJPfZhnupd8VWbWasu6+CkeKYIsvBMNOcBg0cojd07GokR7SIc6kGEba3XAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:44:11.017061Z"},"content_sha256":"c3f78aa01dabffbbc1b0e3678216106c14000c8952afa6f2461e64bb9b611654","schema_version":"1.0","event_id":"sha256:c3f78aa01dabffbbc1b0e3678216106c14000c8952afa6f2461e64bb9b611654"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:T3TZ6GEGEEC6ZRNRITYGSOOPHI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Noncommutative maximal ergodic theorems","license":"","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OA","authors_text":"Marius Junge, Quanhua Xu","submitted_at":"2005-05-14T14:00:03Z","abstract_excerpt":"This paper is devoted to the study of various maximal ergodic theorems in noncommutative $L_p$-spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on $L_p$ and the analogue of Stein's maximal inequality for symmetric positive contractions. We also obtain the corresponding individual ergodic theorems. We apply these results to a family of natural examples which frequently appear in theory of von Neumann algebras and in quantum probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505308","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0505308/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":"2026-07-04T14:50:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZgN2VbnDRfjlmw0t4ZMOS+PmtCFjvhMvCkMHu3QQ1842xFAi+Iy2zQeHXw2Hd2E3XiRBqRGymkJ8Pk3nG9x0AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T16:44:11.017646Z"},"content_sha256":"e7efec547699e69d3e91f77ab7297868d60cb69a54f5c94158d5237e247a9de3","schema_version":"1.0","event_id":"sha256:e7efec547699e69d3e91f77ab7297868d60cb69a54f5c94158d5237e247a9de3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/bundle.json","state_url":"https://pith.science/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/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":"2026-08-10T16:44:11Z","links":{"resolver":"https://pith.science/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI","bundle":"https://pith.science/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/bundle.json","state":"https://pith.science/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T3TZ6GEGEEC6ZRNRITYGSOOPHI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:T3TZ6GEGEEC6ZRNRITYGSOOPHI","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":"f94b0f59c6577491c9c0b6dc273f393461bde6e63ee27ede6053c768c5ad9c23","cross_cats_sorted":["math.DS","math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2005-05-14T14:00:03Z","title_canon_sha256":"ce7ef97d248dd2a2ff0c083cf910a68a2aee7ae3e07f9240f538d5b14a80ec36"},"schema_version":"1.0","source":{"id":"math/0505308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0505308","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"math/0505308v2","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0505308","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"T3TZ6GEGEEC6","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_16","alias_value":"T3TZ6GEGEEC6ZRNR","created_at":"2026-07-04T14:50:13Z"},{"alias_kind":"pith_short_8","alias_value":"T3TZ6GEG","created_at":"2026-07-04T14:50:13Z"}],"graph_snapshots":[{"event_id":"sha256:e7efec547699e69d3e91f77ab7297868d60cb69a54f5c94158d5237e247a9de3","target":"graph","created_at":"2026-07-04T14:50:13Z","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/0505308/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to the study of various maximal ergodic theorems in noncommutative $L_p$-spaces. In particular, we prove the noncommutative analogue of the classical Dunford-Schwartz maximal ergodic inequality for positive contractions on $L_p$ and the analogue of Stein's maximal inequality for symmetric positive contractions. We also obtain the corresponding individual ergodic theorems. We apply these results to a family of natural examples which frequently appear in theory of von Neumann algebras and in quantum probability.","authors_text":"Marius Junge, Quanhua Xu","cross_cats":["math.DS","math.FA"],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2005-05-14T14:00:03Z","title":"Noncommutative maximal ergodic theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0505308","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:c3f78aa01dabffbbc1b0e3678216106c14000c8952afa6f2461e64bb9b611654","target":"record","created_at":"2026-07-04T14:50:13Z","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":"f94b0f59c6577491c9c0b6dc273f393461bde6e63ee27ede6053c768c5ad9c23","cross_cats_sorted":["math.DS","math.FA"],"license":"","primary_cat":"math.OA","submitted_at":"2005-05-14T14:00:03Z","title_canon_sha256":"ce7ef97d248dd2a2ff0c083cf910a68a2aee7ae3e07f9240f538d5b14a80ec36"},"schema_version":"1.0","source":{"id":"math/0505308","kind":"arxiv","version":2}},"canonical_sha256":"9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ee79f18862105ecc5b144f06939cf3a168f33143db0b7249dc8d3f1cdfc4cc7","first_computed_at":"2026-07-04T14:50:13.549399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:50:13.549399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nyeQ/u2duYpg+1z0tfSknMzWpKm+wqkwc7KLk+X2YHGgG7d7MTV5L99cyXhO/Z4Sm2tz4K8etgql7mIt5jpTDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:50:13.549804Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0505308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c3f78aa01dabffbbc1b0e3678216106c14000c8952afa6f2461e64bb9b611654","sha256:e7efec547699e69d3e91f77ab7297868d60cb69a54f5c94158d5237e247a9de3"],"state_sha256":"a3441318fad1b2cae3f75db9c7a646d699bb9c96663b94e757dc20898bff2b16"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ab/WWTOFTFuVDUDtjNsub2DA2pC2WbD6y5pSpIV+nY7iAWzxl4d3jdR+knlZiFCjnNiTbZ6h/dIhNNL3IEApAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T16:44:11.022476Z","bundle_sha256":"07ad458eea67061838d675fdb8dadf524dad0f9c7332afb836e127b0c310ec5a"}}