{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:Q3N7RL5PEEG72IVWWIYLI3GMI2","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":"a2ae865453ecdd3b559e3c4087f5e7bd3eb4933dc92f09fd750b06827aadbd49","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-03-31T09:31:15Z","title_canon_sha256":"a946ee5b5996938e079b10d2e949c03dde700a8e8efc2f561e91ecb03db018c7"},"schema_version":"1.0","source":{"id":"0803.4410","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0803.4410","created_at":"2026-07-04T15:10:31Z"},{"alias_kind":"arxiv_version","alias_value":"0803.4410v1","created_at":"2026-07-04T15:10:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0803.4410","created_at":"2026-07-04T15:10:31Z"},{"alias_kind":"pith_short_12","alias_value":"Q3N7RL5PEEG7","created_at":"2026-07-04T15:10:31Z"},{"alias_kind":"pith_short_16","alias_value":"Q3N7RL5PEEG72IVW","created_at":"2026-07-04T15:10:31Z"},{"alias_kind":"pith_short_8","alias_value":"Q3N7RL5P","created_at":"2026-07-04T15:10:31Z"}],"graph_snapshots":[{"event_id":"sha256:51207264120d661a3c8f4f3e5d54f454801c992a278ca261d6a3a981c7c2f52f","target":"graph","created_at":"2026-07-04T15:10:31Z","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/0803.4410/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study some factorisation and dilation properties of completely positive maps on noncommutative L^p-spaces. We show that Akcoglu's dilation theorem for positive contractions on classical (=commutative) L^p-spaces has no reasonable analog in the noncommutative setting. Our study relies on non symmetric analogs of Pisier's operator space valued noncommutative L^p-spaces that we investigate in the first part of the paper.","authors_text":"Christian Le Merdy, Marius Junge","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-03-31T09:31:15Z","title":"Dilations and rigid factorisations on noncommutative L^p-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0803.4410","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:ba6602cc1c42ba08bb378aa966810b547430acbb8dc1614da9a2048268edd757","target":"record","created_at":"2026-07-04T15:10:31Z","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":"a2ae865453ecdd3b559e3c4087f5e7bd3eb4933dc92f09fd750b06827aadbd49","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2008-03-31T09:31:15Z","title_canon_sha256":"a946ee5b5996938e079b10d2e949c03dde700a8e8efc2f561e91ecb03db018c7"},"schema_version":"1.0","source":{"id":"0803.4410","kind":"arxiv","version":1}},"canonical_sha256":"86dbf8afaf210dfd22b6b230b46ccc46a59f5f1302c45f872353fc6e5c1cdf7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86dbf8afaf210dfd22b6b230b46ccc46a59f5f1302c45f872353fc6e5c1cdf7e","first_computed_at":"2026-07-04T15:10:31.709690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:10:31.709690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CIgz6B7w6ZRd+QJJcUCd34SBYTPHtNrn29G6/kojNFdJqNSUqP55vV4RkwLRqSmiSVPiM3mnOcve+zUueXQZBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:10:31.710410Z","signed_message":"canonical_sha256_bytes"},"source_id":"0803.4410","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba6602cc1c42ba08bb378aa966810b547430acbb8dc1614da9a2048268edd757","sha256:51207264120d661a3c8f4f3e5d54f454801c992a278ca261d6a3a981c7c2f52f"],"state_sha256":"a4136168f86c234f297e2fe08fdc8fef5744e75122f946b09dacbdc5349a2303"}