{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:P6DNA4IQ44OM7BFR6XFKZ7RRJB","short_pith_number":"pith:P6DNA4IQ","canonical_record":{"source":{"id":"1608.05317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-18T16:16:03Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"title_canon_sha256":"bf171dc348e127e213cedb9dde961b42b37ff05b80caac3ce26ac4534b661132","abstract_canon_sha256":"95563afaa89a211354d0c25b6b0bb547fd3c9ebf47514597037e1164ca1778a6"},"schema_version":"1.0"},"canonical_sha256":"7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b","source":{"kind":"arxiv","id":"1608.05317","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05317","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05317v2","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05317","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"P6DNA4IQ44OM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P6DNA4IQ44OM7BFR","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P6DNA4IQ","created_at":"2026-05-18T12:30:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:P6DNA4IQ44OM7BFR6XFKZ7RRJB","target":"record","payload":{"canonical_record":{"source":{"id":"1608.05317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-18T16:16:03Z","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"title_canon_sha256":"bf171dc348e127e213cedb9dde961b42b37ff05b80caac3ce26ac4534b661132","abstract_canon_sha256":"95563afaa89a211354d0c25b6b0bb547fd3c9ebf47514597037e1164ca1778a6"},"schema_version":"1.0"},"canonical_sha256":"7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:42.636755Z","signature_b64":"dJm41KMdu2ZQ2a6DTq6Mi23iK686qPQ18y5/ZzA59eL4cYmPTgCvNgdAyYI5AmQDxDCHfqjrsbJTh0V7LFjvCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b","last_reissued_at":"2026-05-17T23:58:42.636070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:42.636070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.05317","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":"2026-05-17T23:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"882b7bV+FGSPE+DbpSI4qr5ok74cFjovkqgRi3LzmibsDfQiERvGvVhH4GA7NveNRAg+g3glTZ6PC0KAbykHBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T20:08:00.775170Z"},"content_sha256":"640e5fe3a759b24c905b17735ba94d12baa2c97bbc04b6bf96886e84af1b0889","schema_version":"1.0","event_id":"sha256:640e5fe3a759b24c905b17735ba94d12baa2c97bbc04b6bf96886e84af1b0889"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:P6DNA4IQ44OM7BFR6XFKZ7RRJB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"R\\'enyi divergences as weighted non-commutative vector valued $L_p$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"primary_cat":"math-ph","authors_text":"Marco Tomamichel, Mario Berta, Volkher B. Scholz","submitted_at":"2016-08-18T16:16:03Z","abstract_excerpt":"We show that Araki and Masuda's weighted non-commutative vector valued $L_p$-spaces [Araki \\& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched R\\'enyi divergences with parameter $\\alpha = \\frac{p}{2}$. Using complex interpolation theory, we prove various fundamental properties of these divergences in the setup of von Neumann algebras, including a data-processing inequality and monotonicity in $\\alpha$. We thereby also give new proofs for the corresponding finite-dimensional properties. We discuss the limiting cases $\\alpha\\to \\{\\fr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05317","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":"2026-05-17T23:58:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EyWiOheML424QTCWYxhz/RLSY6d2z1yxKOjI34eExkc/1QDJZ8kBJhPKJIKbQ12WOkTi1Qwev0kLIlOnC6vDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T20:08:00.775855Z"},"content_sha256":"4de85f3e84757482df6a7739c404a4ef0ca60f649891c74121568570c0dae52d","schema_version":"1.0","event_id":"sha256:4de85f3e84757482df6a7739c404a4ef0ca60f649891c74121568570c0dae52d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/bundle.json","state_url":"https://pith.science/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/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":"2026-05-20T20:08:00Z","links":{"resolver":"https://pith.science/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB","bundle":"https://pith.science/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/bundle.json","state":"https://pith.science/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P6DNA4IQ44OM7BFR6XFKZ7RRJB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:P6DNA4IQ44OM7BFR6XFKZ7RRJB","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":"95563afaa89a211354d0c25b6b0bb547fd3c9ebf47514597037e1164ca1778a6","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-18T16:16:03Z","title_canon_sha256":"bf171dc348e127e213cedb9dde961b42b37ff05b80caac3ce26ac4534b661132"},"schema_version":"1.0","source":{"id":"1608.05317","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.05317","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"arxiv_version","alias_value":"1608.05317v2","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.05317","created_at":"2026-05-17T23:58:42Z"},{"alias_kind":"pith_short_12","alias_value":"P6DNA4IQ44OM","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"P6DNA4IQ44OM7BFR","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"P6DNA4IQ","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:4de85f3e84757482df6a7739c404a4ef0ca60f649891c74121568570c0dae52d","target":"graph","created_at":"2026-05-17T23:58:42Z","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":"We show that Araki and Masuda's weighted non-commutative vector valued $L_p$-spaces [Araki \\& Masuda, Publ. Res. Inst. Math. Sci., 18:339 (1982)] correspond to an algebraic generalization of the sandwiched R\\'enyi divergences with parameter $\\alpha = \\frac{p}{2}$. Using complex interpolation theory, we prove various fundamental properties of these divergences in the setup of von Neumann algebras, including a data-processing inequality and monotonicity in $\\alpha$. We thereby also give new proofs for the corresponding finite-dimensional properties. We discuss the limiting cases $\\alpha\\to \\{\\fr","authors_text":"Marco Tomamichel, Mario Berta, Volkher B. Scholz","cross_cats":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-18T16:16:03Z","title":"R\\'enyi divergences as weighted non-commutative vector valued $L_p$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.05317","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":"sha256:640e5fe3a759b24c905b17735ba94d12baa2c97bbc04b6bf96886e84af1b0889","target":"record","created_at":"2026-05-17T23:58:42Z","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":"95563afaa89a211354d0c25b6b0bb547fd3c9ebf47514597037e1164ca1778a6","cross_cats_sorted":["cs.IT","math.IT","math.MP","math.OA","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-08-18T16:16:03Z","title_canon_sha256":"bf171dc348e127e213cedb9dde961b42b37ff05b80caac3ce26ac4534b661132"},"schema_version":"1.0","source":{"id":"1608.05317","kind":"arxiv","version":2}},"canonical_sha256":"7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f86d07110e71ccf84b1f5caacfe31487fa19fc8b13f46afe0b096dd67da947b","first_computed_at":"2026-05-17T23:58:42.636070Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:42.636070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dJm41KMdu2ZQ2a6DTq6Mi23iK686qPQ18y5/ZzA59eL4cYmPTgCvNgdAyYI5AmQDxDCHfqjrsbJTh0V7LFjvCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:42.636755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.05317","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:640e5fe3a759b24c905b17735ba94d12baa2c97bbc04b6bf96886e84af1b0889","sha256:4de85f3e84757482df6a7739c404a4ef0ca60f649891c74121568570c0dae52d"],"state_sha256":"c90f50f25a08c3c2384317b569df5379fc7e29a33bf6aa8b288907e44e43197d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e3ANENMd1RLjowVzHhsmgCboi29CHu2mXM3tmhFlYouvxWRbcyZ3aFV9Q+GT8hrucobG4kO+ZY3+tYvprQE2Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T20:08:00.780171Z","bundle_sha256":"4d5d2036456ee4c52757f6055ad7df11f3133bb3611f25e744e3b9289c480c8a"}}