{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CPPK4XCH35NKEXG4NHCC3RWGSL","short_pith_number":"pith:CPPK4XCH","schema_version":"1.0","canonical_sha256":"13deae5c47df5aa25cdc69c42dc6c692d56031f83800d92742bf8f64c58b8dcc","source":{"kind":"arxiv","id":"1707.00047","version":2},"attestation_state":"computed","paper":{"title":"R\\'enyi relative entropies and noncommutative $L_p$-spaces II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Anna Jen\\v{c}ov\\'a","submitted_at":"2017-06-30T21:27:17Z","abstract_excerpt":"We study an extension of the sandwiched R\\'enyi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $\\alpha\\in [1/2,1)$. This work is intended as a continuation of [A. Jen\\v{c}ov\\'a, Ann. Henri Poincar\\'e 19, 2513-2542, 2018], where the values $\\alpha>1$ were studied. We use the Araki-Masuda divergences of [Berta et al., Ann. Henri Poincar\\'e 9, 1843-1867, 2018] and treat them in the framework of Kosaki's noncommutative $L_p$-spaces. Using the variational formula, recently obtained by F. Hiai, for $\\alpha\\in [1/2,1)$, we prove the data processing i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1707.00047","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-06-30T21:27:17Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"37def7cc8f11ea131fd5a4b50e9c1fc67cacf322f2f6138bb181d096edc4473b","abstract_canon_sha256":"59a1f04c4aa25f9507e4a3d9fa4ebb4a7739c74478c6af400d3a671bdca9cc32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:29:12.290101Z","signature_b64":"Ek+dpRaByCdNi4KG2wxM3Y1QSiHpooTmNww8QeZzOzg/f+p3/74YUoeP22Fb18twtQExuxR5Pk5A573mvIxOBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13deae5c47df5aa25cdc69c42dc6c692d56031f83800d92742bf8f64c58b8dcc","last_reissued_at":"2026-07-05T03:29:12.289587Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:29:12.289587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"R\\'enyi relative entropies and noncommutative $L_p$-spaces II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"quant-ph","authors_text":"Anna Jen\\v{c}ov\\'a","submitted_at":"2017-06-30T21:27:17Z","abstract_excerpt":"We study an extension of the sandwiched R\\'enyi relative entropies for normal positive functionals on a von Neumann algebra, for parameter values $\\alpha\\in [1/2,1)$. This work is intended as a continuation of [A. Jen\\v{c}ov\\'a, Ann. Henri Poincar\\'e 19, 2513-2542, 2018], where the values $\\alpha>1$ were studied. We use the Araki-Masuda divergences of [Berta et al., Ann. Henri Poincar\\'e 9, 1843-1867, 2018] and treat them in the framework of Kosaki's noncommutative $L_p$-spaces. Using the variational formula, recently obtained by F. Hiai, for $\\alpha\\in [1/2,1)$, we prove the data processing i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.00047","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/1707.00047/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1707.00047","created_at":"2026-07-05T03:29:12.289650+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.00047v2","created_at":"2026-07-05T03:29:12.289650+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.00047","created_at":"2026-07-05T03:29:12.289650+00:00"},{"alias_kind":"pith_short_12","alias_value":"CPPK4XCH35NK","created_at":"2026-07-05T03:29:12.289650+00:00"},{"alias_kind":"pith_short_16","alias_value":"CPPK4XCH35NKEXG4","created_at":"2026-07-05T03:29:12.289650+00:00"},{"alias_kind":"pith_short_8","alias_value":"CPPK4XCH","created_at":"2026-07-05T03:29:12.289650+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":4,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2607.07799","citing_title":"No off-diagonal quantum focusing for R\\'enyi divergences","ref_index":19,"is_internal_anchor":true},{"citing_arxiv_id":"2607.08760","citing_title":"Hockey stick $f$-divergences","ref_index":26,"is_internal_anchor":true},{"citing_arxiv_id":"2605.15272","citing_title":"A general proof of integer R\\'enyi QNEC","ref_index":29,"is_internal_anchor":false},{"citing_arxiv_id":"2604.18383","citing_title":"Bounding relative entropy for non-unitary excitations in quantum field theory","ref_index":12,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL","json":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL.json","graph_json":"https://pith.science/api/pith-number/CPPK4XCH35NKEXG4NHCC3RWGSL/graph.json","events_json":"https://pith.science/api/pith-number/CPPK4XCH35NKEXG4NHCC3RWGSL/events.json","paper":"https://pith.science/paper/CPPK4XCH"},"agent_actions":{"view_html":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL","download_json":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL.json","view_paper":"https://pith.science/paper/CPPK4XCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.00047&json=true","fetch_graph":"https://pith.science/api/pith-number/CPPK4XCH35NKEXG4NHCC3RWGSL/graph.json","fetch_events":"https://pith.science/api/pith-number/CPPK4XCH35NKEXG4NHCC3RWGSL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL/action/storage_attestation","attest_author":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL/action/author_attestation","sign_citation":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL/action/citation_signature","submit_replication":"https://pith.science/pith/CPPK4XCH35NKEXG4NHCC3RWGSL/action/replication_record"}},"created_at":"2026-07-05T03:29:12.289650+00:00","updated_at":"2026-07-05T03:29:12.289650+00:00"}