{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:2ASEGTRAV3LSJAXAWBNLALWV6R","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":"de6aaaf8ec5dafe98126a634b21ae3e5a94c438fab2dcd985ee280600bc093e0","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"1998-08-30T15:12:04Z","title_canon_sha256":"8307a7359b3a6d380b9c251476a51f9aeab402dd2716c638a733e6550969b079"},"schema_version":"1.0","source":{"id":"math-ph/9808016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/9808016","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/9808016v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/9808016","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"2ASEGTRAV3LS","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"2ASEGTRAV3LSJAXA","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"2ASEGTRA","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:c9b2d3ea80610d3f4a9be733eed8f97ba04691b54fa9f4af92efd83d3922bea4","target":"graph","created_at":"2026-05-18T01:38:30Z","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 use the relative modular operator to define a generalized relative entropy for any convex operator function g on the positive real line satisfying g(1) = 0. We show that these convex operator functions can be partitioned into convex subsets each of which defines a unique symmetrized relative entropy, a unique family (parameterized by density matrices) of continuous monotone Riemannian metrics, a unique geodesic distance on the space of density matrices, and a unique monotone operator function satisfying certain symmetry and normalization conditions. We describe these objects explicitly in s","authors_text":"Andrew Lesniewski, Mary Beth Ruskai","cross_cats":["math.MP","math.OA","quant-ph"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"1998-08-30T15:12:04Z","title":"Monotone Riemannian Metrics and Relative Entropy on Non-Commutative Probability Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9808016","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:a4c20f43f9b19ded0aa82fdd2b6d9f019a452bc5f841867481b93e293d1e2d44","target":"record","created_at":"2026-05-18T01:38:30Z","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":"de6aaaf8ec5dafe98126a634b21ae3e5a94c438fab2dcd985ee280600bc093e0","cross_cats_sorted":["math.MP","math.OA","quant-ph"],"license":"","primary_cat":"math-ph","submitted_at":"1998-08-30T15:12:04Z","title_canon_sha256":"8307a7359b3a6d380b9c251476a51f9aeab402dd2716c638a733e6550969b079"},"schema_version":"1.0","source":{"id":"math-ph/9808016","kind":"arxiv","version":1}},"canonical_sha256":"d024434e20aed72482e0b05ab02ed5f456e28cc341a8d3f9545148a065813257","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d024434e20aed72482e0b05ab02ed5f456e28cc341a8d3f9545148a065813257","first_computed_at":"2026-05-18T01:38:30.731712Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.731712Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sY/P/FG6Gfq25VkIGWyJkBNCrX5bqQdlY2o2vbLO/KDxofUabqWRiMMNX6yqMLCoXKBGfZWEGH2iCBPlFBxGAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.732261Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/9808016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4c20f43f9b19ded0aa82fdd2b6d9f019a452bc5f841867481b93e293d1e2d44","sha256:c9b2d3ea80610d3f4a9be733eed8f97ba04691b54fa9f4af92efd83d3922bea4"],"state_sha256":"5b20d9d41fabb99d218764eb35d46546e02bdcdfc0e28dd7c210f28c4703cf84"}