{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:XAHSAOHYMK3Y74Z5BUGC65VGML","short_pith_number":"pith:XAHSAOHY","canonical_record":{"source":{"id":"1906.10412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-25T09:33:49Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"edd970338ddd788b35485ee2c9e6993d3aa92d63032eaeb87bd8dc83f9e8cebe","abstract_canon_sha256":"f724acc02f854ca9a4c601bdb9f19fc29c408c8a3828d6157e295e9a98428aed"},"schema_version":"1.0"},"canonical_sha256":"b80f2038f862b78ff33d0d0c2f76a662c1e7b7c226d1db962f9a34da48cf9aff","source":{"kind":"arxiv","id":"1906.10412","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10412","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10412v1","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10412","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"XAHSAOHYMK3Y","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XAHSAOHYMK3Y74Z5","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XAHSAOHY","created_at":"2026-05-18T12:33:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:XAHSAOHYMK3Y74Z5BUGC65VGML","target":"record","payload":{"canonical_record":{"source":{"id":"1906.10412","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-25T09:33:49Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"edd970338ddd788b35485ee2c9e6993d3aa92d63032eaeb87bd8dc83f9e8cebe","abstract_canon_sha256":"f724acc02f854ca9a4c601bdb9f19fc29c408c8a3828d6157e295e9a98428aed"},"schema_version":"1.0"},"canonical_sha256":"b80f2038f862b78ff33d0d0c2f76a662c1e7b7c226d1db962f9a34da48cf9aff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:42:18.118917Z","signature_b64":"BVhmYzOBR7BhPaCfaH9A1W0CloarS3u88jCHKTd6IxI4sByM6fDQUb0lFcIzx4DUqsxSyIIaEZYTpkGOrxqECw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b80f2038f862b78ff33d0d0c2f76a662c1e7b7c226d1db962f9a34da48cf9aff","last_reissued_at":"2026-05-17T23:42:18.118559Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:42:18.118559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.10412","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CkszltBPxiDdZISbminMq282vh/8QIR1BoLeKsmnpRlCtr4aJXgxbAUiYnhnSx+bxxEHnlQZWlf+yw7FkRVuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:30:52.761274Z"},"content_sha256":"f7ad9d28012ba8013e659dc46ba4f76b8b92e41303456a82615eac757a8f4a69","schema_version":"1.0","event_id":"sha256:f7ad9d28012ba8013e659dc46ba4f76b8b92e41303456a82615eac757a8f4a69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:XAHSAOHYMK3Y74Z5BUGC65VGML","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum R\\'enyi relative entropies on density spaces of $C^*$-algebras: their symmetries and their essential difference","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Lajos Moln\\'ar","submitted_at":"2019-06-25T09:33:49Z","abstract_excerpt":"We extend the definitions of different types of quantum R\\'enyi relative entropy from the finite dimensional setting of density matrices to density spaces of $C^*$-algebras. We show that those quantities (which trivially coincide in the classical commutative case) are essentially different on non-commutative algebras in the sense that none of them can be transformed to another one by any surjective transformation between density spaces. Besides, we determine the symmetry groups of density spaces corresponding to each of those quantum R\\'enyi relative entropies and find that they are identical."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10412","kind":"arxiv","version":1},"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":"2026-05-17T23:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"84stAOGH3nEwChQW7KsohZ7O5za0zuM9D6hYR84NZNcA6e0ptZTZGsoY6o0Yuk6zvoYtQ4NiJdd4SF5LprhgAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T14:30:52.761716Z"},"content_sha256":"8019031ef36aa0a9d3474755ca015ab9ec600ac710f67216a608707b0c1a72b3","schema_version":"1.0","event_id":"sha256:8019031ef36aa0a9d3474755ca015ab9ec600ac710f67216a608707b0c1a72b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/bundle.json","state_url":"https://pith.science/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/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":"2026-05-30T14:30:52Z","links":{"resolver":"https://pith.science/pith/XAHSAOHYMK3Y74Z5BUGC65VGML","bundle":"https://pith.science/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/bundle.json","state":"https://pith.science/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XAHSAOHYMK3Y74Z5BUGC65VGML/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XAHSAOHYMK3Y74Z5BUGC65VGML","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":"f724acc02f854ca9a4c601bdb9f19fc29c408c8a3828d6157e295e9a98428aed","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-25T09:33:49Z","title_canon_sha256":"edd970338ddd788b35485ee2c9e6993d3aa92d63032eaeb87bd8dc83f9e8cebe"},"schema_version":"1.0","source":{"id":"1906.10412","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.10412","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1906.10412v1","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.10412","created_at":"2026-05-17T23:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"XAHSAOHYMK3Y","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XAHSAOHYMK3Y74Z5","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XAHSAOHY","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:8019031ef36aa0a9d3474755ca015ab9ec600ac710f67216a608707b0c1a72b3","target":"graph","created_at":"2026-05-17T23:42:18Z","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 extend the definitions of different types of quantum R\\'enyi relative entropy from the finite dimensional setting of density matrices to density spaces of $C^*$-algebras. We show that those quantities (which trivially coincide in the classical commutative case) are essentially different on non-commutative algebras in the sense that none of them can be transformed to another one by any surjective transformation between density spaces. Besides, we determine the symmetry groups of density spaces corresponding to each of those quantum R\\'enyi relative entropies and find that they are identical.","authors_text":"Lajos Moln\\'ar","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-25T09:33:49Z","title":"Quantum R\\'enyi relative entropies on density spaces of $C^*$-algebras: their symmetries and their essential difference"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.10412","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:f7ad9d28012ba8013e659dc46ba4f76b8b92e41303456a82615eac757a8f4a69","target":"record","created_at":"2026-05-17T23:42:18Z","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":"f724acc02f854ca9a4c601bdb9f19fc29c408c8a3828d6157e295e9a98428aed","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2019-06-25T09:33:49Z","title_canon_sha256":"edd970338ddd788b35485ee2c9e6993d3aa92d63032eaeb87bd8dc83f9e8cebe"},"schema_version":"1.0","source":{"id":"1906.10412","kind":"arxiv","version":1}},"canonical_sha256":"b80f2038f862b78ff33d0d0c2f76a662c1e7b7c226d1db962f9a34da48cf9aff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b80f2038f862b78ff33d0d0c2f76a662c1e7b7c226d1db962f9a34da48cf9aff","first_computed_at":"2026-05-17T23:42:18.118559Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:18.118559Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BVhmYzOBR7BhPaCfaH9A1W0CloarS3u88jCHKTd6IxI4sByM6fDQUb0lFcIzx4DUqsxSyIIaEZYTpkGOrxqECw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:18.118917Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.10412","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ad9d28012ba8013e659dc46ba4f76b8b92e41303456a82615eac757a8f4a69","sha256:8019031ef36aa0a9d3474755ca015ab9ec600ac710f67216a608707b0c1a72b3"],"state_sha256":"2c7fcb1abbe29326897b444a1c4bad7588b9bebcb94e0ffec254587b608957a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bn2ss7CiVtRb1l7eLR6kcMmrrkbNqbqjIGCdX/wORxWBTJD72NwPWpZJJgn38Oz7eb/HdFXi8hIMWMhdAYmrDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T14:30:52.764634Z","bundle_sha256":"bc46dfc705afaa2a5895e2d3cd84b6ceec8e572bc4c0c7091c3cc4ebca59b95b"}}