{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:HXPWVMGHYB6HV4WCIS66VW2MYZ","short_pith_number":"pith:HXPWVMGH","canonical_record":{"source":{"id":"1810.00906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T18:21:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0524c10788956ce01f856bdd679397f2afda0909776cc90ee2bd952354c36d7c","abstract_canon_sha256":"ce58f6ec8d74a7fc95fe4d074999428d49db54330f02893c3bc608ece4e631f0"},"schema_version":"1.0"},"canonical_sha256":"3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811","source":{"kind":"arxiv","id":"1810.00906","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00906","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00906v2","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00906","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"HXPWVMGHYB6H","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HXPWVMGHYB6HV4WC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HXPWVMGH","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:HXPWVMGHYB6HV4WCIS66VW2MYZ","target":"record","payload":{"canonical_record":{"source":{"id":"1810.00906","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T18:21:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0524c10788956ce01f856bdd679397f2afda0909776cc90ee2bd952354c36d7c","abstract_canon_sha256":"ce58f6ec8d74a7fc95fe4d074999428d49db54330f02893c3bc608ece4e631f0"},"schema_version":"1.0"},"canonical_sha256":"3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:04.426215Z","signature_b64":"NjySzy7z1Vo3Wgc8TQzWCXOTfVYns1cPP0YKE7P+vbCxMQHx7MVlRKJ7sAfB9+ZlDAM0BlnGHRsIADw8RXQuCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811","last_reissued_at":"2026-05-17T23:45:04.425645Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:04.425645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.00906","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M81bbfCcPPv6/Cd3j3uwl60d/dk+738zWrotfWMYArZ+0F6zRQREkxAlDgB0V9CIEvJPJ1PWbsY+xBs7xyLrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:53:27.679095Z"},"content_sha256":"1fd97746b3f6920e95a44379c165b53e400c8bf9337ce85ad0b96dfd218bb765","schema_version":"1.0","event_id":"sha256:1fd97746b3f6920e95a44379c165b53e400c8bf9337ce85ad0b96dfd218bb765"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:HXPWVMGHYB6HV4WCIS66VW2MYZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gradient flow structure and exponential decay of the sandwiched R\\'enyi divergence for primitive Lindblad equations with GNS-detailed balance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.FA","authors_text":"Jianfeng Lu, Yu Cao, Yulong Lu","submitted_at":"2018-10-01T18:21:02Z","abstract_excerpt":"We study the entropy production of the sandwiched R\\'enyi divergence under the primitive Lindblad equation with GNS-detailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$. This extends a previous result by Carlen and Maas [Journal of Functional Analysis, 273(5), 1810-1869] for the quantum relative entropy (i.e., ${\\alpha} = 1$). Moreover, we show that the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$ decays exponentially fast under the time-evolution of suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00906","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":"2026-05-17T23:45:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4BwGof/QZ1WMyEa1fLAJS+wE4myNyRXqXU9SW0AvVI60gl8qAjA9er2lieB2iI3jAvazymB+AoE5hGvKO7WmCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T18:53:27.679805Z"},"content_sha256":"d6bb94beea866f977ace7a3db2c7710c66645ecefa98df711dc5c6df794f5232","schema_version":"1.0","event_id":"sha256:d6bb94beea866f977ace7a3db2c7710c66645ecefa98df711dc5c6df794f5232"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/bundle.json","state_url":"https://pith.science/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/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":"2026-05-25T18:53:27Z","links":{"resolver":"https://pith.science/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ","bundle":"https://pith.science/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/bundle.json","state":"https://pith.science/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HXPWVMGHYB6HV4WCIS66VW2MYZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:HXPWVMGHYB6HV4WCIS66VW2MYZ","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":"ce58f6ec8d74a7fc95fe4d074999428d49db54330f02893c3bc608ece4e631f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T18:21:02Z","title_canon_sha256":"0524c10788956ce01f856bdd679397f2afda0909776cc90ee2bd952354c36d7c"},"schema_version":"1.0","source":{"id":"1810.00906","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00906","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00906v2","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00906","created_at":"2026-05-17T23:45:04Z"},{"alias_kind":"pith_short_12","alias_value":"HXPWVMGHYB6H","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"HXPWVMGHYB6HV4WC","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"HXPWVMGH","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:d6bb94beea866f977ace7a3db2c7710c66645ecefa98df711dc5c6df794f5232","target":"graph","created_at":"2026-05-17T23:45:04Z","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 study the entropy production of the sandwiched R\\'enyi divergence under the primitive Lindblad equation with GNS-detailed balance. We prove that the Lindblad equation can be identified as the gradient flow of the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$. This extends a previous result by Carlen and Maas [Journal of Functional Analysis, 273(5), 1810-1869] for the quantum relative entropy (i.e., ${\\alpha} = 1$). Moreover, we show that the sandwiched R\\'enyi divergence of any order ${\\alpha} \\in (0, \\infty)$ decays exponentially fast under the time-evolution of suc","authors_text":"Jianfeng Lu, Yu Cao, Yulong Lu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T18:21:02Z","title":"Gradient flow structure and exponential decay of the sandwiched R\\'enyi divergence for primitive Lindblad equations with GNS-detailed balance"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00906","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":"sha256:1fd97746b3f6920e95a44379c165b53e400c8bf9337ce85ad0b96dfd218bb765","target":"record","created_at":"2026-05-17T23:45:04Z","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":"ce58f6ec8d74a7fc95fe4d074999428d49db54330f02893c3bc608ece4e631f0","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-10-01T18:21:02Z","title_canon_sha256":"0524c10788956ce01f856bdd679397f2afda0909776cc90ee2bd952354c36d7c"},"schema_version":"1.0","source":{"id":"1810.00906","kind":"arxiv","version":2}},"canonical_sha256":"3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddf6ab0c7c07c7af2c244bdeadb4cc66bef51f44d08821c39d9549ec5b42811","first_computed_at":"2026-05-17T23:45:04.425645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:04.425645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NjySzy7z1Vo3Wgc8TQzWCXOTfVYns1cPP0YKE7P+vbCxMQHx7MVlRKJ7sAfB9+ZlDAM0BlnGHRsIADw8RXQuCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:04.426215Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00906","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1fd97746b3f6920e95a44379c165b53e400c8bf9337ce85ad0b96dfd218bb765","sha256:d6bb94beea866f977ace7a3db2c7710c66645ecefa98df711dc5c6df794f5232"],"state_sha256":"a50ab5c21673786cb1ace4afd89c26337a0f885eedb25efd94fea5b6bb728df9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jYg/w2LvyUi4H5wCJEx76uY1LUboMD9RM4AYXq6YVU+bJYxubioLtPbZFdLaBnLDXnnib4b69yhC1pCXCf/2DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T18:53:27.683776Z","bundle_sha256":"16bd994df83222c37e68cf8d441467355dc182865ed01aa03dee13d5ea2babed"}}