{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:QJAMH7ORPNIPYF4BDLN6MPXXZT","short_pith_number":"pith:QJAMH7OR","canonical_record":{"source":{"id":"2506.00346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-05-31T02:15:00Z","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"title_canon_sha256":"8787c44d0ef14a5aa90e663b2ef4f2d1af768530fb1ad109ff018a32d24cd20d","abstract_canon_sha256":"3df042078c3d14c253d06c1c050cbb960ee459a3309e8c0629bd10200102203e"},"schema_version":"1.0"},"canonical_sha256":"8240c3fdd17b50fc17811adbe63ef7ccd92207ecd6bef415f88d9e050155f795","source":{"kind":"arxiv","id":"2506.00346","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00346","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00346v1","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00346","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"QJAMH7ORPNIP","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"QJAMH7ORPNIPYF4B","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"QJAMH7OR","created_at":"2026-07-05T11:13:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:QJAMH7ORPNIPYF4BDLN6MPXXZT","target":"record","payload":{"canonical_record":{"source":{"id":"2506.00346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-05-31T02:15:00Z","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"title_canon_sha256":"8787c44d0ef14a5aa90e663b2ef4f2d1af768530fb1ad109ff018a32d24cd20d","abstract_canon_sha256":"3df042078c3d14c253d06c1c050cbb960ee459a3309e8c0629bd10200102203e"},"schema_version":"1.0"},"canonical_sha256":"8240c3fdd17b50fc17811adbe63ef7ccd92207ecd6bef415f88d9e050155f795","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:13:32.995374Z","signature_b64":"Kuw5JInkcwTuHqIRO4ZZfNZ8EPTAMxjH7tFVKh2SiOEJ975Y8h7B6laxbTj0PeW9MuqIdLMPaI8YP5rnSUIaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8240c3fdd17b50fc17811adbe63ef7ccd92207ecd6bef415f88d9e050155f795","last_reissued_at":"2026-07-05T11:13:32.994908Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:13:32.994908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.00346","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":"2026-07-05T11:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X7uGVrRogJf7vbgvHhbeq1hhgDwhNAozTgo/ejExEs2nlB/oqHmaFqgcPuurvT3IJrlseYVIgDhYaJQCY3gSDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:46:33.002384Z"},"content_sha256":"fc35e1459a0af994c58b1223f25c1cf26a93b55e114f019c7ce57b6981e5787c","schema_version":"1.0","event_id":"sha256:fc35e1459a0af994c58b1223f25c1cf26a93b55e114f019c7ce57b6981e5787c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:QJAMH7ORPNIPYF4BDLN6MPXXZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full- and low-rank exponential midpoint schemes for forward and adjoint Lindblad equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA","math.OC"],"primary_cat":"quant-ph","authors_text":"Alfio Borzi, Hao Chen","submitted_at":"2025-05-31T02:15:00Z","abstract_excerpt":"The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. This equation is also a fundamental building block to design optimal control functions. In this paper we develop full- and low-rank exponential midpoint integrators for solving both the forward and adjoint Lindblad equations. These schemes are applicable to optimize-then-discretize approaches for optimal control of open quantum systems. We show that the proposed schemes preserve positivity and trace unconditionally. Furthermore,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00346","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.00346/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:13:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z+V3zzc8nnpjboG7SfKdtZAgP8q618wcIeyBGW78kZxnADuplIUgOTjH9irgeWpn1xJoJUcvsLliEhi6kTitAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T04:46:33.002906Z"},"content_sha256":"dd3238447477fca8065310bda57895d5d1614058a3a00220ddf348636f8680de","schema_version":"1.0","event_id":"sha256:dd3238447477fca8065310bda57895d5d1614058a3a00220ddf348636f8680de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/bundle.json","state_url":"https://pith.science/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/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":"2026-08-08T04:46:33Z","links":{"resolver":"https://pith.science/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT","bundle":"https://pith.science/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/bundle.json","state":"https://pith.science/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QJAMH7ORPNIPYF4BDLN6MPXXZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:QJAMH7ORPNIPYF4BDLN6MPXXZT","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":"3df042078c3d14c253d06c1c050cbb960ee459a3309e8c0629bd10200102203e","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-05-31T02:15:00Z","title_canon_sha256":"8787c44d0ef14a5aa90e663b2ef4f2d1af768530fb1ad109ff018a32d24cd20d"},"schema_version":"1.0","source":{"id":"2506.00346","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.00346","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"arxiv_version","alias_value":"2506.00346v1","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.00346","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_12","alias_value":"QJAMH7ORPNIP","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_16","alias_value":"QJAMH7ORPNIPYF4B","created_at":"2026-07-05T11:13:32Z"},{"alias_kind":"pith_short_8","alias_value":"QJAMH7OR","created_at":"2026-07-05T11:13:32Z"}],"graph_snapshots":[{"event_id":"sha256:dd3238447477fca8065310bda57895d5d1614058a3a00220ddf348636f8680de","target":"graph","created_at":"2026-07-05T11:13:32Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.00346/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Lindblad equation is a widely used quantum master equation to model the dynamical evolution of open quantum systems whose states are described by density matrices. This equation is also a fundamental building block to design optimal control functions. In this paper we develop full- and low-rank exponential midpoint integrators for solving both the forward and adjoint Lindblad equations. These schemes are applicable to optimize-then-discretize approaches for optimal control of open quantum systems. We show that the proposed schemes preserve positivity and trace unconditionally. Furthermore,","authors_text":"Alfio Borzi, Hao Chen","cross_cats":["cs.NA","math.NA","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-05-31T02:15:00Z","title":"Full- and low-rank exponential midpoint schemes for forward and adjoint Lindblad equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00346","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:fc35e1459a0af994c58b1223f25c1cf26a93b55e114f019c7ce57b6981e5787c","target":"record","created_at":"2026-07-05T11:13:32Z","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":"3df042078c3d14c253d06c1c050cbb960ee459a3309e8c0629bd10200102203e","cross_cats_sorted":["cs.NA","math.NA","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-05-31T02:15:00Z","title_canon_sha256":"8787c44d0ef14a5aa90e663b2ef4f2d1af768530fb1ad109ff018a32d24cd20d"},"schema_version":"1.0","source":{"id":"2506.00346","kind":"arxiv","version":1}},"canonical_sha256":"8240c3fdd17b50fc17811adbe63ef7ccd92207ecd6bef415f88d9e050155f795","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8240c3fdd17b50fc17811adbe63ef7ccd92207ecd6bef415f88d9e050155f795","first_computed_at":"2026-07-05T11:13:32.994908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:13:32.994908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Kuw5JInkcwTuHqIRO4ZZfNZ8EPTAMxjH7tFVKh2SiOEJ975Y8h7B6laxbTj0PeW9MuqIdLMPaI8YP5rnSUIaAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:13:32.995374Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.00346","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc35e1459a0af994c58b1223f25c1cf26a93b55e114f019c7ce57b6981e5787c","sha256:dd3238447477fca8065310bda57895d5d1614058a3a00220ddf348636f8680de"],"state_sha256":"5a7d2914fc5faaf9f822abb6bdb06a57b8aa7dd45cb311c78bc492d02f817449"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zzqPG9Sh1Db0h1cjXrWfGUnv5ZXfMwGSGu3xjRBwL+5vink6iqOthxE4+TghCjpK30wkCP515bQOfSMuapI0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T04:46:33.006288Z","bundle_sha256":"baa18c1a45141453bfd5eb0c1e74e097530ccf1140d78493e0dde5acdfef51b2"}}