{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:BMRTFGGDRA6KCM3AJTIGSK2XKD","short_pith_number":"pith:BMRTFGGD","canonical_record":{"source":{"id":"1010.5302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-26T02:30:07Z","cross_cats_sorted":[],"title_canon_sha256":"e4ecd347e5744670c41bc6d1095eb2fe8b8351c78e9648a725ca3ffecf1fb92b","abstract_canon_sha256":"7493e503c9e8a0df57245b05aafa6ea6965129c191ff79dcd77814a342963ecf"},"schema_version":"1.0"},"canonical_sha256":"0b233298c3883ca133604cd0692b5750d2a1764217ca858bacf431f949769887","source":{"kind":"arxiv","id":"1010.5302","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5302","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5302v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5302","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"BMRTFGGDRA6K","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BMRTFGGDRA6KCM3A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BMRTFGGD","created_at":"2026-05-18T12:26:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:BMRTFGGDRA6KCM3AJTIGSK2XKD","target":"record","payload":{"canonical_record":{"source":{"id":"1010.5302","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-26T02:30:07Z","cross_cats_sorted":[],"title_canon_sha256":"e4ecd347e5744670c41bc6d1095eb2fe8b8351c78e9648a725ca3ffecf1fb92b","abstract_canon_sha256":"7493e503c9e8a0df57245b05aafa6ea6965129c191ff79dcd77814a342963ecf"},"schema_version":"1.0"},"canonical_sha256":"0b233298c3883ca133604cd0692b5750d2a1764217ca858bacf431f949769887","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:04:58.483139Z","signature_b64":"077uzuNlWpU9dwmHdYewb5qlj3hGyMhrStKDX5MxB5bF9iKxPVlJ9Dxu2B6t7JhhoYfhqWvncRgI0guDSeaWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b233298c3883ca133604cd0692b5750d2a1764217ca858bacf431f949769887","last_reissued_at":"2026-05-18T02:04:58.482305Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:04:58.482305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.5302","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QoyIQbVFRKrr33MJmWOvzBaOSrVHElVArkCSwsyZsRDws8QfG6R+K2RW+pCZLzefxmvZW9Wf6++aJKW8fk+UBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:20:08.121297Z"},"content_sha256":"7a3c8e27565b76e010bd2b7dbdf0c8e101c75777748951523f1b421d9125ec20","schema_version":"1.0","event_id":"sha256:7a3c8e27565b76e010bd2b7dbdf0c8e101c75777748951523f1b421d9125ec20"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:BMRTFGGDRA6KCM3AJTIGSK2XKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nontrivial eigenvalues of the Liouvillian of an open quantum system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Naomichi Hatano, Ruri Nakano, Tomio Petrosky","submitted_at":"2010-10-26T02:30:07Z","abstract_excerpt":"We present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5302","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":"2026-05-18T02:04:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zjMrngCK1MefZkC1jZnyHLN08Dfy7vlThc9RD/GCriPQWHhm4tnwYOXB9tWdYd9wpNehu6y76FrbP5mNah4VAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T12:20:08.121671Z"},"content_sha256":"ca92cf6e8c872d5ae04e60c25a9b45b67a347688f0fff856f5b5e38776e60247","schema_version":"1.0","event_id":"sha256:ca92cf6e8c872d5ae04e60c25a9b45b67a347688f0fff856f5b5e38776e60247"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/bundle.json","state_url":"https://pith.science/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/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":"2026-07-01T12:20:08Z","links":{"resolver":"https://pith.science/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD","bundle":"https://pith.science/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/bundle.json","state":"https://pith.science/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BMRTFGGDRA6KCM3AJTIGSK2XKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:BMRTFGGDRA6KCM3AJTIGSK2XKD","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":"7493e503c9e8a0df57245b05aafa6ea6965129c191ff79dcd77814a342963ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-26T02:30:07Z","title_canon_sha256":"e4ecd347e5744670c41bc6d1095eb2fe8b8351c78e9648a725ca3ffecf1fb92b"},"schema_version":"1.0","source":{"id":"1010.5302","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.5302","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"arxiv_version","alias_value":"1010.5302v1","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.5302","created_at":"2026-05-18T02:04:58Z"},{"alias_kind":"pith_short_12","alias_value":"BMRTFGGDRA6K","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_16","alias_value":"BMRTFGGDRA6KCM3A","created_at":"2026-05-18T12:26:05Z"},{"alias_kind":"pith_short_8","alias_value":"BMRTFGGD","created_at":"2026-05-18T12:26:05Z"}],"graph_snapshots":[{"event_id":"sha256:ca92cf6e8c872d5ae04e60c25a9b45b67a347688f0fff856f5b5e38776e60247","target":"graph","created_at":"2026-05-18T02:04:58Z","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 present methods of finding complex eigenvalues of the Liouvillian of an open quantum system. The goal is to find eigenvalues that cannot be predicted from the eigenvalues of the corresponding Hamiltonian. Our model is a T-type quantum dot with an infinitely long lead. We suggest the existence of the non-trivial eigenvalues of the Liouvillian in two ways: one way is to show that the original problem reduces to the problem of a two-particle Hamiltonian with a two-body interaction and the other way is to show that diagram expansion of the Green's function has correlation between the bra state ","authors_text":"Naomichi Hatano, Ruri Nakano, Tomio Petrosky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-26T02:30:07Z","title":"Nontrivial eigenvalues of the Liouvillian of an open quantum system"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.5302","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":"sha256:7a3c8e27565b76e010bd2b7dbdf0c8e101c75777748951523f1b421d9125ec20","target":"record","created_at":"2026-05-18T02:04:58Z","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":"7493e503c9e8a0df57245b05aafa6ea6965129c191ff79dcd77814a342963ecf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-10-26T02:30:07Z","title_canon_sha256":"e4ecd347e5744670c41bc6d1095eb2fe8b8351c78e9648a725ca3ffecf1fb92b"},"schema_version":"1.0","source":{"id":"1010.5302","kind":"arxiv","version":1}},"canonical_sha256":"0b233298c3883ca133604cd0692b5750d2a1764217ca858bacf431f949769887","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0b233298c3883ca133604cd0692b5750d2a1764217ca858bacf431f949769887","first_computed_at":"2026-05-18T02:04:58.482305Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:04:58.482305Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"077uzuNlWpU9dwmHdYewb5qlj3hGyMhrStKDX5MxB5bF9iKxPVlJ9Dxu2B6t7JhhoYfhqWvncRgI0guDSeaWCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:04:58.483139Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.5302","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a3c8e27565b76e010bd2b7dbdf0c8e101c75777748951523f1b421d9125ec20","sha256:ca92cf6e8c872d5ae04e60c25a9b45b67a347688f0fff856f5b5e38776e60247"],"state_sha256":"f188364a2a22171abf6621a8c40f727970d3f84461d5e199cb3852936ef1d967"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4nJS2iGcJbk2R/88mv6wWx4ZNli05+229tq/uzn371DJlKtfWD6oUw3P8gs5dIielNnyGN9vOPRxfUpg8r0xAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T12:20:08.123672Z","bundle_sha256":"6ad8965850e45203b2d1df626a33ec0d475980ea09352dca6d431b65c6cec857"}}