{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:WVYDRG3MBNQALY2ELTIRTR2Y3R","short_pith_number":"pith:WVYDRG3M","canonical_record":{"source":{"id":"1004.0740","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-06T00:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"35079a9c0e18153ef27633ff342204f993c774d9e9d3a9d2252954296cf1d8af","abstract_canon_sha256":"d8443eeae934cf94214ee38e56cd7b0430f0502eed04ce91c297808f5d3b8dfc"},"schema_version":"1.0"},"canonical_sha256":"b570389b6c0b6005e3445cd119c758dc6849e1e2580330d87e8bea1c3a532cb1","source":{"kind":"arxiv","id":"1004.0740","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0740","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0740v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0740","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"WVYDRG3MBNQA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WVYDRG3MBNQALY2E","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WVYDRG3M","created_at":"2026-05-18T12:26:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:WVYDRG3MBNQALY2ELTIRTR2Y3R","target":"record","payload":{"canonical_record":{"source":{"id":"1004.0740","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-06T00:04:50Z","cross_cats_sorted":[],"title_canon_sha256":"35079a9c0e18153ef27633ff342204f993c774d9e9d3a9d2252954296cf1d8af","abstract_canon_sha256":"d8443eeae934cf94214ee38e56cd7b0430f0502eed04ce91c297808f5d3b8dfc"},"schema_version":"1.0"},"canonical_sha256":"b570389b6c0b6005e3445cd119c758dc6849e1e2580330d87e8bea1c3a532cb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:54.469689Z","signature_b64":"Tl450sE93BJnnzEb2bCztOvSO+1a1i0MfhZCKYf0p+IIaaOptrF5SinPIXsOBF5/yAKnlx6atR2Q9371/J4/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b570389b6c0b6005e3445cd119c758dc6849e1e2580330d87e8bea1c3a532cb1","last_reissued_at":"2026-05-18T04:40:54.468987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:54.468987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1004.0740","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":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PUKOgcTXDljACAfTJDiYwPNwL/0D4MztwefNBgJTNguAcsmuK2L9OyRGIRQ72SrkE6p8RPrMiGDWSXdgqoYQDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:24:46.920878Z"},"content_sha256":"90abba1378476c9746ebcb7e26b0bc906b86f81f8d528bfaf958d3e9eebafe3d","schema_version":"1.0","event_id":"sha256:90abba1378476c9746ebcb7e26b0bc906b86f81f8d528bfaf958d3e9eebafe3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:WVYDRG3MBNQALY2ELTIRTR2Y3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-equilibrium BBGKY Hierarchy from the Redfield Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Jinshan Wu","submitted_at":"2010-04-06T00:04:50Z","abstract_excerpt":"A BBGKY-like hierarchy is derived from the non-equilibrium Redfield equation. Two further approximations are introduced and each can be used to truncate and solve the hierarchy. In the first approximation such a truncation is performed by replacing two-particle Green's functions (GFs) in the hierarchy by their values at equilibrium. The second method is developed based on the cluster expansion, which constructs two-particle GFs from one-particle GFs and neglects the correlation part. A non-equilibrium Wick's Theorem is proved to provide a basis for this non-equilibrium cluster expansion. Using"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0740","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":"2026-05-18T04:40:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GWBkjzfgKGLB5upjLTdvwac2KbPtXJhvr6hfYxnz1HncqiW7rV5pCcypNjya4TnX+PmnhGdjxONjpjYw+l3PDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:24:46.921222Z"},"content_sha256":"ce8cba7fc52f93ffdd95edc313892cc63d1f3fa1b6368ef7e85d93e13e67a5d8","schema_version":"1.0","event_id":"sha256:ce8cba7fc52f93ffdd95edc313892cc63d1f3fa1b6368ef7e85d93e13e67a5d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/bundle.json","state_url":"https://pith.science/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/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":"2026-06-22T23:24:46Z","links":{"resolver":"https://pith.science/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R","bundle":"https://pith.science/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/bundle.json","state":"https://pith.science/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WVYDRG3MBNQALY2ELTIRTR2Y3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:WVYDRG3MBNQALY2ELTIRTR2Y3R","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":"d8443eeae934cf94214ee38e56cd7b0430f0502eed04ce91c297808f5d3b8dfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-06T00:04:50Z","title_canon_sha256":"35079a9c0e18153ef27633ff342204f993c774d9e9d3a9d2252954296cf1d8af"},"schema_version":"1.0","source":{"id":"1004.0740","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.0740","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"arxiv_version","alias_value":"1004.0740v1","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0740","created_at":"2026-05-18T04:40:54Z"},{"alias_kind":"pith_short_12","alias_value":"WVYDRG3MBNQA","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_16","alias_value":"WVYDRG3MBNQALY2E","created_at":"2026-05-18T12:26:17Z"},{"alias_kind":"pith_short_8","alias_value":"WVYDRG3M","created_at":"2026-05-18T12:26:17Z"}],"graph_snapshots":[{"event_id":"sha256:ce8cba7fc52f93ffdd95edc313892cc63d1f3fa1b6368ef7e85d93e13e67a5d8","target":"graph","created_at":"2026-05-18T04:40:54Z","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":"A BBGKY-like hierarchy is derived from the non-equilibrium Redfield equation. Two further approximations are introduced and each can be used to truncate and solve the hierarchy. In the first approximation such a truncation is performed by replacing two-particle Green's functions (GFs) in the hierarchy by their values at equilibrium. The second method is developed based on the cluster expansion, which constructs two-particle GFs from one-particle GFs and neglects the correlation part. A non-equilibrium Wick's Theorem is proved to provide a basis for this non-equilibrium cluster expansion. Using","authors_text":"Jinshan Wu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-06T00:04:50Z","title":"Non-equilibrium BBGKY Hierarchy from the Redfield Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0740","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":"sha256:90abba1378476c9746ebcb7e26b0bc906b86f81f8d528bfaf958d3e9eebafe3d","target":"record","created_at":"2026-05-18T04:40:54Z","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":"d8443eeae934cf94214ee38e56cd7b0430f0502eed04ce91c297808f5d3b8dfc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2010-04-06T00:04:50Z","title_canon_sha256":"35079a9c0e18153ef27633ff342204f993c774d9e9d3a9d2252954296cf1d8af"},"schema_version":"1.0","source":{"id":"1004.0740","kind":"arxiv","version":1}},"canonical_sha256":"b570389b6c0b6005e3445cd119c758dc6849e1e2580330d87e8bea1c3a532cb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b570389b6c0b6005e3445cd119c758dc6849e1e2580330d87e8bea1c3a532cb1","first_computed_at":"2026-05-18T04:40:54.468987Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:54.468987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tl450sE93BJnnzEb2bCztOvSO+1a1i0MfhZCKYf0p+IIaaOptrF5SinPIXsOBF5/yAKnlx6atR2Q9371/J4/Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:54.469689Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.0740","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90abba1378476c9746ebcb7e26b0bc906b86f81f8d528bfaf958d3e9eebafe3d","sha256:ce8cba7fc52f93ffdd95edc313892cc63d1f3fa1b6368ef7e85d93e13e67a5d8"],"state_sha256":"52a18787cdc27b235c56986cc05a55e91337a240273cdd6a612526330076ad50"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wwJQ/F8sU6RuKk1yX5xwo3CqTD22GEvZt/vnxgtzSy6XuopuKst/phGP+LCq38ZTEuglUBQNawsaQLJZkETdBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:24:46.923244Z","bundle_sha256":"232deacf60627f06fae077da180af93ec5f550591f0873ab54c0b38f1c2040a5"}}