{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:L6VVQUGRVTHDJF4X7NK6CBHK2Y","short_pith_number":"pith:L6VVQUGR","canonical_record":{"source":{"id":"1105.5822","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-29T19:40:29Z","cross_cats_sorted":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"title_canon_sha256":"99a398eb0f6c8b770f35be4682f3c0b7dc42cc6e358583a127434480c6964c87","abstract_canon_sha256":"acf3ced406ee123170b41367ca020b7e4841d35826943f92671edfdd8f60c80b"},"schema_version":"1.0"},"canonical_sha256":"5fab5850d1acce349797fb55e104ead63492e3bf6cf79e44fe1da7f3fc9266ff","source":{"kind":"arxiv","id":"1105.5822","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5822","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5822v2","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5822","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"L6VVQUGRVTHD","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L6VVQUGRVTHDJF4X","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L6VVQUGR","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:L6VVQUGRVTHDJF4X7NK6CBHK2Y","target":"record","payload":{"canonical_record":{"source":{"id":"1105.5822","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-29T19:40:29Z","cross_cats_sorted":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"title_canon_sha256":"99a398eb0f6c8b770f35be4682f3c0b7dc42cc6e358583a127434480c6964c87","abstract_canon_sha256":"acf3ced406ee123170b41367ca020b7e4841d35826943f92671edfdd8f60c80b"},"schema_version":"1.0"},"canonical_sha256":"5fab5850d1acce349797fb55e104ead63492e3bf6cf79e44fe1da7f3fc9266ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:07:21.134060Z","signature_b64":"K2/NEutvBieiX0RgsmjIJ8H4vJit96ktMvxIgcNwm6LncAFNG4JV7qX0kqKHphqqxBqqB4TCVozwtBGPxLGgBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5fab5850d1acce349797fb55e104ead63492e3bf6cf79e44fe1da7f3fc9266ff","last_reissued_at":"2026-05-18T03:07:21.133347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:07:21.133347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.5822","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":"2026-05-18T03:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3DgD4uzwjggJecGHljwQdvio0hRCc9t3QDkOukn43FZQtDQMybUL8rQruwGK7oxxcYnvJCqSYNGOpkHLvGhuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:07:41.816855Z"},"content_sha256":"928153538669190ca6d480608390e49f5af12f90cacce24a29caf531e2bcdb0b","schema_version":"1.0","event_id":"sha256:928153538669190ca6d480608390e49f5af12f90cacce24a29caf531e2bcdb0b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:L6VVQUGRVTHDJF4X7NK6CBHK2Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Evolution Equations for Marginal Correlation Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"D.O. Polishchuk, V.I. Gerasimenko","submitted_at":"2011-05-29T19:40:29Z","abstract_excerpt":"This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann hierarchy for correlation operators that give an alternative approach to the description of states in comparison with the density operators. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5822","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":"2026-05-18T03:07:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nNy2yOdRcT6mxrk/PEi14R3YBRpnLLOogLKaeUWGSC5o7mrhPIWYZE/6upm1XOI2G1DNA1e6sM3kTuU53ZQjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:07:41.817206Z"},"content_sha256":"a5f08d5a173f7e6f451355db8e313c1ed5ae2cd9d88ee9759a86908d964b13b5","schema_version":"1.0","event_id":"sha256:a5f08d5a173f7e6f451355db8e313c1ed5ae2cd9d88ee9759a86908d964b13b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/bundle.json","state_url":"https://pith.science/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/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":"2026-06-24T20:07:41Z","links":{"resolver":"https://pith.science/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y","bundle":"https://pith.science/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/bundle.json","state":"https://pith.science/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L6VVQUGRVTHDJF4X7NK6CBHK2Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:L6VVQUGRVTHDJF4X7NK6CBHK2Y","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":"acf3ced406ee123170b41367ca020b7e4841d35826943f92671edfdd8f60c80b","cross_cats_sorted":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-29T19:40:29Z","title_canon_sha256":"99a398eb0f6c8b770f35be4682f3c0b7dc42cc6e358583a127434480c6964c87"},"schema_version":"1.0","source":{"id":"1105.5822","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.5822","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"arxiv_version","alias_value":"1105.5822v2","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.5822","created_at":"2026-05-18T03:07:21Z"},{"alias_kind":"pith_short_12","alias_value":"L6VVQUGRVTHD","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"L6VVQUGRVTHDJF4X","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"L6VVQUGR","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:a5f08d5a173f7e6f451355db8e313c1ed5ae2cd9d88ee9759a86908d964b13b5","target":"graph","created_at":"2026-05-18T03:07:21Z","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":"This paper is devoted to the problem of the description of nonequilibrium correlations in quantum many-particle systems. The nonlinear quantum BBGKY hierarchy for marginal correlation operators is rigorously derived from the von Neumann hierarchy for correlation operators that give an alternative approach to the description of states in comparison with the density operators. A nonperturbative solution of the Cauchy problem of the nonlinear quantum BBGKY hierarchy for marginal correlation operators is constructed.","authors_text":"D.O. Polishchuk, V.I. Gerasimenko","cross_cats":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-29T19:40:29Z","title":"On Evolution Equations for Marginal Correlation Operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5822","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":"sha256:928153538669190ca6d480608390e49f5af12f90cacce24a29caf531e2bcdb0b","target":"record","created_at":"2026-05-18T03:07:21Z","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":"acf3ced406ee123170b41367ca020b7e4841d35826943f92671edfdd8f60c80b","cross_cats_sorted":["cond-mat.stat-mech","math.AP","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-29T19:40:29Z","title_canon_sha256":"99a398eb0f6c8b770f35be4682f3c0b7dc42cc6e358583a127434480c6964c87"},"schema_version":"1.0","source":{"id":"1105.5822","kind":"arxiv","version":2}},"canonical_sha256":"5fab5850d1acce349797fb55e104ead63492e3bf6cf79e44fe1da7f3fc9266ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fab5850d1acce349797fb55e104ead63492e3bf6cf79e44fe1da7f3fc9266ff","first_computed_at":"2026-05-18T03:07:21.133347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:07:21.133347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"K2/NEutvBieiX0RgsmjIJ8H4vJit96ktMvxIgcNwm6LncAFNG4JV7qX0kqKHphqqxBqqB4TCVozwtBGPxLGgBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:07:21.134060Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.5822","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:928153538669190ca6d480608390e49f5af12f90cacce24a29caf531e2bcdb0b","sha256:a5f08d5a173f7e6f451355db8e313c1ed5ae2cd9d88ee9759a86908d964b13b5"],"state_sha256":"5494b6b17eac0a9b9ab6c9e3b4f365f6adb67c8839285fd11c4798ec4bf3b59f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WJ6i/Xo4QbCeOl5+wRzVk/2LD+z08ZGudUhnTK9WoPffe0KEtbsEzcRAYhdy2uqHtMxmgCosKS0t917B+dSHDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:07:41.819575Z","bundle_sha256":"1087662bb55c006f04c4b416e9ca837d8ad9a5f05191bd035cdd41432b95780e"}}