{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NWUS2QWUCHME66DDCZFXZBMXWG","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":"9a9b98d1636ff511fc07124db1a85dd1d141c8cf14abf51c4c6ebb7171f00bb1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-24T11:55:59Z","title_canon_sha256":"f529d2674aa2bf67e3b5b1ce348f5d74c007a8b9b4de70247e4cfa0162d76170"},"schema_version":"1.0","source":{"id":"1106.4946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.4946","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"arxiv_version","alias_value":"1106.4946v1","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.4946","created_at":"2026-05-18T03:29:40Z"},{"alias_kind":"pith_short_12","alias_value":"NWUS2QWUCHME","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NWUS2QWUCHME66DD","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NWUS2QWU","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:6868b67d70bcae4900e3b60ca1ca906b61b1a8e1f0ef9d42a8fda26b9d3cd3b7","target":"graph","created_at":"2026-05-18T03:29:40Z","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":"General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We also present sufficient conditions that allows us to consider these equations on suitable Banach spaces.","authors_text":"Dmitri L. Finkelshtein, Maria Jo\\~ao Oliveira, Yuri G. Kondratiev","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-24T11:55:59Z","title":"Markov evolutions and hierarchical equations in the continuum: II. Multicomponent systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.4946","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":"sha256:1846bffb51529ad7227cc478b8cd4c164298cc5d53f443e108eb359b9d8d854a","target":"record","created_at":"2026-05-18T03:29:40Z","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":"9a9b98d1636ff511fc07124db1a85dd1d141c8cf14abf51c4c6ebb7171f00bb1","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-06-24T11:55:59Z","title_canon_sha256":"f529d2674aa2bf67e3b5b1ce348f5d74c007a8b9b4de70247e4cfa0162d76170"},"schema_version":"1.0","source":{"id":"1106.4946","kind":"arxiv","version":1}},"canonical_sha256":"6da92d42d411d84f7863164b7c8597b18d75b1ef4dc8c80262c640bbc322fb5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6da92d42d411d84f7863164b7c8597b18d75b1ef4dc8c80262c640bbc322fb5c","first_computed_at":"2026-05-18T03:29:40.907452Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:40.907452Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EBfRK7BthS+Xml87ACLnWG4dYo1S07sG5Nt6P7mjFXYSxDUBoDvjsqNMGmqH1KBCOHKL4N1q/SuazwZVw/+cCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:40.908048Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.4946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1846bffb51529ad7227cc478b8cd4c164298cc5d53f443e108eb359b9d8d854a","sha256:6868b67d70bcae4900e3b60ca1ca906b61b1a8e1f0ef9d42a8fda26b9d3cd3b7"],"state_sha256":"285a9b45d0a4623d7f6d77ea3300cc1b477961cf8675e308e2e470bdc9f82b53"}