{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:DZPY5PZTOG3NYALZPIWQZGZJUD","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":"db949bb4f7364571e6f090a753f0a05b3ffe57998d8c7a3a842d8f1f75afbf34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-31T19:42:36Z","title_canon_sha256":"31abeb4db9c94b61e7ccc1645e97e7bd16c8cb2253cf771ccb947585235c3e72"},"schema_version":"1.0","source":{"id":"0908.4340","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0908.4340","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"arxiv_version","alias_value":"0908.4340v3","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.4340","created_at":"2026-05-18T04:30:02Z"},{"alias_kind":"pith_short_12","alias_value":"DZPY5PZTOG3N","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"DZPY5PZTOG3NYALZ","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"DZPY5PZT","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:b1199f5e9569430c1dca787c53a65e1549d2b46ae93640b19cf0ddfc206df46a","target":"graph","created_at":"2026-05-18T04:30:02Z","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":"Reconstruction of equations of motion from incomplete or noisy data and dimension reduction are two fundamental problems in the study of dynamical systems with many degrees of freedom. For the latter extensive efforts have been made but with limited success to generalize the Zwanzig-Mori projection formalism, originally developed for Hamiltonian systems close to thermodynamic equilibrium, to general non-Hamiltonian systems lacking detailed-balance. One difficulty introduced by such systems is the lack of an invariant measure, needed to define a statistical distribution. Based on a recent disco","authors_text":"Jianhua Xing, Kenneth S Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-31T19:42:36Z","title":"Application of the projection operator formalism to non-Hamiltonian dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.4340","kind":"arxiv","version":3},"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":"sha256:62c198df251a8b352fcb9b5c1e58e648aaa61ba8844198327f2e95f6d365d01a","target":"record","created_at":"2026-05-18T04:30:02Z","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":"db949bb4f7364571e6f090a753f0a05b3ffe57998d8c7a3a842d8f1f75afbf34","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2009-08-31T19:42:36Z","title_canon_sha256":"31abeb4db9c94b61e7ccc1645e97e7bd16c8cb2253cf771ccb947585235c3e72"},"schema_version":"1.0","source":{"id":"0908.4340","kind":"arxiv","version":3}},"canonical_sha256":"1e5f8ebf3371b6dc01797a2d0c9b29a0eac486116b7bcb7603dcd95d706f2818","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e5f8ebf3371b6dc01797a2d0c9b29a0eac486116b7bcb7603dcd95d706f2818","first_computed_at":"2026-05-18T04:30:02.950097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:02.950097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XjPHdkVijhBozpyy2Ts/Q5umyy3M4BsDuU8xX1YZttPiREeMa5SQJ/5U2HiOMYiPqC0E4Fg2A0FjdoT7K7OHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:02.950711Z","signed_message":"canonical_sha256_bytes"},"source_id":"0908.4340","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:62c198df251a8b352fcb9b5c1e58e648aaa61ba8844198327f2e95f6d365d01a","sha256:b1199f5e9569430c1dca787c53a65e1549d2b46ae93640b19cf0ddfc206df46a"],"state_sha256":"f8ed357be4afc498aa297457fbaf0a25307af9979c083a75ebfbddf4180afb91"}