{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:PKSGGVMZL77LKEGGMDGRMAGSPD","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":"1cfa5f8aec3dedb4c33cae2859aa7e5cf432cd569085b4c0f23f128011dbfb0a","cross_cats_sorted":["cs.AI","cs.SY","math.PR","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-09-04T13:31:36Z","title_canon_sha256":"fc11572b4a33a7b4a8c35b97857f8975392f46f4e862ff2c14ebf5e01fc0d333"},"schema_version":"1.0","source":{"id":"1609.00932","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.00932","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"arxiv_version","alias_value":"1609.00932v2","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.00932","created_at":"2026-05-18T00:41:58Z"},{"alias_kind":"pith_short_12","alias_value":"PKSGGVMZL77L","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_16","alias_value":"PKSGGVMZL77LKEGG","created_at":"2026-05-18T12:30:39Z"},{"alias_kind":"pith_short_8","alias_value":"PKSGGVMZ","created_at":"2026-05-18T12:30:39Z"}],"graph_snapshots":[{"event_id":"sha256:a0f9aae5c97329040c9cf6365059668d5beec3bbd3abe4b11dd0c81f5a156af9","target":"graph","created_at":"2026-05-18T00:41:58Z","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":"Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They exactly describe dynamics of finite-rank systems and can be efficiently and consistently estimated through spectral learning under the assumption of identically distributed data. In this paper, we investigate the properties of spectral learning without this assumption due to the requirements of analyzing large-time scale systems, and show that the equilibrium dynamics of a system can be extracted from nonequilibrium observation data by imposi","authors_text":"Frank No\\'e, Hao Wu","cross_cats":["cs.AI","cs.SY","math.PR","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-09-04T13:31:36Z","title":"Spectral learning of dynamic systems from nonequilibrium data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00932","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":"sha256:052ac54bba7718cbd39dfac4e631945c47457aef6c9d547d9d9ab3ecf01c7ed5","target":"record","created_at":"2026-05-18T00:41:58Z","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":"1cfa5f8aec3dedb4c33cae2859aa7e5cf432cd569085b4c0f23f128011dbfb0a","cross_cats_sorted":["cs.AI","cs.SY","math.PR","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2016-09-04T13:31:36Z","title_canon_sha256":"fc11572b4a33a7b4a8c35b97857f8975392f46f4e862ff2c14ebf5e01fc0d333"},"schema_version":"1.0","source":{"id":"1609.00932","kind":"arxiv","version":2}},"canonical_sha256":"7aa46355995ffeb510c660cd1600d278e2e66ea21865aa2adedb8e06e28a9e70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7aa46355995ffeb510c660cd1600d278e2e66ea21865aa2adedb8e06e28a9e70","first_computed_at":"2026-05-18T00:41:58.252998Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:58.252998Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yEPT3FM9V+m4oIayZE3RcgxLfKlfC4CiK3AdypD+WlabIii3KaO+TW3vSPWQQQ5o/7jaYQEfi7F1jNhLYBcKDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:58.253503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.00932","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:052ac54bba7718cbd39dfac4e631945c47457aef6c9d547d9d9ab3ecf01c7ed5","sha256:a0f9aae5c97329040c9cf6365059668d5beec3bbd3abe4b11dd0c81f5a156af9"],"state_sha256":"93c1ea444e63aacde95f83dae853e7a96fd6bf06698aa4d8369a8b1f801875e9"}