{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5NWW4YL6DQM7RFF6QWA66MME5L","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":"2d4b43917de67c9903905f0f524f6d0c6c6bfcf215827b3951560e72223152f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-18T23:51:53Z","title_canon_sha256":"7266572f9322fd4b000ee6113382402f6b09400cf98736002e27802f80dc27cf"},"schema_version":"1.0","source":{"id":"1611.06277","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.06277","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"arxiv_version","alias_value":"1611.06277v2","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06277","created_at":"2026-05-18T00:34:31Z"},{"alias_kind":"pith_short_12","alias_value":"5NWW4YL6DQM7","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_16","alias_value":"5NWW4YL6DQM7RFF6","created_at":"2026-05-18T12:30:01Z"},{"alias_kind":"pith_short_8","alias_value":"5NWW4YL6","created_at":"2026-05-18T12:30:01Z"}],"graph_snapshots":[{"event_id":"sha256:e7c751ccf41b76d29b665f515685b4885eaf7d8bf0ad7f91c621440a0beb534c","target":"graph","created_at":"2026-05-18T00:34:31Z","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":"Reduced Order Models (ROMs) of complex, nonlinear dynamical systems often require closure, which is the process of representing the contribution of the unresolved physics on the resolved physics. The Mori-Zwanzig (M-Z) procedure allows one to write down formally closed evolution equations for the resolved physics. In these equations, the unclosed terms are recast as a memory integral involving the past history of the resolved variables, and a \"noise\" term. While the M-Z procedure does not directly reduce the complexity of the original system, these equations can serve as a mathematically consi","authors_text":"Ayoub Gouasmi, Eric Parish, Karthik Duraisamy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-18T23:51:53Z","title":"A Priori Estimation Of Memory Effects In Coarse-Grained Nonlinear Systems Using The Mori-Zwanzig Formalism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06277","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:be00d48c9819f4926ae83428f66a2447515f0caeacfce7e95d4fb491d27e4792","target":"record","created_at":"2026-05-18T00:34:31Z","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":"2d4b43917de67c9903905f0f524f6d0c6c6bfcf215827b3951560e72223152f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-18T23:51:53Z","title_canon_sha256":"7266572f9322fd4b000ee6113382402f6b09400cf98736002e27802f80dc27cf"},"schema_version":"1.0","source":{"id":"1611.06277","kind":"arxiv","version":2}},"canonical_sha256":"eb6d6e617e1c19f894be8581ef3184eaf9df763029f10671b26cf29fa86dc0f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb6d6e617e1c19f894be8581ef3184eaf9df763029f10671b26cf29fa86dc0f4","first_computed_at":"2026-05-18T00:34:31.424155Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:31.424155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Tc5CRr0gdpeKruMJjQMOC3jVzBr0R+U6px1Bfoyu2dGw0aYyq7JaX/5nghI7rQER9ZbwHlZ05eb2WWF7I56ZDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:31.424611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.06277","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be00d48c9819f4926ae83428f66a2447515f0caeacfce7e95d4fb491d27e4792","sha256:e7c751ccf41b76d29b665f515685b4885eaf7d8bf0ad7f91c621440a0beb534c"],"state_sha256":"bfc973e0e288766beee717c003a41188a895efba1a750da784f13922916b95e2"}