{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:W45TIIWMUYLQY2CKMAYYST2QDB","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":"94395a2aa04c821561c78e70d23f4904e3fdd2df3637a5e0abc6209989033100","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-09-30T20:55:41Z","title_canon_sha256":"a4d0181297d8e7e970d892188e4cf1abe2381ef61cbb25617efe812510dfd956"},"schema_version":"1.0","source":{"id":"1310.0053","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0053","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0053v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0053","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"W45TIIWMUYLQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"W45TIIWMUYLQY2CK","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"W45TIIWM","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:8608f54e8106d66e7ede092233739f39e2ef7166c7654319bb93425e070dd068","target":"graph","created_at":"2026-05-18T03:11:45Z","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":"We investigate linear-quadratic dynamical systems with energy preserving quadratic terms. These systems arise for instance as Galerkin systems of incompressible flows. A criterion is presented to ensure long-term boundedness of the system dynamics. If the criterion is violated, a globally stable attractor cannot exist for an effective nonlinearity. Thus, the criterion represents a minimum requirement for a physically justified Galerkin model of viscous fluid flows. The criterion is exemplified e.g. for Galerkin systems of two-dimensional cylinder wake flow models in the transient and the post-","authors_text":"Bernd R. Noack, Michael Schlegel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-09-30T20:55:41Z","title":"On long-term boundedness of Galerkin models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0053","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":"sha256:15262896ac651b92feea5ea74fd6bfa836d640b077d0924cc5642f2ee2bd79c0","target":"record","created_at":"2026-05-18T03:11:45Z","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":"94395a2aa04c821561c78e70d23f4904e3fdd2df3637a5e0abc6209989033100","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.flu-dyn","submitted_at":"2013-09-30T20:55:41Z","title_canon_sha256":"a4d0181297d8e7e970d892188e4cf1abe2381ef61cbb25617efe812510dfd956"},"schema_version":"1.0","source":{"id":"1310.0053","kind":"arxiv","version":1}},"canonical_sha256":"b73b3422cca6170c684a6031894f50184a66ceaaf761c1a8736b41af34a0cd33","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b73b3422cca6170c684a6031894f50184a66ceaaf761c1a8736b41af34a0cd33","first_computed_at":"2026-05-18T03:11:45.804000Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:45.804000Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5dLPUiM2oJmL0ql+bkFnGVdzt6F4FNpXvtl6t31cNOa7gYLDtq/0WpQ9TCf9nR4ZVAeCG51SBYhUdp8n45pyCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:45.804811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0053","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15262896ac651b92feea5ea74fd6bfa836d640b077d0924cc5642f2ee2bd79c0","sha256:8608f54e8106d66e7ede092233739f39e2ef7166c7654319bb93425e070dd068"],"state_sha256":"608ccf271e0aaad2021697a75aed108cc9462f2e46575e265b88d0ce9b1ffc1d"}