{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4K62J5MXII74KAWZCPKKMIHZIO","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":"3e8edf8c97b5340c8a19257dc065f8d08105326207d9f0fd219fb1956cd08e80","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-01-28T08:20:53Z","title_canon_sha256":"c6a4c6ceaa9c257ba1defe3193dda8bd82b54d0d02e5dd75a7cc1f826b106326"},"schema_version":"1.0","source":{"id":"0901.4412","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.4412","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"arxiv_version","alias_value":"0901.4412v4","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.4412","created_at":"2026-05-18T02:14:55Z"},{"alias_kind":"pith_short_12","alias_value":"4K62J5MXII74","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4K62J5MXII74KAWZ","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4K62J5MX","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:6054ef06010f4264e7bb1fa2dc8232f048e3520708aa0ef52f3b8de38c029b86","target":"graph","created_at":"2026-05-18T02:14:55Z","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 consider a general family of regularized Navier-Stokes and Magnetohydrodynamics (MHD) models on n-dimensional smooth compact Riemannian manifolds with or without boundary, with n greater than or equal to 2. This family captures most of the specific regularized models that have been proposed and analyzed in the literature, including the Navier-Stokes equations, the Navier-Stokes-alpha model, the Leray-alpha model, the Modified Leray-alpha model, the Simplified Bardina model, the Navier-Stokes-Voight model, the Navier-Stokes-alpha-like models, and certain MHD models, in addition to representi","authors_text":"Evelyn Lunasin, Gantumur Tsogtgerel, Michael Holst","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-01-28T08:20:53Z","title":"Analysis of a General Family of Regularized Navier-Stokes and MHD Models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.4412","kind":"arxiv","version":4},"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:e58c53cdc2abdf1c568c4ce6da0b23b46a6304ad9b0930d774fd72f18e1ffb00","target":"record","created_at":"2026-05-18T02:14:55Z","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":"3e8edf8c97b5340c8a19257dc065f8d08105326207d9f0fd219fb1956cd08e80","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-01-28T08:20:53Z","title_canon_sha256":"c6a4c6ceaa9c257ba1defe3193dda8bd82b54d0d02e5dd75a7cc1f826b106326"},"schema_version":"1.0","source":{"id":"0901.4412","kind":"arxiv","version":4}},"canonical_sha256":"e2bda4f597423fc502d913d4a620f943a780b70194518c3c7ac364a38389b890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2bda4f597423fc502d913d4a620f943a780b70194518c3c7ac364a38389b890","first_computed_at":"2026-05-18T02:14:55.506664Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:55.506664Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kzDOhAk7c+8B/zBVRP2hSPTQ21nA8tXkYhLf+KHypC+2Pyki25W1wfKKTmTFkjNUmvowQyxm3+Y0goSWc3gBCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:55.507149Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.4412","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e58c53cdc2abdf1c568c4ce6da0b23b46a6304ad9b0930d774fd72f18e1ffb00","sha256:6054ef06010f4264e7bb1fa2dc8232f048e3520708aa0ef52f3b8de38c029b86"],"state_sha256":"4a7bab35147a14c68cbb19fe6e88041e4098d8aa9ded28501c8e586dac6fd0c2"}