{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:OQEGY36GFKA6BI77UKC6U7VYTG","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":"5acf411fb6ca84c38b8e4b48e442f247e85fda5318ee9b125256339be237dd6b","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-18T14:44:00Z","title_canon_sha256":"bf4392692543fed8274fdcaaeec0521209775d67656c1aad6c3e76ceac80c755"},"schema_version":"1.0","source":{"id":"1005.3218","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3218","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3218v2","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3218","created_at":"2026-05-18T04:22:02Z"},{"alias_kind":"pith_short_12","alias_value":"OQEGY36GFKA6","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"OQEGY36GFKA6BI77","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"OQEGY36G","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:660dce7b6ec6ce9b6e5730041576c927d69729e6ba692dd1c1080aa987251e90","target":"graph","created_at":"2026-05-18T04:22:02Z","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":"Main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a rectangular domain in $\\mathbb{R}^{3}$. Our analysis shows that the system undergoes a first dynamic transition either to multiple equilibria or to periodic solutions. In the case of transition to multiple equilibria, the transition is a type-I (continuous) transition. In the case of transition to periodic solutions, the transition can be either type-I or type-II (jump).","authors_text":"Taylan \\c{S}eng\\\"ul","cross_cats":["physics.flu-dyn"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-18T14:44:00Z","title":"Dynamic Transition for Magnetohydrodynamic Convection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3218","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":"sha256:717ea2ed330e9b93b08c8a2d4b04483bf6c3099b89812803727d1fd11295cae5","target":"record","created_at":"2026-05-18T04:22:02Z","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":"5acf411fb6ca84c38b8e4b48e442f247e85fda5318ee9b125256339be237dd6b","cross_cats_sorted":["physics.flu-dyn"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-05-18T14:44:00Z","title_canon_sha256":"bf4392692543fed8274fdcaaeec0521209775d67656c1aad6c3e76ceac80c755"},"schema_version":"1.0","source":{"id":"1005.3218","kind":"arxiv","version":2}},"canonical_sha256":"74086c6fc62a81e0a3ffa285ea7eb89991fe4ab7e5a746754a6e7d6d926134c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"74086c6fc62a81e0a3ffa285ea7eb89991fe4ab7e5a746754a6e7d6d926134c2","first_computed_at":"2026-05-18T04:22:02.433952Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:02.433952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nGCgNC/RsT/SxlzK76/5ru+oZOUAaJ0zy1UAdesGStY2u2g6aKTJ9U8MMbtft7EiGjXXLWd2aGKu6XGH42H9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:02.434664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3218","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:717ea2ed330e9b93b08c8a2d4b04483bf6c3099b89812803727d1fd11295cae5","sha256:660dce7b6ec6ce9b6e5730041576c927d69729e6ba692dd1c1080aa987251e90"],"state_sha256":"37d9e063749c32be9530b24f30fefa05113467f351236265be8a0d6a7b0085a9"}