{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7UEBA3V4O3T4LC4K2PRFARKGSA","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":"4cd9b5a0763d92bb6319c717ac3f6e87ebf60a9229750c53119a1e1c9cb325b8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-27T10:32:47Z","title_canon_sha256":"59b3da062997c238dc344118505ede8038799d6f2ff0e9a0ba32b884371ab452"},"schema_version":"1.0","source":{"id":"2410.20404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.20404","created_at":"2026-07-05T09:26:44Z"},{"alias_kind":"arxiv_version","alias_value":"2410.20404v1","created_at":"2026-07-05T09:26:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.20404","created_at":"2026-07-05T09:26:44Z"},{"alias_kind":"pith_short_12","alias_value":"7UEBA3V4O3T4","created_at":"2026-07-05T09:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"7UEBA3V4O3T4LC4K","created_at":"2026-07-05T09:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"7UEBA3V4","created_at":"2026-07-05T09:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:c2a929822dcd4ee89461a2c000a1a9372d6346f63817f1117d4d3eedc0692946","target":"graph","created_at":"2026-07-05T09:26:44Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.20404/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We address a threshold problem of the Couette flow $(y,0)$ in a uniform magnetic field $(\\beta,0)$ for the 2D MHD equation on $\\mathbb{T}\\times\\mathbb{R}$ with fluid viscosity $\\nu$ and magnetic resistivity $\\mu$. The nonlinear enhanced dissipation and inviscid damping are also established. In particularly, when $0<\\nu\\leq\\mu^3\\leq1$, we get a threshold $\\nu^{\\frac{1}{2}}\\mu^{\\frac{1}{3}}$ in $H^N(N\\geq4)$. When $0<\\mu^3\\leq\\nu\\leq1$, we obtain a threshold $\\min\\{\\nu^{\\frac{1}{2}},\\mu^{\\frac{1}{2}}\\}\\min\\{1,\\nu^{-1}\\mu^{\\frac{1}{3}}\\}$, hence improving the results in [19,14,21].","authors_text":"Fei Wang, Zeren Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-27T10:32:47Z","title":"The stability threshold for 2D MHD equations around Couette with general viscosity and magnetic resistivity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.20404","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":"sha256:7845998435ee8cb1215c2eda2cb4211a1c9e5c1a61fcf8a771c845b99b0a3b82","target":"record","created_at":"2026-07-05T09:26:44Z","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":"4cd9b5a0763d92bb6319c717ac3f6e87ebf60a9229750c53119a1e1c9cb325b8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-27T10:32:47Z","title_canon_sha256":"59b3da062997c238dc344118505ede8038799d6f2ff0e9a0ba32b884371ab452"},"schema_version":"1.0","source":{"id":"2410.20404","kind":"arxiv","version":1}},"canonical_sha256":"fd08106ebc76e7c58b8ad3e25045469019edfb9c0cf47a6001b21d315f7505b6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd08106ebc76e7c58b8ad3e25045469019edfb9c0cf47a6001b21d315f7505b6","first_computed_at":"2026-07-05T09:26:44.433109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:26:44.433109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i+kuYz+z83BgKs+5vtwfMqqK6xsN/FqIf1kRsG5lmrzLcPDh4QPVJ+IY6t31Vj5l1CMEdDlk58YB9yTIUhUXCg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:26:44.433650Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.20404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7845998435ee8cb1215c2eda2cb4211a1c9e5c1a61fcf8a771c845b99b0a3b82","sha256:c2a929822dcd4ee89461a2c000a1a9372d6346f63817f1117d4d3eedc0692946"],"state_sha256":"fbb7fcb974cf06c1f4d80561d3a0a2fcf1abf531abc287ce098c567f89ad4b12"}