{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ZT2NJPJIWDJHUOTUY56JPEER4R","short_pith_number":"pith:ZT2NJPJI","canonical_record":{"source":{"id":"2401.12548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f4a46f6d4881e3d631147c8b3259c42a2ab9e4357a2174a49c7e4ab50f0625cf","abstract_canon_sha256":"11a365dc1bad49101a69fd9c4aad0129c58af4c34a9a819b0c744031aca832a2"},"schema_version":"1.0"},"canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","source":{"kind":"arxiv","id":"2401.12548","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12548","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12548v1","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12548","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZT2NJPJIWDJH","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZT2NJPJIWDJHUOTU","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZT2NJPJI","created_at":"2026-07-05T07:36:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ZT2NJPJIWDJHUOTUY56JPEER4R","target":"record","payload":{"canonical_record":{"source":{"id":"2401.12548","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"f4a46f6d4881e3d631147c8b3259c42a2ab9e4357a2174a49c7e4ab50f0625cf","abstract_canon_sha256":"11a365dc1bad49101a69fd9c4aad0129c58af4c34a9a819b0c744031aca832a2"},"schema_version":"1.0"},"canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:36:32.341764Z","signature_b64":"ix1RdH/X+jl8+GwCKJZz+lr7mBMH0fEptRJ06rGTSo8QB3Agg73V3Jd68x054O/PG62s8KmT64WCJRpZEl8FBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","last_reissued_at":"2026-07-05T07:36:32.341326Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:36:32.341326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2401.12548","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tf7ZrVf6qBrL4tQQDXhry8O9nqYltRxTjQ2mtn6BkOmBjgVQOysWgmCSEg/RyozlHNrnc4mg6JSo0hBwFku9Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:40:44.422439Z"},"content_sha256":"e54abd99ee6487f485cd202c1472f875720c15e48a810881bac83b30941f63c5","schema_version":"1.0","event_id":"sha256:e54abd99ee6487f485cd202c1472f875720c15e48a810881bac83b30941f63c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ZT2NJPJIWDJHUOTUY56JPEER4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Niklas Knobel","submitted_at":"2024-01-23T08:13:08Z","abstract_excerpt":"In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $\\nu$ is larger than resistivity $\\kappa$, $\\nu\\ge \\kappa>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $\\kappa\\le \\nu^3$ this system exhibits instability, which leads to norm inflation of size $\\nu \\kappa^{-\\frac 1 3 }$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12548","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2401.12548/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:36:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vdCK7wXLfsouYcqEFy1ZVOEaDGvxCaMjJPXoMiDuzl1B4EwX7DzTkGhsuur123a2TV3nYGHinGw+Oh3i1qNVAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T14:40:44.422979Z"},"content_sha256":"9e20d6b3ee064aaf61b0757a06716992dfac616ba1362d46f635ec54309f4266","schema_version":"1.0","event_id":"sha256:9e20d6b3ee064aaf61b0757a06716992dfac616ba1362d46f635ec54309f4266"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/bundle.json","state_url":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-12T14:40:44Z","links":{"resolver":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R","bundle":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/bundle.json","state":"https://pith.science/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZT2NJPJIWDJHUOTUY56JPEER4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZT2NJPJIWDJHUOTUY56JPEER4R","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":"11a365dc1bad49101a69fd9c4aad0129c58af4c34a9a819b0c744031aca832a2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","title_canon_sha256":"f4a46f6d4881e3d631147c8b3259c42a2ab9e4357a2174a49c7e4ab50f0625cf"},"schema_version":"1.0","source":{"id":"2401.12548","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2401.12548","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"arxiv_version","alias_value":"2401.12548v1","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.12548","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_12","alias_value":"ZT2NJPJIWDJH","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_16","alias_value":"ZT2NJPJIWDJHUOTU","created_at":"2026-07-05T07:36:32Z"},{"alias_kind":"pith_short_8","alias_value":"ZT2NJPJI","created_at":"2026-07-05T07:36:32Z"}],"graph_snapshots":[{"event_id":"sha256:9e20d6b3ee064aaf61b0757a06716992dfac616ba1362d46f635ec54309f4266","target":"graph","created_at":"2026-07-05T07:36:32Z","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/2401.12548/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this article, we consider the stability of the 2D magnetohydrodynamics (MHD) equations close to a combination of Couette flow and a constant magnetic field. We consider the ideal conductor limit for the case when viscosity $\\nu$ is larger than resistivity $\\kappa$, $\\nu\\ge \\kappa>0$. For this regime, we establish a bound on the Sobolev stability threshold. Furthermore, for $\\kappa\\le \\nu^3$ this system exhibits instability, which leads to norm inflation of size $\\nu \\kappa^{-\\frac 1 3 }$.","authors_text":"Niklas Knobel","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","title":"Sobolev Stability for the 2D MHD Equations in the Non-Resistive Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.12548","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:e54abd99ee6487f485cd202c1472f875720c15e48a810881bac83b30941f63c5","target":"record","created_at":"2026-07-05T07:36:32Z","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":"11a365dc1bad49101a69fd9c4aad0129c58af4c34a9a819b0c744031aca832a2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-01-23T08:13:08Z","title_canon_sha256":"f4a46f6d4881e3d631147c8b3259c42a2ab9e4357a2174a49c7e4ab50f0625cf"},"schema_version":"1.0","source":{"id":"2401.12548","kind":"arxiv","version":1}},"canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ccf4d4bd28b0d27a3a74c77c979091e47618892cb1da8e82f1a43340d66ba4be","first_computed_at":"2026-07-05T07:36:32.341326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:36:32.341326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ix1RdH/X+jl8+GwCKJZz+lr7mBMH0fEptRJ06rGTSo8QB3Agg73V3Jd68x054O/PG62s8KmT64WCJRpZEl8FBA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:36:32.341764Z","signed_message":"canonical_sha256_bytes"},"source_id":"2401.12548","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e54abd99ee6487f485cd202c1472f875720c15e48a810881bac83b30941f63c5","sha256:9e20d6b3ee064aaf61b0757a06716992dfac616ba1362d46f635ec54309f4266"],"state_sha256":"a6e8875271e12375919a824f4c42019277277cb2f7b47cb93ed6b45d07aa272b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAo2BKGKYat2faX5/MMfn6wxknFSQkmpWsgTJi+vgxGL/Hmi+rSAnVa1sQuJ9Vh0wqfYDPGCF9in8rPJQrigBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T14:40:44.427221Z","bundle_sha256":"ee86c78bb91c7916217932e360fd35b6484305dccbeae1f75c85c7ba80ec4675"}}