{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:QA2ZV7SZSMHZQIMIMVKR6ADLQL","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":"3aeb4fd8fb2eea1d6036a900eff1f662842125b2ef90dcd1e7698796e0492dac","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2007-08-01T09:07:32Z","title_canon_sha256":"2c5db6aad86458535839a59689eb864b14764c9ccef5a1249ee99da93766334b"},"schema_version":"1.0","source":{"id":"0708.0099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.0099","created_at":"2026-07-04T17:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"0708.0099v2","created_at":"2026-07-04T17:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.0099","created_at":"2026-07-04T17:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"QA2ZV7SZSMHZ","created_at":"2026-07-04T17:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"QA2ZV7SZSMHZQIMI","created_at":"2026-07-04T17:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"QA2ZV7SZ","created_at":"2026-07-04T17:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:3c9a2bb7ee25f3f7b428d9096a2c4af3d9b90e297776d1cdb3a4b653793b0878","target":"graph","created_at":"2026-07-04T17:18:13Z","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/0708.0099/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove the local well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces and obtain blow-up criterion of smooth solutions. Specially, we fill a gap in a step of the proof of the local well-posedness part for the incompressible Euler equation in \\cite{Chae1}.","authors_text":"Changxing Miao, Qionglei Chen, Zhifei Zhang","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2007-08-01T09:07:32Z","title":"On the well-posedness for the Ideal MHD equations in the Triebel-Lizorkin spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.0099","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:e0b121f6817e2d406a94565a230765f20b1bfb6af2299c79bc54109b25fa6b2b","target":"record","created_at":"2026-07-04T17:18:13Z","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":"3aeb4fd8fb2eea1d6036a900eff1f662842125b2ef90dcd1e7698796e0492dac","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2007-08-01T09:07:32Z","title_canon_sha256":"2c5db6aad86458535839a59689eb864b14764c9ccef5a1249ee99da93766334b"},"schema_version":"1.0","source":{"id":"0708.0099","kind":"arxiv","version":2}},"canonical_sha256":"80359afe59930f98218865551f006b82cab2c3413810525c542ccc3bc4f44528","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80359afe59930f98218865551f006b82cab2c3413810525c542ccc3bc4f44528","first_computed_at":"2026-07-04T17:18:13.679650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:18:13.679650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q0vl7vckFVcS6qaD4MMKmNNjfHMa/yisQQ7dmTIxqtsSoec9XXQkPUngtwW38uAYDIN6akfrPtIp7OFYJEs3Cg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:18:13.680072Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.0099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0b121f6817e2d406a94565a230765f20b1bfb6af2299c79bc54109b25fa6b2b","sha256:3c9a2bb7ee25f3f7b428d9096a2c4af3d9b90e297776d1cdb3a4b653793b0878"],"state_sha256":"9739cfd50ed8de30edd85dd7e6569089603c2d31e4742226b3ca513da6063b64"}