{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ETQLQZ55TP3H7URNTG47Y44SD3","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":"d68013b4de76e157c80d22dffe2523b93e382ff720d5c1a49ad793c2563302e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-28T04:03:41Z","title_canon_sha256":"5661b79875597e3e5ba3d75898559107e75c001bf2a3b3e5238ca109301f772c"},"schema_version":"1.0","source":{"id":"1109.6089","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.6089","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"arxiv_version","alias_value":"1109.6089v1","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.6089","created_at":"2026-05-18T04:12:09Z"},{"alias_kind":"pith_short_12","alias_value":"ETQLQZ55TP3H","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"ETQLQZ55TP3H7URN","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"ETQLQZ55","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:9d86ad25fc784d75c726b306759df92376a94cf4350434fc900f60718fd6007d","target":"graph","created_at":"2026-05-18T04:12:09Z","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":"Existence of local-in-time unique solution and loss of smoothness of full Magnet-Hydro-Dynamics system (MHD) is considered for periodic initial data. The result is proven using Fujita-Kato's method in $\\ell^1$ based (for the Fourier coefficients) functional spaces enabling us to easily estimate nonlinear terms in the system as well as solutions to Maxwells's equations. A loss of smoothness result is shown for the velocity and magnetic field. It comes from the damped-wave operator which does not have any smoothing effect.","authors_text":"Slim Ibrahim, Tsuyoshi Yoneda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-28T04:03:41Z","title":"Local solvability and loss of smoothness of the Navier-Stokes-Maxwell equations with large initial data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6089","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:fdbb91bc47f215745c81616b3a8f2c234718266cb14d82ec8afd67baeeadcf12","target":"record","created_at":"2026-05-18T04:12:09Z","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":"d68013b4de76e157c80d22dffe2523b93e382ff720d5c1a49ad793c2563302e6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-28T04:03:41Z","title_canon_sha256":"5661b79875597e3e5ba3d75898559107e75c001bf2a3b3e5238ca109301f772c"},"schema_version":"1.0","source":{"id":"1109.6089","kind":"arxiv","version":1}},"canonical_sha256":"24e0b867bd9bf67fd22d99b9fc73921ec0221baa14f647529e2995d8fbe19a31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24e0b867bd9bf67fd22d99b9fc73921ec0221baa14f647529e2995d8fbe19a31","first_computed_at":"2026-05-18T04:12:09.763877Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:09.763877Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HRIIUcsJdp/iPzjbeeJryAojh7ChM2VF+StH47rnficSYIJHOHFZPve1UlqGygr9S9rNb3aUE4essiA7moOcAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:09.764393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.6089","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fdbb91bc47f215745c81616b3a8f2c234718266cb14d82ec8afd67baeeadcf12","sha256:9d86ad25fc784d75c726b306759df92376a94cf4350434fc900f60718fd6007d"],"state_sha256":"3568f37fe8696b1336e92e55e6ed84809013a24712be80e5539d0cfa096bab53"}