{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M7XIVU3GVEAORNOGGWUCJ7HCGG","short_pith_number":"pith:M7XIVU3G","canonical_record":{"source":{"id":"1411.0917","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T14:18:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d3cb317e4e83b016f972a58920746b32ddf72e2328ded4b53edd7f39208e93da","abstract_canon_sha256":"8d2355f3db511dd114a5f6457da7be07f00513356147ce99ad616ef1b2ce0b7c"},"schema_version":"1.0"},"canonical_sha256":"67ee8ad366a900e8b5c635a824fce23180c9d87de306c7bb60d9a301a731566b","source":{"kind":"arxiv","id":"1411.0917","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0917","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0917v3","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0917","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"M7XIVU3GVEAO","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M7XIVU3GVEAORNOG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M7XIVU3G","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M7XIVU3GVEAORNOGGWUCJ7HCGG","target":"record","payload":{"canonical_record":{"source":{"id":"1411.0917","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T14:18:56Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d3cb317e4e83b016f972a58920746b32ddf72e2328ded4b53edd7f39208e93da","abstract_canon_sha256":"8d2355f3db511dd114a5f6457da7be07f00513356147ce99ad616ef1b2ce0b7c"},"schema_version":"1.0"},"canonical_sha256":"67ee8ad366a900e8b5c635a824fce23180c9d87de306c7bb60d9a301a731566b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:39.141657Z","signature_b64":"xLL/32eKnCbkFm54Zx16SI1ww3AIZVFXjotByU0atDIHWrDl8uI9xo8nCWBITHzF9vcJCvTZY9txCi8P4tetCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ee8ad366a900e8b5c635a824fce23180c9d87de306c7bb60d9a301a731566b","last_reissued_at":"2026-05-18T00:44:39.141198Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:39.141198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.0917","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nGMfrnTVe4o31WoP6ShSW9eQNt1gicJWZ0Q+UjKonhliSGdw/1wVNs9J6xO6Kr3BzpHICKyb+0Il9JcJJQTkCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:38:16.812617Z"},"content_sha256":"95f9de33660df89270faefebb4b3c5c330a48a76b6451e0fe94f60319ae8e859","schema_version":"1.0","event_id":"sha256:95f9de33660df89270faefebb4b3c5c330a48a76b6451e0fe94f60319ae8e859"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M7XIVU3GVEAORNOGGWUCJ7HCGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global well posedness for a two-fluid model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Shengyi Shen, Slim Ibrahim, Tsuyoshi Yoneda, Yoshikazu Giga","submitted_at":"2014-11-04T14:18:56Z","abstract_excerpt":"We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions \\`a la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial da"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0917","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"2026-05-18T00:44:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kyGhcdvxQof+6gWdxUuJBNnNBm6VTScO9caeIrlL/WdOZMalYylhawKdy3i6ReYmNAHZpfXRHNM6kyon1M1pDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T07:38:16.812960Z"},"content_sha256":"527426de0d63d7f3378ebdd21934c9cc46c4fd3bc7ccc30da83ae2e6c4c2cf00","schema_version":"1.0","event_id":"sha256:527426de0d63d7f3378ebdd21934c9cc46c4fd3bc7ccc30da83ae2e6c4c2cf00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/bundle.json","state_url":"https://pith.science/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/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":"2026-06-20T07:38:16Z","links":{"resolver":"https://pith.science/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG","bundle":"https://pith.science/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/bundle.json","state":"https://pith.science/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M7XIVU3GVEAORNOGGWUCJ7HCGG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M7XIVU3GVEAORNOGGWUCJ7HCGG","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":"8d2355f3db511dd114a5f6457da7be07f00513356147ce99ad616ef1b2ce0b7c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T14:18:56Z","title_canon_sha256":"d3cb317e4e83b016f972a58920746b32ddf72e2328ded4b53edd7f39208e93da"},"schema_version":"1.0","source":{"id":"1411.0917","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0917","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0917v3","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0917","created_at":"2026-05-18T00:44:39Z"},{"alias_kind":"pith_short_12","alias_value":"M7XIVU3GVEAO","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M7XIVU3GVEAORNOG","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M7XIVU3G","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:527426de0d63d7f3378ebdd21934c9cc46c4fd3bc7ccc30da83ae2e6c4c2cf00","target":"graph","created_at":"2026-05-18T00:44:39Z","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":"We study a two fluid system which models the motion of a charged fluid with Rayleigh friction, and in the presence of an electro-magnetic field satisfying Maxwell's equations. We study the well-posdness of the system in both space dimensions two and three. Regardless of the size of the initial data, we first prove the global well-posedness of the Cauchy problem when the space dimension is two. However, in space dimension three, we construct global weak-solutions \\`a la Leray, and we prove the local well-posedness of Kato-type solutions. These solutions turn out to be global when the initial da","authors_text":"Shengyi Shen, Slim Ibrahim, Tsuyoshi Yoneda, Yoshikazu Giga","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T14:18:56Z","title":"Global well posedness for a two-fluid model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0917","kind":"arxiv","version":3},"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":"sha256:95f9de33660df89270faefebb4b3c5c330a48a76b6451e0fe94f60319ae8e859","target":"record","created_at":"2026-05-18T00:44:39Z","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":"8d2355f3db511dd114a5f6457da7be07f00513356147ce99ad616ef1b2ce0b7c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-11-04T14:18:56Z","title_canon_sha256":"d3cb317e4e83b016f972a58920746b32ddf72e2328ded4b53edd7f39208e93da"},"schema_version":"1.0","source":{"id":"1411.0917","kind":"arxiv","version":3}},"canonical_sha256":"67ee8ad366a900e8b5c635a824fce23180c9d87de306c7bb60d9a301a731566b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ee8ad366a900e8b5c635a824fce23180c9d87de306c7bb60d9a301a731566b","first_computed_at":"2026-05-18T00:44:39.141198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:39.141198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xLL/32eKnCbkFm54Zx16SI1ww3AIZVFXjotByU0atDIHWrDl8uI9xo8nCWBITHzF9vcJCvTZY9txCi8P4tetCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:39.141657Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0917","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:95f9de33660df89270faefebb4b3c5c330a48a76b6451e0fe94f60319ae8e859","sha256:527426de0d63d7f3378ebdd21934c9cc46c4fd3bc7ccc30da83ae2e6c4c2cf00"],"state_sha256":"4d92266da86f91d831bb949236002483ae3f7b2bafb6bfdc89173408569c9de7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tzAp4kbekxJhLuidbsxGGPzCLkiYBmaIB2thUECnJah4R1LYxSH1uo7nufuNiOe536zXqjohzhgRX5uTeREpBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T07:38:16.814865Z","bundle_sha256":"99a969dde706a38d82c8278749ebc37f3a567bb52723cd6d89ac3d28da0f84bc"}}