{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BGXXRZ57DM2FEQM2OR5XJVYMTH","short_pith_number":"pith:BGXXRZ57","canonical_record":{"source":{"id":"1304.5636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T14:55:53Z","cross_cats_sorted":[],"title_canon_sha256":"8523c277e237a259e1dcb23fe2c834506e604359ff44e7fa3c1b1e8b8ff1aae7","abstract_canon_sha256":"f71a9e2338b6507bee75e76913a23cbc82b4578486c91cf17c1e98cbb2c1cc38"},"schema_version":"1.0"},"canonical_sha256":"09af78e7bf1b3452419a747b74d70c99d93146f62cc47d1b125d9054847307fb","source":{"kind":"arxiv","id":"1304.5636","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5636","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5636v2","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5636","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"BGXXRZ57DM2F","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGXXRZ57DM2FEQM2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGXXRZ57","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BGXXRZ57DM2FEQM2OR5XJVYMTH","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T14:55:53Z","cross_cats_sorted":[],"title_canon_sha256":"8523c277e237a259e1dcb23fe2c834506e604359ff44e7fa3c1b1e8b8ff1aae7","abstract_canon_sha256":"f71a9e2338b6507bee75e76913a23cbc82b4578486c91cf17c1e98cbb2c1cc38"},"schema_version":"1.0"},"canonical_sha256":"09af78e7bf1b3452419a747b74d70c99d93146f62cc47d1b125d9054847307fb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:31.721673Z","signature_b64":"0fZfugOsz9VszRAFV3LdvLvVBXuIaQ8RQFyOKAnzxBt9WnZqlcrWnjS0D3axkrFL3DRqL3uCzotCFErDBbg7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09af78e7bf1b3452419a747b74d70c99d93146f62cc47d1b125d9054847307fb","last_reissued_at":"2026-05-18T02:32:31.721204Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:31.721204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5636","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qQQnlODWltpOEhhQjUWzfGKJ5LyR8jG0Rw0Tgsoaa/m21hp0eT+lQKWDsJsjD9FaEFvFQlKEYNLIQokj4k5KBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:21:01.899047Z"},"content_sha256":"1afbfd9d9d8912ce0fa9c489b6e62e5fdadde6e20bc71c68122b68e5285f82d6","schema_version":"1.0","event_id":"sha256:1afbfd9d9d8912ce0fa9c489b6e62e5fdadde6e20bc71c68122b68e5285f82d6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BGXXRZ57DM2FEQM2OR5XJVYMTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible Viscous Magnetohydrodynamic Flows","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fei Jiang, Song Jiang, Weiwei Wang","submitted_at":"2013-04-20T14:55:53Z","abstract_excerpt":"We investigate the nonlinear instability of a smooth Rayleigh-Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible nonhomogeneous magnetohydrodynamic (MHD) equations of zero resistivity in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady-state solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space $H^k$, thus leading to the linear instability. With the help of the constructed unstable solutions of the linearized"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5636","kind":"arxiv","version":2},"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":"2026-05-18T02:32:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FQ6NZ9tBql0B0S+2lNrNC7M+9Jo6UN65WVUFGSWJrEWxL3MJOoDCWUgtziHaE1x3j/bFLsq22CUYZVgH7s//Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T16:21:01.899407Z"},"content_sha256":"1dbeba7e0885bb94668c3dfb038b23738d6da1d4c7edc225c36b91b6bbab7157","schema_version":"1.0","event_id":"sha256:1dbeba7e0885bb94668c3dfb038b23738d6da1d4c7edc225c36b91b6bbab7157"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/bundle.json","state_url":"https://pith.science/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/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":"2026-06-09T16:21:01Z","links":{"resolver":"https://pith.science/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH","bundle":"https://pith.science/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/bundle.json","state":"https://pith.science/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BGXXRZ57DM2FEQM2OR5XJVYMTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BGXXRZ57DM2FEQM2OR5XJVYMTH","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":"f71a9e2338b6507bee75e76913a23cbc82b4578486c91cf17c1e98cbb2c1cc38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T14:55:53Z","title_canon_sha256":"8523c277e237a259e1dcb23fe2c834506e604359ff44e7fa3c1b1e8b8ff1aae7"},"schema_version":"1.0","source":{"id":"1304.5636","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5636","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5636v2","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5636","created_at":"2026-05-18T02:32:31Z"},{"alias_kind":"pith_short_12","alias_value":"BGXXRZ57DM2F","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BGXXRZ57DM2FEQM2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BGXXRZ57","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:1dbeba7e0885bb94668c3dfb038b23738d6da1d4c7edc225c36b91b6bbab7157","target":"graph","created_at":"2026-05-18T02:32:31Z","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 investigate the nonlinear instability of a smooth Rayleigh-Taylor steady-state solution (including the case of heavier density with increasing height) to the three-dimensional incompressible nonhomogeneous magnetohydrodynamic (MHD) equations of zero resistivity in the presence of a uniform gravitational field. We first analyze the linearized equations around the steady-state solution. Then we construct solutions of the linearized problem that grow in time in the Sobolev space $H^k$, thus leading to the linear instability. With the help of the constructed unstable solutions of the linearized","authors_text":"Fei Jiang, Song Jiang, Weiwei Wang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T14:55:53Z","title":"Nonlinear Rayleigh-Taylor Instability for Nonhomogeneous Incompressible Viscous Magnetohydrodynamic Flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5636","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":"sha256:1afbfd9d9d8912ce0fa9c489b6e62e5fdadde6e20bc71c68122b68e5285f82d6","target":"record","created_at":"2026-05-18T02:32:31Z","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":"f71a9e2338b6507bee75e76913a23cbc82b4578486c91cf17c1e98cbb2c1cc38","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-20T14:55:53Z","title_canon_sha256":"8523c277e237a259e1dcb23fe2c834506e604359ff44e7fa3c1b1e8b8ff1aae7"},"schema_version":"1.0","source":{"id":"1304.5636","kind":"arxiv","version":2}},"canonical_sha256":"09af78e7bf1b3452419a747b74d70c99d93146f62cc47d1b125d9054847307fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"09af78e7bf1b3452419a747b74d70c99d93146f62cc47d1b125d9054847307fb","first_computed_at":"2026-05-18T02:32:31.721204Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:32:31.721204Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0fZfugOsz9VszRAFV3LdvLvVBXuIaQ8RQFyOKAnzxBt9WnZqlcrWnjS0D3axkrFL3DRqL3uCzotCFErDBbg7AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:32:31.721673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5636","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1afbfd9d9d8912ce0fa9c489b6e62e5fdadde6e20bc71c68122b68e5285f82d6","sha256:1dbeba7e0885bb94668c3dfb038b23738d6da1d4c7edc225c36b91b6bbab7157"],"state_sha256":"1f8a120c72ffe6123e964d62a73e3d6e4e699ab4ae188c1c67c9431aa5ca949c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y61oLuw441A4HTLLb3NOBye3J/uMjotXXs3rKIw1J+HgRCYHaBe9eWvN8WyF2LNVUFGRovRtxRaIg1nM5vjbDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T16:21:01.901380Z","bundle_sha256":"4bea47aa762b52f323b5af23ff1a79f3678c8b7b4a5eba9d9f36ea9ef74898d1"}}