{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:FQX56KLROD6TISCUVID73UGHZP","short_pith_number":"pith:FQX56KLR","canonical_record":{"source":{"id":"1803.00393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"af3f8efd90b7177781d86a1fd717b412ed27aaacfe1de662e524b6004eaead04","abstract_canon_sha256":"7a5329aef3e0bae0c0331d9ae3a495ae95045bbdb9d74a0d982d594ed1bc40ad"},"schema_version":"1.0"},"canonical_sha256":"2c2fdf297170fd344854aa07fdd0c7cbf06164e096b7204c5772bf57ffe3ba40","source":{"kind":"arxiv","id":"1803.00393","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00393","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00393v2","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00393","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"FQX56KLROD6T","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FQX56KLROD6TISCU","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FQX56KLR","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:FQX56KLROD6TISCUVID73UGHZP","target":"record","payload":{"canonical_record":{"source":{"id":"1803.00393","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:45:04Z","cross_cats_sorted":[],"title_canon_sha256":"af3f8efd90b7177781d86a1fd717b412ed27aaacfe1de662e524b6004eaead04","abstract_canon_sha256":"7a5329aef3e0bae0c0331d9ae3a495ae95045bbdb9d74a0d982d594ed1bc40ad"},"schema_version":"1.0"},"canonical_sha256":"2c2fdf297170fd344854aa07fdd0c7cbf06164e096b7204c5772bf57ffe3ba40","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:43.383739Z","signature_b64":"nkjTzKP+ZWeXBQNC1uxSP/BKiI5oh71+TsuzSmFY17jtHFh998WZk/i50R64sHPJat24j1UGHIuhQGpkql3VCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c2fdf297170fd344854aa07fdd0c7cbf06164e096b7204c5772bf57ffe3ba40","last_reissued_at":"2026-05-18T00:12:43.383114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:43.383114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.00393","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":"2026-05-18T00:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EP252rOsJSetyJ77z2+jdQvz5j9U9DDzm+pw8GTRN7nNqKukhdPVEms8UlYVl6lzgzWCdb3gQq5k94Tj89hOCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:58:56.276504Z"},"content_sha256":"424d2c1b1063bb7b1d8ac8872d7096e2e3291a21dc01221dffa4758a26953260","schema_version":"1.0","event_id":"sha256:424d2c1b1063bb7b1d8ac8872d7096e2e3291a21dc01221dffa4758a26953260"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:FQX56KLROD6TISCUVID73UGHZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lifespan of Solution to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Feng Xie, Tong Yang","submitted_at":"2018-03-01T14:45:04Z","abstract_excerpt":"In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in \\cite{LXY1}, the lifespan of solution is shown to have a lower bound in the order of $\\varepsilon^{-2+}$ if the strength of the perturbation is of the order of $\\varepsilon$. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00393","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":"2026-05-18T00:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CmDfos7qxqNJuwvnvHHWQGWdWwgYGsOoxpZ4A8X5/BCM5qySX3LMflTEgA5POItV1c5DuctYvBQCF4wR4QwdAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T15:58:56.276943Z"},"content_sha256":"a8f79892b702b2aa4e5bb0f575b6b52a30e5c58eb3b52f08ba4998c57208a313","schema_version":"1.0","event_id":"sha256:a8f79892b702b2aa4e5bb0f575b6b52a30e5c58eb3b52f08ba4998c57208a313"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FQX56KLROD6TISCUVID73UGHZP/bundle.json","state_url":"https://pith.science/pith/FQX56KLROD6TISCUVID73UGHZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FQX56KLROD6TISCUVID73UGHZP/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":"2026-05-25T15:58:56Z","links":{"resolver":"https://pith.science/pith/FQX56KLROD6TISCUVID73UGHZP","bundle":"https://pith.science/pith/FQX56KLROD6TISCUVID73UGHZP/bundle.json","state":"https://pith.science/pith/FQX56KLROD6TISCUVID73UGHZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FQX56KLROD6TISCUVID73UGHZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:FQX56KLROD6TISCUVID73UGHZP","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":"7a5329aef3e0bae0c0331d9ae3a495ae95045bbdb9d74a0d982d594ed1bc40ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:45:04Z","title_canon_sha256":"af3f8efd90b7177781d86a1fd717b412ed27aaacfe1de662e524b6004eaead04"},"schema_version":"1.0","source":{"id":"1803.00393","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.00393","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1803.00393v2","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.00393","created_at":"2026-05-18T00:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"FQX56KLROD6T","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"FQX56KLROD6TISCU","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"FQX56KLR","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:a8f79892b702b2aa4e5bb0f575b6b52a30e5c58eb3b52f08ba4998c57208a313","target":"graph","created_at":"2026-05-18T00:12:43Z","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":"In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in \\cite{LXY1}, the lifespan of solution is shown to have a lower bound in the order of $\\varepsilon^{-2+}$ if the strength of the perturbation is of the order of $\\varepsilon$. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field","authors_text":"Feng Xie, Tong Yang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:45:04Z","title":"Lifespan of Solution to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.00393","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":"sha256:424d2c1b1063bb7b1d8ac8872d7096e2e3291a21dc01221dffa4758a26953260","target":"record","created_at":"2026-05-18T00:12:43Z","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":"7a5329aef3e0bae0c0331d9ae3a495ae95045bbdb9d74a0d982d594ed1bc40ad","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-03-01T14:45:04Z","title_canon_sha256":"af3f8efd90b7177781d86a1fd717b412ed27aaacfe1de662e524b6004eaead04"},"schema_version":"1.0","source":{"id":"1803.00393","kind":"arxiv","version":2}},"canonical_sha256":"2c2fdf297170fd344854aa07fdd0c7cbf06164e096b7204c5772bf57ffe3ba40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2c2fdf297170fd344854aa07fdd0c7cbf06164e096b7204c5772bf57ffe3ba40","first_computed_at":"2026-05-18T00:12:43.383114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:43.383114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nkjTzKP+ZWeXBQNC1uxSP/BKiI5oh71+TsuzSmFY17jtHFh998WZk/i50R64sHPJat24j1UGHIuhQGpkql3VCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:43.383739Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.00393","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:424d2c1b1063bb7b1d8ac8872d7096e2e3291a21dc01221dffa4758a26953260","sha256:a8f79892b702b2aa4e5bb0f575b6b52a30e5c58eb3b52f08ba4998c57208a313"],"state_sha256":"e30b38fdea2a54296179b8cb68d361b7940ca6414e96242f3f2c5808f7cf09eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twSYmKa+X1yhhKPhKMuMWM5Il8z6cPPLIupX1L156gZ7DiBWVBAnE+FZdF9m7V868AsyxMsf2BeM35DQ/3/dCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T15:58:56.280102Z","bundle_sha256":"b440ed03815c7e4f052bdab6431d425e45a942f8b04560159fdd0d9e3db2fd1b"}}