{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BXXDE45Q3I2B2YBOQRVMNFDH2F","short_pith_number":"pith:BXXDE45Q","canonical_record":{"source":{"id":"1702.08209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-27T09:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"7b27bbbfe4c4e5f8fa2e861fd66899f35fa86e21c94b00474307eab3b2607406","abstract_canon_sha256":"b8b41267c7d6277810c40181bc1941cf22e8669da731225f9ecde097c254b12a"},"schema_version":"1.0"},"canonical_sha256":"0dee3273b0da341d602e846ac69467d16bc409302af89eb72507e74f114bbeb7","source":{"kind":"arxiv","id":"1702.08209","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08209","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08209v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08209","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"BXXDE45Q3I2B","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BXXDE45Q3I2B2YBO","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BXXDE45Q","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BXXDE45Q3I2B2YBOQRVMNFDH2F","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08209","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-27T09:55:29Z","cross_cats_sorted":[],"title_canon_sha256":"7b27bbbfe4c4e5f8fa2e861fd66899f35fa86e21c94b00474307eab3b2607406","abstract_canon_sha256":"b8b41267c7d6277810c40181bc1941cf22e8669da731225f9ecde097c254b12a"},"schema_version":"1.0"},"canonical_sha256":"0dee3273b0da341d602e846ac69467d16bc409302af89eb72507e74f114bbeb7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:55.590811Z","signature_b64":"2CfVAvC+CPWmdY+ZssUNxZJ8eg320ksUpPR1kPnFuMmYL5ZG1BEmUAcn6MfYq+9EBbNeBVfmkjg6JVufbbEvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0dee3273b0da341d602e846ac69467d16bc409302af89eb72507e74f114bbeb7","last_reissued_at":"2026-05-18T00:49:55.590080Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:55.590080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08209","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qi6GJjaSe1UoBX1ViUqmDbF6X4pLweDiR27fNs6DYv56Xz/L9cKcs5JHRTDXW3IhoOmm+qyvuoZK/mQ0EEYQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:25:09.599424Z"},"content_sha256":"ac3cbf029759437a90b45a3f06323b6fcaf4fcc2e62481cac4f45f821c061b01","schema_version":"1.0","event_id":"sha256:ac3cbf029759437a90b45a3f06323b6fcaf4fcc2e62481cac4f45f821c061b01"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BXXDE45Q3I2B2YBOQRVMNFDH2F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dongfen Bian, Jitao Liu","submitted_at":"2017-02-27T09:55:29Z","abstract_excerpt":"This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay estimate of the solution is obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08209","kind":"arxiv","version":1},"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":"2026-05-18T00:49:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KoCPeR3d69qKd8vDupIco5poE71+OsoIo47baye1zKZo27J6PZ9IUA9evSMjIs8fA+HUKlBO2IGm5cRAZZGxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:25:09.600101Z"},"content_sha256":"a30920272b9c84b918cf104a0f3ab1b2d084f94d418761d0a1f9b476faf52525","schema_version":"1.0","event_id":"sha256:a30920272b9c84b918cf104a0f3ab1b2d084f94d418761d0a1f9b476faf52525"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/bundle.json","state_url":"https://pith.science/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/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":"2026-05-27T13:25:09Z","links":{"resolver":"https://pith.science/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F","bundle":"https://pith.science/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/bundle.json","state":"https://pith.science/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BXXDE45Q3I2B2YBOQRVMNFDH2F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BXXDE45Q3I2B2YBOQRVMNFDH2F","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":"b8b41267c7d6277810c40181bc1941cf22e8669da731225f9ecde097c254b12a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-27T09:55:29Z","title_canon_sha256":"7b27bbbfe4c4e5f8fa2e861fd66899f35fa86e21c94b00474307eab3b2607406"},"schema_version":"1.0","source":{"id":"1702.08209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08209","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08209v1","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08209","created_at":"2026-05-18T00:49:55Z"},{"alias_kind":"pith_short_12","alias_value":"BXXDE45Q3I2B","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BXXDE45Q3I2B2YBO","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BXXDE45Q","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:a30920272b9c84b918cf104a0f3ab1b2d084f94d418761d0a1f9b476faf52525","target":"graph","created_at":"2026-05-18T00:49:55Z","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":"This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay estimate of the solution is obtained.","authors_text":"Dongfen Bian, Jitao Liu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-27T09:55:29Z","title":"Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08209","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:ac3cbf029759437a90b45a3f06323b6fcaf4fcc2e62481cac4f45f821c061b01","target":"record","created_at":"2026-05-18T00:49:55Z","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":"b8b41267c7d6277810c40181bc1941cf22e8669da731225f9ecde097c254b12a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-02-27T09:55:29Z","title_canon_sha256":"7b27bbbfe4c4e5f8fa2e861fd66899f35fa86e21c94b00474307eab3b2607406"},"schema_version":"1.0","source":{"id":"1702.08209","kind":"arxiv","version":1}},"canonical_sha256":"0dee3273b0da341d602e846ac69467d16bc409302af89eb72507e74f114bbeb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0dee3273b0da341d602e846ac69467d16bc409302af89eb72507e74f114bbeb7","first_computed_at":"2026-05-18T00:49:55.590080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:55.590080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2CfVAvC+CPWmdY+ZssUNxZJ8eg320ksUpPR1kPnFuMmYL5ZG1BEmUAcn6MfYq+9EBbNeBVfmkjg6JVufbbEvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:55.590811Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac3cbf029759437a90b45a3f06323b6fcaf4fcc2e62481cac4f45f821c061b01","sha256:a30920272b9c84b918cf104a0f3ab1b2d084f94d418761d0a1f9b476faf52525"],"state_sha256":"fc7d5c2b8ee4cc1f945eb0f88486f7f69ef1d1be05caaae5b56db1a2636a3a30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O3pKUQuRzSL6RdhaqhVBkpVX/ZwQE51KFcfKzB6pVCg3TGhQF8fwaXF6mfVxlIZv84yFSoLxYvCWJormPE4TBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:25:09.603623Z","bundle_sha256":"0ca329c78864c74f8142e6b6c69ad2b9b4773271207729d15795d78ec5788190"}}