{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4JOJSPTUIPHIMCCL4MUTFF2NDR","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":"f5e3b928f678b77c300088568177a337315cdcbd21a29c5b395b9272fb48fb27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-03T23:02:04Z","title_canon_sha256":"98e3ee22aa8d45a63c26545eba9d5f9a8d7aacb93a371474444cf9063f71238c"},"schema_version":"1.0","source":{"id":"1402.0542","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.0542","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"arxiv_version","alias_value":"1402.0542v2","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0542","created_at":"2026-05-18T02:41:01Z"},{"alias_kind":"pith_short_12","alias_value":"4JOJSPTUIPHI","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4JOJSPTUIPHIMCCL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4JOJSPTU","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:c93f4689ff1582b1ecc19e791666dfdf79ef5624d8e18a61caccffdcf343e769","target":"graph","created_at":"2026-05-18T02:41:01Z","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, the 3-D compressible MHD equations with initial vacuum or infinity electric conductivity is considered. We prove that the $L^\\infty$ norms of the deformation tensor $D(u)$ and the absolute temperature $\\theta$ control the possible blow-up (see [5][18][20]) for strong solutions, which means that if a solution of the compressible MHD equations is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of $D(u)$ and $\\theta$ as the critical time approaches. The viscosity coefficients are only restricted by ","authors_text":"Shengguo Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-03T23:02:04Z","title":"Blow-up criterion for the compressible magnetohydrodynamic equations with vacuum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0542","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":"sha256:29074b75efcf8ca28b0a29d5cfa72959f7cc1fa9a1de3eaa597a9e3920faadd0","target":"record","created_at":"2026-05-18T02:41:01Z","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":"f5e3b928f678b77c300088568177a337315cdcbd21a29c5b395b9272fb48fb27","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-02-03T23:02:04Z","title_canon_sha256":"98e3ee22aa8d45a63c26545eba9d5f9a8d7aacb93a371474444cf9063f71238c"},"schema_version":"1.0","source":{"id":"1402.0542","kind":"arxiv","version":2}},"canonical_sha256":"e25c993e7443ce86084be32932974d1c689cd2abc252a87b91641decaa6f65ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e25c993e7443ce86084be32932974d1c689cd2abc252a87b91641decaa6f65ee","first_computed_at":"2026-05-18T02:41:01.741975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:01.741975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EI9K8bYl9j/DhhyBCAcIc+2Wj2Txhff1B47AV5VXLBfZ5+0fYv7RzOs091Hc3RBF9DGaROGtGAaYvqCo3tlXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:01.742469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.0542","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29074b75efcf8ca28b0a29d5cfa72959f7cc1fa9a1de3eaa597a9e3920faadd0","sha256:c93f4689ff1582b1ecc19e791666dfdf79ef5624d8e18a61caccffdcf343e769"],"state_sha256":"f6f040fbda6f30bd30b2dd6850a3aee1078521d197d1e1f74a20cc41eb06d0a5"}