{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PIRDG2OBCCUZEECQE3E2W6KGBG","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":"0fec947acd51e03093cbb048296bc48e012b53a9c4a38f80288f66b5349a9567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-25T04:58:43Z","title_canon_sha256":"3feca49c8666c37adc7e6481aebf33e9907923c7e0dca08eecf58afc408ed8ef"},"schema_version":"1.0","source":{"id":"2506.20131","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.20131","created_at":"2026-07-05T11:27:00Z"},{"alias_kind":"arxiv_version","alias_value":"2506.20131v1","created_at":"2026-07-05T11:27:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.20131","created_at":"2026-07-05T11:27:00Z"},{"alias_kind":"pith_short_12","alias_value":"PIRDG2OBCCUZ","created_at":"2026-07-05T11:27:00Z"},{"alias_kind":"pith_short_16","alias_value":"PIRDG2OBCCUZEECQ","created_at":"2026-07-05T11:27:00Z"},{"alias_kind":"pith_short_8","alias_value":"PIRDG2OB","created_at":"2026-07-05T11:27:00Z"}],"graph_snapshots":[{"event_id":"sha256:1c75bd840137180f5f68b5785769aeffe9b33eef2e4de4f2f0f7a2226e4855fd","target":"graph","created_at":"2026-07-05T11:27:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.20131/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the axisymmetric self-similar solutions $(\\mathbf{u},\\mathbf{B})$ to the stationary MHD equations without magnetic diffusion, where $\\mathbf{B}$ has only the swirl component. Our first result states that in $\\mathbb{R}^3\\setminus\\{0\\}$, $\\mathbf{u}$ is a Landau solution and $\\mathbf{B}=0$. Our second result proves the triviality of axisymmetric self-similar solutions in the half-space $\\mathbb{R}^3_+$ with the no-slip boundary condition or the Navier slip boundary condition.","authors_text":"Shaoheng Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-25T04:58:43Z","title":"Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.20131","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:d4fdcbc9555176b8a4aac8355d69b7545cc34504b972a3536c73a1fb2fd39663","target":"record","created_at":"2026-07-05T11:27:00Z","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":"0fec947acd51e03093cbb048296bc48e012b53a9c4a38f80288f66b5349a9567","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-06-25T04:58:43Z","title_canon_sha256":"3feca49c8666c37adc7e6481aebf33e9907923c7e0dca08eecf58afc408ed8ef"},"schema_version":"1.0","source":{"id":"2506.20131","kind":"arxiv","version":1}},"canonical_sha256":"7a223369c110a992105026c9ab794609bc4ca5b3326e1d025e06d4bb24e65c66","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7a223369c110a992105026c9ab794609bc4ca5b3326e1d025e06d4bb24e65c66","first_computed_at":"2026-07-05T11:27:00.790972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:27:00.790972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bHD0X/U6GNE8rkBIOsZKeju5Pnda8C5fF0EalhVgWCqB73dWwpwUuBvlaovZf7LRcOGUF+c0wHWld+njxm/9DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:27:00.791450Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.20131","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d4fdcbc9555176b8a4aac8355d69b7545cc34504b972a3536c73a1fb2fd39663","sha256:1c75bd840137180f5f68b5785769aeffe9b33eef2e4de4f2f0f7a2226e4855fd"],"state_sha256":"7d11c7b8561af3f13cfa99f8e7659f07468253a632f13b29313f4cd1a656ba0e"}