{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:7KB2O7BRAJWDEVIKRL6Y7R7EEV","short_pith_number":"pith:7KB2O7BR","schema_version":"1.0","canonical_sha256":"fa83a77c31026c32550a8afd8fc7e4255c15c862a3f34b5e9ceac945b685bc33","source":{"kind":"arxiv","id":"1806.03427","version":2},"attestation_state":"computed","paper":{"title":"On some Liouville type theorems for the stationary equations of MHD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pan Liu, Zhouyu Li","submitted_at":"2018-06-09T07:16:59Z","abstract_excerpt":"We prove several Liouville type results for the stationary Hall-MHD and MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1806.03427","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-06-09T07:16:59Z","cross_cats_sorted":[],"title_canon_sha256":"8edebd323fdbf28adf62c3c292e55726eca45bce3b420d14b7d5a0164a2c8f9d","abstract_canon_sha256":"017bf804dfcb080f167a51abebb5cf984e2b080f2398254f296a483c67413503"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:24.121705Z","signature_b64":"hZ/iWpev5s/5XKF376iDEXKAdWBoMr9e1e5oSiVxyv0Cyqe4Q7nkiaiRfrzpwIQ/bRuNV2zjvRyt2coWCmioAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fa83a77c31026c32550a8afd8fc7e4255c15c862a3f34b5e9ceac945b685bc33","last_reissued_at":"2026-05-18T00:12:24.121052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:24.121052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some Liouville type theorems for the stationary equations of MHD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pan Liu, Zhouyu Li","submitted_at":"2018-06-09T07:16:59Z","abstract_excerpt":"We prove several Liouville type results for the stationary Hall-MHD and MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.03427","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1806.03427","created_at":"2026-05-18T00:12:24.121140+00:00"},{"alias_kind":"arxiv_version","alias_value":"1806.03427v2","created_at":"2026-05-18T00:12:24.121140+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.03427","created_at":"2026-05-18T00:12:24.121140+00:00"},{"alias_kind":"pith_short_12","alias_value":"7KB2O7BRAJWD","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_16","alias_value":"7KB2O7BRAJWDEVIK","created_at":"2026-05-18T12:32:11.075285+00:00"},{"alias_kind":"pith_short_8","alias_value":"7KB2O7BR","created_at":"2026-05-18T12:32:11.075285+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV","json":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV.json","graph_json":"https://pith.science/api/pith-number/7KB2O7BRAJWDEVIKRL6Y7R7EEV/graph.json","events_json":"https://pith.science/api/pith-number/7KB2O7BRAJWDEVIKRL6Y7R7EEV/events.json","paper":"https://pith.science/paper/7KB2O7BR"},"agent_actions":{"view_html":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV","download_json":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV.json","view_paper":"https://pith.science/paper/7KB2O7BR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1806.03427&json=true","fetch_graph":"https://pith.science/api/pith-number/7KB2O7BRAJWDEVIKRL6Y7R7EEV/graph.json","fetch_events":"https://pith.science/api/pith-number/7KB2O7BRAJWDEVIKRL6Y7R7EEV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV/action/storage_attestation","attest_author":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV/action/author_attestation","sign_citation":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV/action/citation_signature","submit_replication":"https://pith.science/pith/7KB2O7BRAJWDEVIKRL6Y7R7EEV/action/replication_record"}},"created_at":"2026-05-18T00:12:24.121140+00:00","updated_at":"2026-05-18T00:12:24.121140+00:00"}