{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:K6BDJHV55NAI3K4BOFCR7H35TG","short_pith_number":"pith:K6BDJHV5","schema_version":"1.0","canonical_sha256":"5782349ebdeb408dab8171451f9f7d999d763ba300f0f17bf5086dc5f20107b6","source":{"kind":"arxiv","id":"1412.3519","version":1},"attestation_state":"computed","paper":{"title":"On a power-type coupled system of Monge-Amp\\`{e}re equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zexin Qi, Zhitao Zhang","submitted_at":"2014-12-11T02:18:47Z","abstract_excerpt":"We study an elliptic system coupled by Monge-Amp\\`{e}re equations:\n  \\begin{center}\n  $\\left\\{\n  \\begin{array}{ll}\n  det~D^{2}u_{1}={(-u_{2})}^\\alpha, & \\hbox{in $\\Omega,$}\n  det~D^{2}u_{2}={(-u_{1})}^\\beta, & \\hbox{in $\\Omega,$}\n  u_{1}<0, u_{2}<0,& \\hbox{in $\\Omega,$}\n  u_{1}=u_{2}=0, & \\hbox{on $ \\partial \\Omega,$}\n  \\end{array}\n  \\right.$\n  \\end{center} here $\\Omega$~is a smooth, bounded and strictly convex domain in~$\\mathbb{R}^{N}$,~$N\\geq2,~\\alpha >0,~\\beta >0$. When $\\Omega$ is the unit ball in $\\mathbb{R}^{N}$, we use index theory of fixed points for completely continuous operators to"},"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":"1412.3519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-12-11T02:18:47Z","cross_cats_sorted":[],"title_canon_sha256":"fa44189d2ef5c6d76cc78721590e23c52cef481c6abc00db21ca21946f3addcb","abstract_canon_sha256":"60f22c46878c11a153258716795f7e0314b82d1d706d40a9a061c1ab242dc62b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:30.919958Z","signature_b64":"bppXuOnLSUI/7VVFe6Y8OPC6Y2HvRY0cfazp5MWU9oOwCR9SQHOhcrBIkRNW9DGAKp7pLoXnuGqH9b4FlJnjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5782349ebdeb408dab8171451f9f7d999d763ba300f0f17bf5086dc5f20107b6","last_reissued_at":"2026-05-18T02:31:30.919374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:30.919374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On a power-type coupled system of Monge-Amp\\`{e}re equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Zexin Qi, Zhitao Zhang","submitted_at":"2014-12-11T02:18:47Z","abstract_excerpt":"We study an elliptic system coupled by Monge-Amp\\`{e}re equations:\n  \\begin{center}\n  $\\left\\{\n  \\begin{array}{ll}\n  det~D^{2}u_{1}={(-u_{2})}^\\alpha, & \\hbox{in $\\Omega,$}\n  det~D^{2}u_{2}={(-u_{1})}^\\beta, & \\hbox{in $\\Omega,$}\n  u_{1}<0, u_{2}<0,& \\hbox{in $\\Omega,$}\n  u_{1}=u_{2}=0, & \\hbox{on $ \\partial \\Omega,$}\n  \\end{array}\n  \\right.$\n  \\end{center} here $\\Omega$~is a smooth, bounded and strictly convex domain in~$\\mathbb{R}^{N}$,~$N\\geq2,~\\alpha >0,~\\beta >0$. When $\\Omega$ is the unit ball in $\\mathbb{R}^{N}$, we use index theory of fixed points for completely continuous operators to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.3519","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1412.3519","created_at":"2026-05-18T02:31:30.919482+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.3519v1","created_at":"2026-05-18T02:31:30.919482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.3519","created_at":"2026-05-18T02:31:30.919482+00:00"},{"alias_kind":"pith_short_12","alias_value":"K6BDJHV55NAI","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_16","alias_value":"K6BDJHV55NAI3K4B","created_at":"2026-05-18T12:28:35.611951+00:00"},{"alias_kind":"pith_short_8","alias_value":"K6BDJHV5","created_at":"2026-05-18T12:28:35.611951+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/K6BDJHV55NAI3K4BOFCR7H35TG","json":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG.json","graph_json":"https://pith.science/api/pith-number/K6BDJHV55NAI3K4BOFCR7H35TG/graph.json","events_json":"https://pith.science/api/pith-number/K6BDJHV55NAI3K4BOFCR7H35TG/events.json","paper":"https://pith.science/paper/K6BDJHV5"},"agent_actions":{"view_html":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG","download_json":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG.json","view_paper":"https://pith.science/paper/K6BDJHV5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.3519&json=true","fetch_graph":"https://pith.science/api/pith-number/K6BDJHV55NAI3K4BOFCR7H35TG/graph.json","fetch_events":"https://pith.science/api/pith-number/K6BDJHV55NAI3K4BOFCR7H35TG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG/action/storage_attestation","attest_author":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG/action/author_attestation","sign_citation":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG/action/citation_signature","submit_replication":"https://pith.science/pith/K6BDJHV55NAI3K4BOFCR7H35TG/action/replication_record"}},"created_at":"2026-05-18T02:31:30.919482+00:00","updated_at":"2026-05-18T02:31:30.919482+00:00"}