{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:C6DRGYCHDJA6A5DPZM27B73XQZ","short_pith_number":"pith:C6DRGYCH","schema_version":"1.0","canonical_sha256":"17871360471a41e0746fcb35f0ff77864a31034527b240b6ae72c6edfbf52899","source":{"kind":"arxiv","id":"1004.0543","version":2},"attestation_state":"computed","paper":{"title":"The complex Monge-Ampere equation on compact Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Weiyong He, Xiuxiong Chen","submitted_at":"2010-04-04T23:59:37Z","abstract_excerpt":"We consider the complex Monge-Amp\\`ere equation on a compact K\\\"ahler manifold $(M, g)$ when the right hand side $F$ has rather weak regularity. In particular we prove that estimate of $\\t\\phi$ and the gradient estimate hold when $F$ is in $W^{1, p_0}$ for any $p_0>2n$. As an application, we show that there exists a classical solution in $W^{3, p_0}$ for the complex Monge-Amp\\`ere equation when $F$ is in $W^{1, p_0}$."},"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":"1004.0543","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2010-04-04T23:59:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"09b175b8ca367af6c104bd351905ebc60bd4c5c3a2654ac7b197664a3bb78133","abstract_canon_sha256":"b8809b2e0a55a26163cb18e9fba68f4cda72b42c4e75dcbe65d251a13297c4b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:58.746168Z","signature_b64":"SHtN9B/IzKXd37eNhrj1bfkJsMGik04CLU0ttSXiPC3faF7+bSYyjnk6ERx008AYJ+xUXQzlmfy9IKKJw9BNDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17871360471a41e0746fcb35f0ff77864a31034527b240b6ae72c6edfbf52899","last_reissued_at":"2026-05-18T04:27:58.745517Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:58.745517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complex Monge-Ampere equation on compact Kaehler manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Weiyong He, Xiuxiong Chen","submitted_at":"2010-04-04T23:59:37Z","abstract_excerpt":"We consider the complex Monge-Amp\\`ere equation on a compact K\\\"ahler manifold $(M, g)$ when the right hand side $F$ has rather weak regularity. In particular we prove that estimate of $\\t\\phi$ and the gradient estimate hold when $F$ is in $W^{1, p_0}$ for any $p_0>2n$. As an application, we show that there exists a classical solution in $W^{3, p_0}$ for the complex Monge-Amp\\`ere equation when $F$ is in $W^{1, p_0}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0543","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":"1004.0543","created_at":"2026-05-18T04:27:58.745620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.0543v2","created_at":"2026-05-18T04:27:58.745620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.0543","created_at":"2026-05-18T04:27:58.745620+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6DRGYCHDJA6","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6DRGYCHDJA6A5DP","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6DRGYCH","created_at":"2026-05-18T12:26:05.355336+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/C6DRGYCHDJA6A5DPZM27B73XQZ","json":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ.json","graph_json":"https://pith.science/api/pith-number/C6DRGYCHDJA6A5DPZM27B73XQZ/graph.json","events_json":"https://pith.science/api/pith-number/C6DRGYCHDJA6A5DPZM27B73XQZ/events.json","paper":"https://pith.science/paper/C6DRGYCH"},"agent_actions":{"view_html":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ","download_json":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ.json","view_paper":"https://pith.science/paper/C6DRGYCH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.0543&json=true","fetch_graph":"https://pith.science/api/pith-number/C6DRGYCHDJA6A5DPZM27B73XQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/C6DRGYCHDJA6A5DPZM27B73XQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ/action/storage_attestation","attest_author":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ/action/author_attestation","sign_citation":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ/action/citation_signature","submit_replication":"https://pith.science/pith/C6DRGYCHDJA6A5DPZM27B73XQZ/action/replication_record"}},"created_at":"2026-05-18T04:27:58.745620+00:00","updated_at":"2026-05-18T04:27:58.745620+00:00"}