{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:UDXNBFQQOY7WJOECUSXGADGKFU","short_pith_number":"pith:UDXNBFQQ","schema_version":"1.0","canonical_sha256":"a0eed09610763f64b882a4ae600cca2d17f13174f6e99070ec8be10c4cafd94e","source":{"kind":"arxiv","id":"1501.00891","version":1},"attestation_state":"computed","paper":{"title":"The complex Monge-Amp\\`ere type equation on compact Hermitian manifolds and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ngoc Cuong Nguyen","submitted_at":"2015-01-05T15:26:22Z","abstract_excerpt":"We prove the existence and uniqueness of continuous solutions to the complex Monge-Amp\\`ere type equation with the right hand side in $L^p$, $p>1$, on compact Hermitian manifolds. Next, we generalise results of Eyssidieux, Guedj and Zeriahi \\cite{EGZ09, EGZ11} to compact Hermitian manifolds which {\\em a priori} are not in the Fujiki class. These generalisations lead to a number of applications: we obtain partial results on a conjecture of Tosatti and Weinkove \\cite{TW12a} and on a weak form of a conjecture of Demailly and Paun \\cite{DP04}."},"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":"1501.00891","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-01-05T15:26:22Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"37ed45c2c0b0d7c564aa8e0f3c4a2fe82efce969639fa65ff2101af278975f21","abstract_canon_sha256":"e1b08c5a79eed27991d87e00b8dc739bbbf25fb38cde7e24fdb3ff704c3158b5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:31.769517Z","signature_b64":"3VSncN5aKmBDrlck6abIg6CiugKFLwi8CstX5XfKjmQVXee070FGSh1kx1zzt4EB6b+VMixDzcH6OsSSD+8dCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0eed09610763f64b882a4ae600cca2d17f13174f6e99070ec8be10c4cafd94e","last_reissued_at":"2026-05-18T01:26:31.768989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:31.768989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The complex Monge-Amp\\`ere type equation on compact Hermitian manifolds and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Ngoc Cuong Nguyen","submitted_at":"2015-01-05T15:26:22Z","abstract_excerpt":"We prove the existence and uniqueness of continuous solutions to the complex Monge-Amp\\`ere type equation with the right hand side in $L^p$, $p>1$, on compact Hermitian manifolds. Next, we generalise results of Eyssidieux, Guedj and Zeriahi \\cite{EGZ09, EGZ11} to compact Hermitian manifolds which {\\em a priori} are not in the Fujiki class. These generalisations lead to a number of applications: we obtain partial results on a conjecture of Tosatti and Weinkove \\cite{TW12a} and on a weak form of a conjecture of Demailly and Paun \\cite{DP04}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.00891","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":"1501.00891","created_at":"2026-05-18T01:26:31.769072+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.00891v1","created_at":"2026-05-18T01:26:31.769072+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.00891","created_at":"2026-05-18T01:26:31.769072+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDXNBFQQOY7W","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDXNBFQQOY7WJOEC","created_at":"2026-05-18T12:29:44.643036+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDXNBFQQ","created_at":"2026-05-18T12:29:44.643036+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/UDXNBFQQOY7WJOECUSXGADGKFU","json":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU.json","graph_json":"https://pith.science/api/pith-number/UDXNBFQQOY7WJOECUSXGADGKFU/graph.json","events_json":"https://pith.science/api/pith-number/UDXNBFQQOY7WJOECUSXGADGKFU/events.json","paper":"https://pith.science/paper/UDXNBFQQ"},"agent_actions":{"view_html":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU","download_json":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU.json","view_paper":"https://pith.science/paper/UDXNBFQQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.00891&json=true","fetch_graph":"https://pith.science/api/pith-number/UDXNBFQQOY7WJOECUSXGADGKFU/graph.json","fetch_events":"https://pith.science/api/pith-number/UDXNBFQQOY7WJOECUSXGADGKFU/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU/action/storage_attestation","attest_author":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU/action/author_attestation","sign_citation":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU/action/citation_signature","submit_replication":"https://pith.science/pith/UDXNBFQQOY7WJOECUSXGADGKFU/action/replication_record"}},"created_at":"2026-05-18T01:26:31.769072+00:00","updated_at":"2026-05-18T01:26:31.769072+00:00"}