{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:CE2XD2DBGFBHJRLFYIHOTR2ZVT","short_pith_number":"pith:CE2XD2DB","schema_version":"1.0","canonical_sha256":"113571e861314274c565c20ee9c759acd53e1d711640d83be1bbd87d95ac4a5c","source":{"kind":"arxiv","id":"1109.1263","version":1},"attestation_state":"computed","paper":{"title":"Moser-Trudinger type inequalities for complex Monge-Amp\\`ere operators and Aubin's \"hypoth\\`ese fondamentale\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Bo Berndtsson, Robert J. Berman","submitted_at":"2011-09-06T18:38:07Z","abstract_excerpt":"We prove Aubin's \"Hypothese fondamentale\" concerning the existence of Moser-Trudinger type inequalities on any integral compact K\\\"ahler manifold X. In the case of the anti-canonical class on a Fano manifold the constants in the inequalities are shown to only depend on the dimension of X (but there are counterexamples to the precise value proposed by Aubin). In the different setting of pseudoconvex domains in complex space we also obtain a quasi-sharp version of the inequalities and relate it to Brezis-Merle type inequalities. The inequalities are shown to be sharp for S^{1}-invariant function"},"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":"1109.1263","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-09-06T18:38:07Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"823b279ec73922d47931a7f8a5bc43d3fb4cc6f1f5f5d616095d4c654224eb28","abstract_canon_sha256":"e9c36f2af382127f4fa201eafca8dfa65cbc694b927e4610f5092519033fba36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:05.054907Z","signature_b64":"j9ZDnyu8Fx0IdMY2BRffuwgtJ5Twf9/Rpa1Ufa8u2kkG0WaJ0Tjh1Tpsuh+ahimXOAJyFbdyAnwT269w4OdhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"113571e861314274c565c20ee9c759acd53e1d711640d83be1bbd87d95ac4a5c","last_reissued_at":"2026-05-18T04:14:05.054269Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:05.054269Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Moser-Trudinger type inequalities for complex Monge-Amp\\`ere operators and Aubin's \"hypoth\\`ese fondamentale\"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Bo Berndtsson, Robert J. Berman","submitted_at":"2011-09-06T18:38:07Z","abstract_excerpt":"We prove Aubin's \"Hypothese fondamentale\" concerning the existence of Moser-Trudinger type inequalities on any integral compact K\\\"ahler manifold X. In the case of the anti-canonical class on a Fano manifold the constants in the inequalities are shown to only depend on the dimension of X (but there are counterexamples to the precise value proposed by Aubin). In the different setting of pseudoconvex domains in complex space we also obtain a quasi-sharp version of the inequalities and relate it to Brezis-Merle type inequalities. The inequalities are shown to be sharp for S^{1}-invariant function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1263","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":"1109.1263","created_at":"2026-05-18T04:14:05.054395+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.1263v1","created_at":"2026-05-18T04:14:05.054395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1263","created_at":"2026-05-18T04:14:05.054395+00:00"},{"alias_kind":"pith_short_12","alias_value":"CE2XD2DBGFBH","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_16","alias_value":"CE2XD2DBGFBHJRLF","created_at":"2026-05-18T12:26:26.731475+00:00"},{"alias_kind":"pith_short_8","alias_value":"CE2XD2DB","created_at":"2026-05-18T12:26:26.731475+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.18855","citing_title":"Regularity of rooftop envelopes","ref_index":7,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT","json":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT.json","graph_json":"https://pith.science/api/pith-number/CE2XD2DBGFBHJRLFYIHOTR2ZVT/graph.json","events_json":"https://pith.science/api/pith-number/CE2XD2DBGFBHJRLFYIHOTR2ZVT/events.json","paper":"https://pith.science/paper/CE2XD2DB"},"agent_actions":{"view_html":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT","download_json":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT.json","view_paper":"https://pith.science/paper/CE2XD2DB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.1263&json=true","fetch_graph":"https://pith.science/api/pith-number/CE2XD2DBGFBHJRLFYIHOTR2ZVT/graph.json","fetch_events":"https://pith.science/api/pith-number/CE2XD2DBGFBHJRLFYIHOTR2ZVT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT/action/storage_attestation","attest_author":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT/action/author_attestation","sign_citation":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT/action/citation_signature","submit_replication":"https://pith.science/pith/CE2XD2DBGFBHJRLFYIHOTR2ZVT/action/replication_record"}},"created_at":"2026-05-18T04:14:05.054395+00:00","updated_at":"2026-05-18T04:14:05.054395+00:00"}