{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:6RIRQ7PLEBMQV35JRKC4XSTISA","short_pith_number":"pith:6RIRQ7PL","schema_version":"1.0","canonical_sha256":"f451187deb20590aefa98a85cbca689025e8a2a8f0454dd2ce74f087758f11c6","source":{"kind":"arxiv","id":"2306.07900","version":1},"attestation_state":"computed","paper":{"title":"K\\\"ahler-Einstein metrics with positive curvature near an isolated log terminal singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Antonio Trusiani, S\\'ebastien Boucksom, Vincent Guedj","submitted_at":"2023-06-13T16:50:13Z","abstract_excerpt":"We analyze the existence of K\\\"ahler-Einstein metrics of positive curvature in the neighborhood of a germ of a log terminal singularity $(X,p)$. This boils down to solve a Dirichlet problem for certain complex Monge-Amp\\`ere equations. We show that the solvability of the latter is independent of the shape of the domain and of the boundary data. We establish a Moser-Trudinger $(MT)_{\\gamma}$ inequality in subcritical regimes $\\gamma<\\gamma_p$ and establish the existence of smooth solutions in that cases. We show that the expected critical exponent $\\hat{\\gamma}_p=\\frac{n+1}{n} \\widehat{\\mathrm{"},"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":"2306.07900","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2023-06-13T16:50:13Z","cross_cats_sorted":["math.AG","math.CV"],"title_canon_sha256":"4b819894d739492dc1219d7a46d957ff4047482e82ad26a094c4b02fa9783444","abstract_canon_sha256":"40971f280c4eaf8bfcdfb9b44f68e26b3531d2b8cbe5553b7ac62db066f68a04"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:20:10.375687Z","signature_b64":"xCxZn8raxKjsCTkt3uzo9fsiaAITnEApYRLmqoa2PavIAsRhSuAaGPHofjnzuw/3Us26XQsR1cib9gBlmVfADg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f451187deb20590aefa98a85cbca689025e8a2a8f0454dd2ce74f087758f11c6","last_reissued_at":"2026-07-05T06:20:10.375199Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:20:10.375199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"K\\\"ahler-Einstein metrics with positive curvature near an isolated log terminal singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.DG","authors_text":"Antonio Trusiani, S\\'ebastien Boucksom, Vincent Guedj","submitted_at":"2023-06-13T16:50:13Z","abstract_excerpt":"We analyze the existence of K\\\"ahler-Einstein metrics of positive curvature in the neighborhood of a germ of a log terminal singularity $(X,p)$. This boils down to solve a Dirichlet problem for certain complex Monge-Amp\\`ere equations. We show that the solvability of the latter is independent of the shape of the domain and of the boundary data. We establish a Moser-Trudinger $(MT)_{\\gamma}$ inequality in subcritical regimes $\\gamma<\\gamma_p$ and establish the existence of smooth solutions in that cases. We show that the expected critical exponent $\\hat{\\gamma}_p=\\frac{n+1}{n} \\widehat{\\mathrm{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2306.07900","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2306.07900/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2306.07900","created_at":"2026-07-05T06:20:10.375264+00:00"},{"alias_kind":"arxiv_version","alias_value":"2306.07900v1","created_at":"2026-07-05T06:20:10.375264+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2306.07900","created_at":"2026-07-05T06:20:10.375264+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RIRQ7PLEBMQ","created_at":"2026-07-05T06:20:10.375264+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RIRQ7PLEBMQV35J","created_at":"2026-07-05T06:20:10.375264+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RIRQ7PL","created_at":"2026-07-05T06:20:10.375264+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2409.01705","citing_title":"On the geometry of spaces of filtrations on local rings","ref_index":33,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA","json":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA.json","graph_json":"https://pith.science/api/pith-number/6RIRQ7PLEBMQV35JRKC4XSTISA/graph.json","events_json":"https://pith.science/api/pith-number/6RIRQ7PLEBMQV35JRKC4XSTISA/events.json","paper":"https://pith.science/paper/6RIRQ7PL"},"agent_actions":{"view_html":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA","download_json":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA.json","view_paper":"https://pith.science/paper/6RIRQ7PL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2306.07900&json=true","fetch_graph":"https://pith.science/api/pith-number/6RIRQ7PLEBMQV35JRKC4XSTISA/graph.json","fetch_events":"https://pith.science/api/pith-number/6RIRQ7PLEBMQV35JRKC4XSTISA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA/action/storage_attestation","attest_author":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA/action/author_attestation","sign_citation":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA/action/citation_signature","submit_replication":"https://pith.science/pith/6RIRQ7PLEBMQV35JRKC4XSTISA/action/replication_record"}},"created_at":"2026-07-05T06:20:10.375264+00:00","updated_at":"2026-07-05T06:20:10.375264+00:00"}