{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4CVEUBJRPKM6FW3NYYGOAC55NT","short_pith_number":"pith:4CVEUBJR","canonical_record":{"source":{"id":"1111.7158","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-30T13:41:43Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b27221f602c121430ae367690e5b7745170d9d772407187bd4985ad02241e51f","abstract_canon_sha256":"e654632e14722f12a1a721868290f06312aae7a664dd11b17d14af1f09c38de4"},"schema_version":"1.0"},"canonical_sha256":"e0aa4a05317a99e2db6dc60ce00bbd6cd1eb1b13806659ce5e7a6152cc4aed62","source":{"kind":"arxiv","id":"1111.7158","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7158","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7158v3","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7158","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"pith_short_12","alias_value":"4CVEUBJRPKM6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4CVEUBJRPKM6FW3N","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4CVEUBJR","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4CVEUBJRPKM6FW3NYYGOAC55NT","target":"record","payload":{"canonical_record":{"source":{"id":"1111.7158","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-30T13:41:43Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"b27221f602c121430ae367690e5b7745170d9d772407187bd4985ad02241e51f","abstract_canon_sha256":"e654632e14722f12a1a721868290f06312aae7a664dd11b17d14af1f09c38de4"},"schema_version":"1.0"},"canonical_sha256":"e0aa4a05317a99e2db6dc60ce00bbd6cd1eb1b13806659ce5e7a6152cc4aed62","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:10.751916Z","signature_b64":"MjEto12XV9HR3x7kN4W3dRkmirugBzXG3uOTC9oePEX6fZg9ZAam5OR3M/z/ExofqWZI5QDB2p38DDMrXco/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0aa4a05317a99e2db6dc60ce00bbd6cd1eb1b13806659ce5e7a6152cc4aed62","last_reissued_at":"2026-05-18T01:23:10.751395Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:10.751395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.7158","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tDGoaNm6e0gMzsyozaEkC9TP2Nmfb0+qh2GNg3NMNUKWFFSOlQRwxiFRgnCQsCyFAueNUhDL5DsoE1Ij4CfiBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:52:46.148458Z"},"content_sha256":"f4d5d53b4386af3d461da5a21a6886bdee0aa54ac9faa931d155094abf868229","schema_version":"1.0","event_id":"sha256:f4d5d53b4386af3d461da5a21a6886bdee0aa54ac9faa931d155094abf868229"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4CVEUBJRPKM6FW3NYYGOAC55NT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K\\\"ahler-Einstein metrics and the K\\\"ahler-Ricci flow on log Fano varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Ahmed Zeriahi, Philippe Eyssidieux, Robert J. Berman, S\\'ebastien Boucksom, Vincent Guedj","submitted_at":"2011-11-30T13:41:43Z","abstract_excerpt":"We prove the existence and uniqueness of K\\\"ahler-Einstein metrics on Q-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized K\\\"ahler-Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (non-singular) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the K\\\"ahler-Ricci flow provides weak converge"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7158","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:23:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ho49tHpeUJbKl/S+SJvsPmKtk8b1/alTGCGn8hsG+GNRmft7bUIWoyTmAIG2ob6nO69ohQRDmXJ9gWa9pQQPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:52:46.148808Z"},"content_sha256":"86233ffcd67bf0c54f5fd7cfe323d3449258d1427d2df4525763956e0910cffc","schema_version":"1.0","event_id":"sha256:86233ffcd67bf0c54f5fd7cfe323d3449258d1427d2df4525763956e0910cffc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/bundle.json","state_url":"https://pith.science/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T02:52:46Z","links":{"resolver":"https://pith.science/pith/4CVEUBJRPKM6FW3NYYGOAC55NT","bundle":"https://pith.science/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/bundle.json","state":"https://pith.science/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4CVEUBJRPKM6FW3NYYGOAC55NT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4CVEUBJRPKM6FW3NYYGOAC55NT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e654632e14722f12a1a721868290f06312aae7a664dd11b17d14af1f09c38de4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-30T13:41:43Z","title_canon_sha256":"b27221f602c121430ae367690e5b7745170d9d772407187bd4985ad02241e51f"},"schema_version":"1.0","source":{"id":"1111.7158","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.7158","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"arxiv_version","alias_value":"1111.7158v3","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.7158","created_at":"2026-05-18T01:23:10Z"},{"alias_kind":"pith_short_12","alias_value":"4CVEUBJRPKM6","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4CVEUBJRPKM6FW3N","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4CVEUBJR","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:86233ffcd67bf0c54f5fd7cfe323d3449258d1427d2df4525763956e0910cffc","target":"graph","created_at":"2026-05-18T01:23:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove the existence and uniqueness of K\\\"ahler-Einstein metrics on Q-Fano varieties with log terminal singularities (and more generally on log Fano pairs) whose Mabuchi functional is proper. We study analogues of the works of Perelman on the convergence of the normalized K\\\"ahler-Ricci flow, and of Keller, Rubinstein on its discrete version, Ricci iteration. In the special case of (non-singular) Fano manifolds, our results on Ricci iteration yield smooth convergence without any additional condition, improving on previous results. Our result for the K\\\"ahler-Ricci flow provides weak converge","authors_text":"Ahmed Zeriahi, Philippe Eyssidieux, Robert J. Berman, S\\'ebastien Boucksom, Vincent Guedj","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-30T13:41:43Z","title":"K\\\"ahler-Einstein metrics and the K\\\"ahler-Ricci flow on log Fano varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.7158","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:f4d5d53b4386af3d461da5a21a6886bdee0aa54ac9faa931d155094abf868229","target":"record","created_at":"2026-05-18T01:23:10Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e654632e14722f12a1a721868290f06312aae7a664dd11b17d14af1f09c38de4","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-11-30T13:41:43Z","title_canon_sha256":"b27221f602c121430ae367690e5b7745170d9d772407187bd4985ad02241e51f"},"schema_version":"1.0","source":{"id":"1111.7158","kind":"arxiv","version":3}},"canonical_sha256":"e0aa4a05317a99e2db6dc60ce00bbd6cd1eb1b13806659ce5e7a6152cc4aed62","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0aa4a05317a99e2db6dc60ce00bbd6cd1eb1b13806659ce5e7a6152cc4aed62","first_computed_at":"2026-05-18T01:23:10.751395Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:10.751395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MjEto12XV9HR3x7kN4W3dRkmirugBzXG3uOTC9oePEX6fZg9ZAam5OR3M/z/ExofqWZI5QDB2p38DDMrXco/Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:10.751916Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.7158","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4d5d53b4386af3d461da5a21a6886bdee0aa54ac9faa931d155094abf868229","sha256:86233ffcd67bf0c54f5fd7cfe323d3449258d1427d2df4525763956e0910cffc"],"state_sha256":"2f76af03c57d73ad5f2991ff9ee9e30792e089cc4a73f9935f3693698debf108"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JKRigwuyhadJaB5aWq8INs7tXN6wQKgoI5W91fdYXTX/MOC5uvWvDHQZJvMReHqu0cZpQ+Fo+vkpdE2zN/MeCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:52:46.150746Z","bundle_sha256":"395edca10434af79a64eeaf566990cbea794c72c2d0259612d6dd80726eaf908"}}