{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DQDWYTA33PVAMQOJX2TCVJGDFZ","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":"b9a9e5aeb46ae4b595a5581a3cfb480bb7b643f928e343312354587a3a5138e1","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-24T14:42:09Z","title_canon_sha256":"c8cd1cee3065c7c751badafa67c9f4dcf80fdd4947243e59fdd6c76d4de0630e"},"schema_version":"1.0","source":{"id":"1606.07706","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07706","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07706v3","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07706","created_at":"2026-05-17T23:53:13Z"},{"alias_kind":"pith_short_12","alias_value":"DQDWYTA33PVA","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQDWYTA33PVAMQOJ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQDWYTA3","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:ec06cc8a0698c333c3a24d7d6dc12fe66b8c118fd3368ac7b24536ab34a6473a","target":"graph","created_at":"2026-05-17T23:53:13Z","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":"Let $Y$ be a compact K\\\"ahler normal space and $\\alpha \\in H^{1,1}(Y,\\mathbb{R})$ a K\\\"ahler class. We study metric properties of the space $\\mathcal{H}_\\alpha$ of K\\\"ahler metrics in $\\alpha$ using Mabuchi geodesics. We extend several results by Calabi, Chen, Darvas previously established when the underlying space is smooth. As an application we analytically characterize the existence of K\\\"ahler-Einstein metrics on $\\mathbb{Q}$-Fano varieties, generalizing a result of Tian, and illustrate these concepts in the case of toric varieties.","authors_text":"Eleonora Di Nezza, Vincent Guedj","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-24T14:42:09Z","title":"Geometry and Topology of the space of K\\\"ahler metrics on singular varieties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07706","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":"sha256:55b5b9050f26c5da976a8d69628768ca0f8df797f25ef91ce6af0590a2d75f4b","target":"record","created_at":"2026-05-17T23:53:13Z","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":"b9a9e5aeb46ae4b595a5581a3cfb480bb7b643f928e343312354587a3a5138e1","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-06-24T14:42:09Z","title_canon_sha256":"c8cd1cee3065c7c751badafa67c9f4dcf80fdd4947243e59fdd6c76d4de0630e"},"schema_version":"1.0","source":{"id":"1606.07706","kind":"arxiv","version":3}},"canonical_sha256":"1c076c4c1bdbea0641c9bea62aa4c32e75bfd2024d7bc89060acfc3b893f8eac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c076c4c1bdbea0641c9bea62aa4c32e75bfd2024d7bc89060acfc3b893f8eac","first_computed_at":"2026-05-17T23:53:13.104541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:13.104541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jKL7iW02vP+JBCYwpYzpGtn5s1u6PXK39Niqiu2U+KIvs5WGbmPn4vMjcFVwVjWsI2YWssCWHTSWpg+Z14bvAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:13.105160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07706","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:55b5b9050f26c5da976a8d69628768ca0f8df797f25ef91ce6af0590a2d75f4b","sha256:ec06cc8a0698c333c3a24d7d6dc12fe66b8c118fd3368ac7b24536ab34a6473a"],"state_sha256":"a8c7c2981a1547bbf91e9752926c6d0e297773f75f00ffb5a3fd151bf35a36d3"}