{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:4APXNN2IQFNH5NQB7MWAJUVYNO","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":"d98b10c51e8af539cb6e983f348b6b7205ee4c91ea22cc7d13754d83fa7a771e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-22T19:39:47Z","title_canon_sha256":"e8f3734744002437b4a6d5e39c6640491c56363e5a41172fc65dd9f26dedf348"},"schema_version":"1.0","source":{"id":"1512.07213","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.07213","created_at":"2026-05-17T23:44:15Z"},{"alias_kind":"arxiv_version","alias_value":"1512.07213v2","created_at":"2026-05-17T23:44:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.07213","created_at":"2026-05-17T23:44:15Z"},{"alias_kind":"pith_short_12","alias_value":"4APXNN2IQFNH","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"4APXNN2IQFNH5NQB","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"4APXNN2I","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:ec47a6549a380aa2881b3e1f07ce890d08afe2ee195c3a9e3919e7669aecc93c","target":"graph","created_at":"2026-05-17T23:44:15Z","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 show that a polarized affine variety admits a Ricci flat K\\\"ahler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\\\"ahler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.","authors_text":"G\\'abor Sz\\'ekelyhidi, Tristan C. Collins","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-22T19:39:47Z","title":"Sasaki-Einstein metrics and K-stability"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07213","kind":"arxiv","version":2},"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":"sha256:459fc778d384449b15691c9625bf5ce3bb7148b567ed4124bf07ed81eeb04949","target":"record","created_at":"2026-05-17T23:44:15Z","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":"d98b10c51e8af539cb6e983f348b6b7205ee4c91ea22cc7d13754d83fa7a771e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-12-22T19:39:47Z","title_canon_sha256":"e8f3734744002437b4a6d5e39c6640491c56363e5a41172fc65dd9f26dedf348"},"schema_version":"1.0","source":{"id":"1512.07213","kind":"arxiv","version":2}},"canonical_sha256":"e01f76b748815a7eb601fb2c04d2b86bad35505c488660bd8ff5d894fb555f54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e01f76b748815a7eb601fb2c04d2b86bad35505c488660bd8ff5d894fb555f54","first_computed_at":"2026-05-17T23:44:15.766085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:44:15.766085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wD+4im9pRE3LZwhejlWscGW/IVG5Q9RkcwoBjWM72YgV5VHSv/35jKL/dlI849sRQUrBFgjPLf0lXeB0MqBTAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:44:15.766696Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.07213","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:459fc778d384449b15691c9625bf5ce3bb7148b567ed4124bf07ed81eeb04949","sha256:ec47a6549a380aa2881b3e1f07ce890d08afe2ee195c3a9e3919e7669aecc93c"],"state_sha256":"bc2b8ae00c44aa3c9efb0a303fcc38de603ae09d6e3025008a0473e5119dc016"}