{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:TAA725YNY7EB7SKTQ27AUTAOCP","short_pith_number":"pith:TAA725YN","canonical_record":{"source":{"id":"1205.6214","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T20:30:01Z","cross_cats_sorted":[],"title_canon_sha256":"474bae84e8816d876214d891848b32d6b482e824e437c20273142a29c7e3d58e","abstract_canon_sha256":"66c49d1970994c2a3147a9e580e24bfbfd7854bcc028a6f5afba286e8995f49c"},"schema_version":"1.0"},"canonical_sha256":"9801fd770dc7c81fc95386be0a4c0e13c3e4dedab555f883403ca0d0ab4164a4","source":{"kind":"arxiv","id":"1205.6214","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6214","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6214v3","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6214","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"TAA725YNY7EB","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TAA725YNY7EB7SKT","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TAA725YN","created_at":"2026-05-18T12:27:23Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:TAA725YNY7EB7SKTQ27AUTAOCP","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6214","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T20:30:01Z","cross_cats_sorted":[],"title_canon_sha256":"474bae84e8816d876214d891848b32d6b482e824e437c20273142a29c7e3d58e","abstract_canon_sha256":"66c49d1970994c2a3147a9e580e24bfbfd7854bcc028a6f5afba286e8995f49c"},"schema_version":"1.0"},"canonical_sha256":"9801fd770dc7c81fc95386be0a4c0e13c3e4dedab555f883403ca0d0ab4164a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:43.544204Z","signature_b64":"ri1S/Sz2HmtmshyNSodqP0Ao3ksWNW6ditPuMyW1h6dVZVdIq3NfyML0S0LFJmuP4aQtogtEr6684Gc+7tH4Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9801fd770dc7c81fc95386be0a4c0e13c3e4dedab555f883403ca0d0ab4164a4","last_reissued_at":"2026-05-18T01:55:43.543326Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:43.543326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6214","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":"2026-05-18T01:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1IGbxnaJQbkI9oxnYBZdIbZ8TPKzhs3DjYkaoAVZjr5Omxws0aLKvOaSzwqmnp8iJ8JdLba7sptRJ0H8/DFLDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:43:43.492077Z"},"content_sha256":"54e1cc7f26140d379c23f4b150a69b581c1b2216c667ddba2ff22b58b21bd228","schema_version":"1.0","event_id":"sha256:54e1cc7f26140d379c23f4b150a69b581c1b2216c667ddba2ff22b58b21bd228"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:TAA725YNY7EB7SKTQ27AUTAOCP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Robert J. Berman","submitted_at":"2012-05-28T20:30:01Z","abstract_excerpt":"It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof exploits convexity properties of the Ding functional along weak geodesic rays in the space of all bounded positively curved metrics on the anti-canonical line bundle of X and also gives a new proof in the non-singular case. One consequence is that a toric Fano variety X is K-polystable iff it is K-polystable along toric degenerat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6214","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":"2026-05-18T01:55:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DhFfHNuCHNFpch/+7hC/oKGhrURrnNjXsZaGpJhAkbHitRdLnU3lOrnnnh1Oty6CwQ0X6vkXienkH6TrYKToDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:43:43.492574Z"},"content_sha256":"4b1056fcc95c9d2c10bc20e49ec9478a02a705093aaf72a29afee879a8e7451e","schema_version":"1.0","event_id":"sha256:4b1056fcc95c9d2c10bc20e49ec9478a02a705093aaf72a29afee879a8e7451e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TAA725YNY7EB7SKTQ27AUTAOCP/bundle.json","state_url":"https://pith.science/pith/TAA725YNY7EB7SKTQ27AUTAOCP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TAA725YNY7EB7SKTQ27AUTAOCP/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":"2026-06-01T02:43:43Z","links":{"resolver":"https://pith.science/pith/TAA725YNY7EB7SKTQ27AUTAOCP","bundle":"https://pith.science/pith/TAA725YNY7EB7SKTQ27AUTAOCP/bundle.json","state":"https://pith.science/pith/TAA725YNY7EB7SKTQ27AUTAOCP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TAA725YNY7EB7SKTQ27AUTAOCP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TAA725YNY7EB7SKTQ27AUTAOCP","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":"66c49d1970994c2a3147a9e580e24bfbfd7854bcc028a6f5afba286e8995f49c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T20:30:01Z","title_canon_sha256":"474bae84e8816d876214d891848b32d6b482e824e437c20273142a29c7e3d58e"},"schema_version":"1.0","source":{"id":"1205.6214","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6214","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6214v3","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6214","created_at":"2026-05-18T01:55:43Z"},{"alias_kind":"pith_short_12","alias_value":"TAA725YNY7EB","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TAA725YNY7EB7SKT","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TAA725YN","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:4b1056fcc95c9d2c10bc20e49ec9478a02a705093aaf72a29afee879a8e7451e","target":"graph","created_at":"2026-05-18T01:55:43Z","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":"It is shown that any, possibly singular, Fano variety X admitting a Kahler-Einstein metric is K-polystable, thus confirming one direction of the Yau-Tian-Donaldson conjecture in the setting of Q-Fano varieties equipped with their anti-canonical polarization. The proof exploits convexity properties of the Ding functional along weak geodesic rays in the space of all bounded positively curved metrics on the anti-canonical line bundle of X and also gives a new proof in the non-singular case. One consequence is that a toric Fano variety X is K-polystable iff it is K-polystable along toric degenerat","authors_text":"Robert J. Berman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T20:30:01Z","title":"K-polystability of Q-Fano varieties admitting Kahler-Einstein metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6214","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":"sha256:54e1cc7f26140d379c23f4b150a69b581c1b2216c667ddba2ff22b58b21bd228","target":"record","created_at":"2026-05-18T01:55:43Z","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":"66c49d1970994c2a3147a9e580e24bfbfd7854bcc028a6f5afba286e8995f49c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-05-28T20:30:01Z","title_canon_sha256":"474bae84e8816d876214d891848b32d6b482e824e437c20273142a29c7e3d58e"},"schema_version":"1.0","source":{"id":"1205.6214","kind":"arxiv","version":3}},"canonical_sha256":"9801fd770dc7c81fc95386be0a4c0e13c3e4dedab555f883403ca0d0ab4164a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9801fd770dc7c81fc95386be0a4c0e13c3e4dedab555f883403ca0d0ab4164a4","first_computed_at":"2026-05-18T01:55:43.543326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:43.543326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ri1S/Sz2HmtmshyNSodqP0Ao3ksWNW6ditPuMyW1h6dVZVdIq3NfyML0S0LFJmuP4aQtogtEr6684Gc+7tH4Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:43.544204Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6214","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:54e1cc7f26140d379c23f4b150a69b581c1b2216c667ddba2ff22b58b21bd228","sha256:4b1056fcc95c9d2c10bc20e49ec9478a02a705093aaf72a29afee879a8e7451e"],"state_sha256":"7c3e8dda4c9f3886e89b7b54f8e478978811d5c447cad4f2af3d79ecde2b9dde"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caJ8IzX+IqYNewnJJufXxX6IqCXXRwPQF0puz23CxQg+quEQfURvBxegvuPURQXNQh9MDImvgdcGKMTAUsvwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:43:43.495368Z","bundle_sha256":"28394895364706999d373392816d2024b80189d4b5732d4ddc13db5932197ab7"}}