{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5BIT6SB4CPHANXX74AHSBXQF6E","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":"f9db0b81524678b0e51807ce832a45c7f761de554d4bc9658ae62d043783929a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-05T10:46:40Z","title_canon_sha256":"140894bdfb1f7e0a3c011e0afc294800ae3d728c863a3ed455ea2f362b10f514"},"schema_version":"1.0","source":{"id":"1809.01429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.01429","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"arxiv_version","alias_value":"1809.01429v1","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.01429","created_at":"2026-05-18T00:06:27Z"},{"alias_kind":"pith_short_12","alias_value":"5BIT6SB4CPHA","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5BIT6SB4CPHANXX7","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5BIT6SB4","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:c72ec3c70d6228cd4a91e7a8e99e73af74f0193c54a1bd398d474484447dde76","target":"graph","created_at":"2026-05-18T00:06:27Z","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":"There is an obstruction to the existence of K\\\"ahler -Einstein metrics which is used to define the GIT weight for K-stability, and it has been extended to various geometric problems. This survey paper considers such extended obstructions to the existence problem of K\\\"ahler -Ricci solitons, Sasaki-Einstein metrics and (conformally) Einstein-Maxwell K\\\"ahler metrics. These three cases have a common feature that the obstructions are parametrized by a space of vector fields. We see, in these three cases, the obstructions are obtained as the derivative of suitable volume functionals. This tells us","authors_text":"Akito Futaki, Hajime Ono","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-05T10:46:40Z","title":"Volume minimization and obstructions to solving some problems in K\\\"ahler geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01429","kind":"arxiv","version":1},"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":"sha256:90952a01528ee91dfd766ccaa7cafd7dbdaa709d32d2be82262546f266b39b05","target":"record","created_at":"2026-05-18T00:06:27Z","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":"f9db0b81524678b0e51807ce832a45c7f761de554d4bc9658ae62d043783929a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-09-05T10:46:40Z","title_canon_sha256":"140894bdfb1f7e0a3c011e0afc294800ae3d728c863a3ed455ea2f362b10f514"},"schema_version":"1.0","source":{"id":"1809.01429","kind":"arxiv","version":1}},"canonical_sha256":"e8513f483c13ce06deffe00f20de05f13c35a73f1c31cd5850f8a21cce5807c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8513f483c13ce06deffe00f20de05f13c35a73f1c31cd5850f8a21cce5807c8","first_computed_at":"2026-05-18T00:06:27.705968Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:27.705968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rj0yOZ4NCLgyOOZ9myo+GY7lnRi+fdipc0yl3OGqtyLM5LZk3/rTtCHwJdvPEDyjb5N9Hdyo3nBEdK94sSKvAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:27.706622Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.01429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90952a01528ee91dfd766ccaa7cafd7dbdaa709d32d2be82262546f266b39b05","sha256:c72ec3c70d6228cd4a91e7a8e99e73af74f0193c54a1bd398d474484447dde76"],"state_sha256":"3cffdbff71f9fb8d39e38b3048765a949012868e5d8802baa0747973593886e8"}