{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:R6DNG7OSL2TFV4UK2ERJV7A4GQ","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":"c308b44b398b23e11320f6dd22567d2935db60565e2a96185306c7d519fd9d52","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-07T13:10:52Z","title_canon_sha256":"63f109fe67a89e0b8055b10552559e52a05f8c32310100c616c648603b316d7a"},"schema_version":"1.0","source":{"id":"1204.1630","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1630","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1630v2","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1630","created_at":"2026-05-18T01:25:40Z"},{"alias_kind":"pith_short_12","alias_value":"R6DNG7OSL2TF","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"R6DNG7OSL2TFV4UK","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"R6DNG7OS","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:b1b113b716316c4faabdd2b5bb288138b5fef882d9dce0481b854413bfe298ea","target":"graph","created_at":"2026-05-18T01:25:40Z","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 consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relative Futaki invariant for the deformations to contain Sasaki-extremal structures.\n  Deformations of Sasaki-Einstein metrics are also considered, where it suffices that the deformation preserve a maximal torus. As an application, new families of Sasaki-Einstein and Sasaki-extremal m","authors_text":"Craig van Coevering","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-07T13:10:52Z","title":"Stability of Sasaki-extremal metrics under complex deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1630","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":"sha256:053559d51eccea94aa124cb7aad13ae38d2282c07272759359002966ca35cf4e","target":"record","created_at":"2026-05-18T01:25:40Z","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":"c308b44b398b23e11320f6dd22567d2935db60565e2a96185306c7d519fd9d52","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-07T13:10:52Z","title_canon_sha256":"63f109fe67a89e0b8055b10552559e52a05f8c32310100c616c648603b316d7a"},"schema_version":"1.0","source":{"id":"1204.1630","kind":"arxiv","version":2}},"canonical_sha256":"8f86d37dd25ea65af28ad1229afc1c342d05b069879f01d16b5161a429d323a6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f86d37dd25ea65af28ad1229afc1c342d05b069879f01d16b5161a429d323a6","first_computed_at":"2026-05-18T01:25:40.089446Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:40.089446Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Iz+Bf7E0rCxcMX0nm/oYezXe1DuQL+ANQaPI+pJOVsLBz3DI2G2dBeY8OvQU3Dbj3nO7rjwaH+RwQuSu+Lc2DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:40.090015Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1630","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:053559d51eccea94aa124cb7aad13ae38d2282c07272759359002966ca35cf4e","sha256:b1b113b716316c4faabdd2b5bb288138b5fef882d9dce0481b854413bfe298ea"],"state_sha256":"a01d963cffdd6b6d0ce4da047b0d9b1404939769ef441393af8a41adaf68de98"}