{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UVD4BOQKGGGWM66HD5PHJPU4FY","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":"246fe3a6781542a6b41fb0485276477c3e486cc1a84e5d99e85ba6886c5dcfcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-18T01:06:33Z","title_canon_sha256":"761469cc45ec8199790c59d927412f95a528c7c030354bbf8a2ea0dc564eeb1a"},"schema_version":"1.0","source":{"id":"1410.4891","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.4891","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"arxiv_version","alias_value":"1410.4891v2","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.4891","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"pith_short_12","alias_value":"UVD4BOQKGGGW","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UVD4BOQKGGGWM66H","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UVD4BOQK","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:1967c36d075d8a84ef058edd1a63106514d670267b0014feb8940df0f3448835","target":"graph","created_at":"2026-05-18T01:12:40Z","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":"It is known that a necessary condition for the existence of K\\\"ahler-Ricci solitons is the vanishing of the modified Futaki invariant introduced by Tian-Zhu. In a recent work of Berman-Nystr\\\"om, it was generalized for (singular) Fano varieties and the notion of algebro-geometric stability of the pair $(M,V)$ of a Fano manifold $M$ and a holomorphic vector field $V$ was introduced. In this paper, we propose a method of computing the modified Futaki invariant for Fano complete intersections in projective spaces.","authors_text":"Ryosuke Takahashi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-18T01:06:33Z","title":"On the modified Futaki invariant of complete intersections in projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.4891","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":"sha256:8739f22553d2ee4bf397a1b0688efa93a8aab8493fcbd24394d50a55510d97a6","target":"record","created_at":"2026-05-18T01:12:40Z","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":"246fe3a6781542a6b41fb0485276477c3e486cc1a84e5d99e85ba6886c5dcfcc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-10-18T01:06:33Z","title_canon_sha256":"761469cc45ec8199790c59d927412f95a528c7c030354bbf8a2ea0dc564eeb1a"},"schema_version":"1.0","source":{"id":"1410.4891","kind":"arxiv","version":2}},"canonical_sha256":"a547c0ba0a318d667bc71f5e74be9c2e3e244c8c0ed93adae4a38e951638d4e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a547c0ba0a318d667bc71f5e74be9c2e3e244c8c0ed93adae4a38e951638d4e1","first_computed_at":"2026-05-18T01:12:40.677662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:40.677662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oYbtu8tKJjlXGhRFBmzHAivpA99U90j+LH3mC67NmN+9u8qkQsiXr5+S1TbwKCYxVyr7m/NwQUbOys6DHBUoCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:40.678202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.4891","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8739f22553d2ee4bf397a1b0688efa93a8aab8493fcbd24394d50a55510d97a6","sha256:1967c36d075d8a84ef058edd1a63106514d670267b0014feb8940df0f3448835"],"state_sha256":"78489e2bd59ee94a9278be551cc7cb3196121bf2efc0c4deee4e35a1b839e442"}