{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZLZ3D7RUCTGQC3ZKYZXNGHIHG4","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":"536295b5ffb582241c0578abc9db5547b9decc595751765f65b6b24311144d68","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-29T14:43:20Z","title_canon_sha256":"d4458fba109d76219a2345cb9a80ad5ffaece26e500644caa2737edd310297e0"},"schema_version":"1.0","source":{"id":"1602.08983","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.08983","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"arxiv_version","alias_value":"1602.08983v3","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.08983","created_at":"2026-05-18T00:54:10Z"},{"alias_kind":"pith_short_12","alias_value":"ZLZ3D7RUCTGQ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZLZ3D7RUCTGQC3ZK","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZLZ3D7RU","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:3a9f48c17ee56492029fe9fffb7ac5e39e0aeed945f40524ea8e23977af9bea2","target":"graph","created_at":"2026-05-18T00:54:10Z","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 formulate a notion of K-stability for K\\\"ahler manifolds, and prove one direction of the Yau-Tian-Donaldson conjecture in this setting. More precisely, we prove that the Mabuchi functional being bounded below (resp. coercive) implies K-semistability (resp. uniformly K-stable). In particular this shows that the existence of a constant scalar curvature K\\\"ahler metric implies K-semistability, and K-stability if one assumes the automorphism group is discrete. We also show how Stoppa's argument holds in the K\\\"ahler case, giving a simpler proof of this K-stability statement.","authors_text":"Julius Ross, Ruadha\\'i Dervan","cross_cats":["math.AG","math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-29T14:43:20Z","title":"K-stability for K\\\"ahler Manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.08983","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":"sha256:90e6627d91611637bc80a04fb3655ed971a5cb3a5932e4e86fc42c541e2ed75c","target":"record","created_at":"2026-05-18T00:54:10Z","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":"536295b5ffb582241c0578abc9db5547b9decc595751765f65b6b24311144d68","cross_cats_sorted":["math.AG","math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-02-29T14:43:20Z","title_canon_sha256":"d4458fba109d76219a2345cb9a80ad5ffaece26e500644caa2737edd310297e0"},"schema_version":"1.0","source":{"id":"1602.08983","kind":"arxiv","version":3}},"canonical_sha256":"caf3b1fe3414cd016f2ac66ed31d07371e4aed6abe410029adfc40e0b3d4244e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"caf3b1fe3414cd016f2ac66ed31d07371e4aed6abe410029adfc40e0b3d4244e","first_computed_at":"2026-05-18T00:54:10.824254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:10.824254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D6kqVQVXOK2MjWXOP6hNdmGpCFuNBYNRnUNpFW44wayOounRwan9zLNby/DJK03eB5N7IhH9tLagwoWnf1sLAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:10.824876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.08983","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90e6627d91611637bc80a04fb3655ed971a5cb3a5932e4e86fc42c541e2ed75c","sha256:3a9f48c17ee56492029fe9fffb7ac5e39e0aeed945f40524ea8e23977af9bea2"],"state_sha256":"d74ad160c2b1b548ac3f0e9d502dc66c4421220a97db92f0a5a2f61a9d460744"}