{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6TAUYYDTTXBLIFEECO5EBBRKO4","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":"4c70551960d4ecfb085855a2710d4a5da835163c701f4373a3d507ef0c43c859","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T20:56:08Z","title_canon_sha256":"da9ae2b75d15f769c87e64e81d2830588516e49857e00888f28100ebce0feac3"},"schema_version":"1.0","source":{"id":"1412.0648","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.0648","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"arxiv_version","alias_value":"1412.0648v3","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.0648","created_at":"2026-05-18T01:42:47Z"},{"alias_kind":"pith_short_12","alias_value":"6TAUYYDTTXBL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6TAUYYDTTXBLIFEE","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6TAUYYDT","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:3a322e8d39e4e0e270f01b060026c27b60d3ad45cfacbd0afbcdacade8b9b6a3","target":"graph","created_at":"2026-05-18T01:42:47Z","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 introduce a norm on the space of test configurations, which we call the minimum norm. We conjecture that uniform K-stability with respect to this norm is equivalent to the existence of a constant scalar curvature K\\\"ahler metric. This notion of uniform K-stability is analogous to coercivity of the Mabuchi functional. We characterise the triviality of test configurations, by showing that a test configuration has zero minimum norm if and only if it has zero $L^2$-norm, if and only if it is almost trivial.\n  We prove that the existence of a twisted constant scalar curvature K\\\"ahler metric imp","authors_text":"Ruadha\\'i Dervan","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T20:56:08Z","title":"Uniform stability of twisted constant scalar curvature K\\\"ahler metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0648","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:b058945c01fa588a1294f59dac344a0797c430e354f6d074a52fb8a80b4d6b8f","target":"record","created_at":"2026-05-18T01:42:47Z","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":"4c70551960d4ecfb085855a2710d4a5da835163c701f4373a3d507ef0c43c859","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-12-01T20:56:08Z","title_canon_sha256":"da9ae2b75d15f769c87e64e81d2830588516e49857e00888f28100ebce0feac3"},"schema_version":"1.0","source":{"id":"1412.0648","kind":"arxiv","version":3}},"canonical_sha256":"f4c14c60739dc2b4148413ba40862a77118b1ccb68aa00d3128623bf61a3ceac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4c14c60739dc2b4148413ba40862a77118b1ccb68aa00d3128623bf61a3ceac","first_computed_at":"2026-05-18T01:42:47.898799Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:42:47.898799Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4fICYSP0ZjM3KbHT8OHXWNal8jh5efpGnX5JgBG00nEHHghIHzAtPNQIA1my79g1MNyxF0CV4PChg6o0YFEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:42:47.899328Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.0648","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b058945c01fa588a1294f59dac344a0797c430e354f6d074a52fb8a80b4d6b8f","sha256:3a322e8d39e4e0e270f01b060026c27b60d3ad45cfacbd0afbcdacade8b9b6a3"],"state_sha256":"496cf24fdf54340793f0e41327627d5c2b8080b0a33d3ec45fa094963e35dbcd"}