{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3XFK7JG53RBHNLNFPJKYUTAV54","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":"5ef8dfd1013003826c187f48f7fabbeeb9d9ddb893d81687becb443838dfe114","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-19T18:32:32Z","title_canon_sha256":"e477b41d698bca5b76ac6112530d04ae2768f58ef2cbcbfcf6b0fb5c41a7772d"},"schema_version":"1.0","source":{"id":"1201.4137","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4137","created_at":"2026-05-18T03:29:27Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4137v4","created_at":"2026-05-18T03:29:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4137","created_at":"2026-05-18T03:29:27Z"},{"alias_kind":"pith_short_12","alias_value":"3XFK7JG53RBH","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"3XFK7JG53RBHNLNF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"3XFK7JG5","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:bb1e4be4041b1a5d55eeb66ffd8e36cbed9a0d763e7bf550b8334d15d9bb9588","target":"graph","created_at":"2026-05-18T03:29:27Z","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":"Let $X$ be a compact toric extremal K\\\"ahler manifold. Using the work of Sz\\'ekelyhidi, we provide a combinatorial criterion on the fan describing $X$ to ensure the existence of complex deformations of $X$ that carry extremal metrics. As an example, we find new CSC metrics on 4-points blow-ups of $\\C\\P^1\\times\\C\\P^1$.","authors_text":"Carl Tipler, Yann Rollin","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-19T18:32:32Z","title":"Deformations of extremal toric manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4137","kind":"arxiv","version":4},"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":"sha256:2a3a6edfb9217d8af83627c3f4ae0bb41abf1fee0a30ae0e32e64a1b354d54dd","target":"record","created_at":"2026-05-18T03:29:27Z","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":"5ef8dfd1013003826c187f48f7fabbeeb9d9ddb893d81687becb443838dfe114","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-01-19T18:32:32Z","title_canon_sha256":"e477b41d698bca5b76ac6112530d04ae2768f58ef2cbcbfcf6b0fb5c41a7772d"},"schema_version":"1.0","source":{"id":"1201.4137","kind":"arxiv","version":4}},"canonical_sha256":"ddcaafa4dddc4276ada57a558a4c15ef39e4b4f5256de35f3cc2f156a7c85422","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddcaafa4dddc4276ada57a558a4c15ef39e4b4f5256de35f3cc2f156a7c85422","first_computed_at":"2026-05-18T03:29:27.769009Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:27.769009Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BEOV1nu6Es11DR8yz4QumfIW/P7tihLRFUyS3DvNz00Mr+A1nzsBkuBTGtB2SCnqF3sPm9FC7fWF1LziCQzqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:27.769710Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4137","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a3a6edfb9217d8af83627c3f4ae0bb41abf1fee0a30ae0e32e64a1b354d54dd","sha256:bb1e4be4041b1a5d55eeb66ffd8e36cbed9a0d763e7bf550b8334d15d9bb9588"],"state_sha256":"f11342467cf8cf5f4acfba1713ea68aa31dd072268d8d9f618476d6c2bb7e7bf"}