{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:H22YBQLV2Y5ZI5A3QR5HQO57MQ","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":"a732a93c533ac30ebd75b911facc1ff786826b694f01602635eef4a8c475d37b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-21T17:27:15Z","title_canon_sha256":"26a1cc310ede45e372fc7d49a092187bb8aa11ee147b27f14fad8eb868cc4b87"},"schema_version":"1.0","source":{"id":"1610.06865","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06865","created_at":"2026-05-18T01:01:21Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06865v2","created_at":"2026-05-18T01:01:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06865","created_at":"2026-05-18T01:01:21Z"},{"alias_kind":"pith_short_12","alias_value":"H22YBQLV2Y5Z","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"H22YBQLV2Y5ZI5A3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"H22YBQLV","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:bba1cc3d548cf70c4cd8ba6917dd00241dbf95a8b875901dea2a2a9f21a34095","target":"graph","created_at":"2026-05-18T01:01:21Z","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 give conditions under which the blowup of an extremal K\\\"ahler manifold along a submanifold of codimension greater than two admits an extremal metric. This generalizes work of Arezzo-Pacard-Singer, who considered blowups in points.","authors_text":"G\\'abor Sz\\'ekelyhidi, Reza Seyyedali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-21T17:27:15Z","title":"Extremal metrics on blowups along submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06865","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:f4467bcbb50bd01bc7b76dc7a1d6e1a2dcdffd880be24f87a95ae7f8fd626a3d","target":"record","created_at":"2026-05-18T01:01:21Z","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":"a732a93c533ac30ebd75b911facc1ff786826b694f01602635eef4a8c475d37b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-10-21T17:27:15Z","title_canon_sha256":"26a1cc310ede45e372fc7d49a092187bb8aa11ee147b27f14fad8eb868cc4b87"},"schema_version":"1.0","source":{"id":"1610.06865","kind":"arxiv","version":2}},"canonical_sha256":"3eb580c175d63b94741b847a783bbf643534b6b75eb81ed8cf8fa0bc0184e852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3eb580c175d63b94741b847a783bbf643534b6b75eb81ed8cf8fa0bc0184e852","first_computed_at":"2026-05-18T01:01:21.729661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:01:21.729661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eKZ7hnxsPlU8Dc0/GOj237lxkK8A8kUqd/IJmeK8xuZGCmGPJqJL1K3OykwtjcXsx9fTzBS5g3j8JNCDsQ3pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:01:21.730182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06865","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4467bcbb50bd01bc7b76dc7a1d6e1a2dcdffd880be24f87a95ae7f8fd626a3d","sha256:bba1cc3d548cf70c4cd8ba6917dd00241dbf95a8b875901dea2a2a9f21a34095"],"state_sha256":"cd9d6dd29c2fba13326e6b1affa27018a083b91cb868b8e9bd5dfd069567b587"}