{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:G3YDI324AMN3YLMPJERBVK57JN","short_pith_number":"pith:G3YDI324","canonical_record":{"source":{"id":"0905.0498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T21:41:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c570f57f7773f645bc99f6da39160a99f572a133eceea654ce8e8bebdfd8acf7","abstract_canon_sha256":"d42042a98a6800f0b81b6d0ab20950bcaf096789ee6ed3f3052720d4515eeb5c"},"schema_version":"1.0"},"canonical_sha256":"36f0346f5c031bbc2d8f49221aabbf4b47c8e0322394d0b74c5071e194a4a66e","source":{"kind":"arxiv","id":"0905.0498","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0498","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0498v2","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0498","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"G3YDI324AMN3","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G3YDI324AMN3YLMP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G3YDI324","created_at":"2026-05-18T12:25:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:G3YDI324AMN3YLMPJERBVK57JN","target":"record","payload":{"canonical_record":{"source":{"id":"0905.0498","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T21:41:27Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c570f57f7773f645bc99f6da39160a99f572a133eceea654ce8e8bebdfd8acf7","abstract_canon_sha256":"d42042a98a6800f0b81b6d0ab20950bcaf096789ee6ed3f3052720d4515eeb5c"},"schema_version":"1.0"},"canonical_sha256":"36f0346f5c031bbc2d8f49221aabbf4b47c8e0322394d0b74c5071e194a4a66e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:39.857168Z","signature_b64":"EXdm2x26/HnZO0LmbXoCptIn0ghV5UEKq8RW2GXj7x2Ckwzlu0lz+7JINUxFM1KB69yXE6o4ByisMSx89eu5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36f0346f5c031bbc2d8f49221aabbf4b47c8e0322394d0b74c5071e194a4a66e","last_reissued_at":"2026-05-18T03:26:39.856568Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:39.856568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0905.0498","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KXgni7qkaBjK9Lg8z2zd6F8OmgTpOOSC6iZT/r4VrJIylcSMMNTmbMA81gojusf4UyYTaIevR4y5A39XuA+/Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:31.544193Z"},"content_sha256":"5d2e4281449d698c52b552e4c99fbac6c848473cc9cdcc7cfc1322216f756f8a","schema_version":"1.0","event_id":"sha256:5d2e4281449d698c52b552e4c99fbac6c848473cc9cdcc7cfc1322216f756f8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:G3YDI324AMN3YLMPJERBVK57JN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Extremal K\\\"ahler metrics on projective bundles over a curve","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.DG","authors_text":"Christina W. T{\\o}nnesen-Friedman, David M. J. Calderbank, Paul Gauduchon, Vestislav Apostolov","submitted_at":"2009-05-04T21:41:27Z","abstract_excerpt":"Let $M=P(E)$ be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle $E \\to \\Sigma$ over a compact complex curve $\\Sigma$ of genus $\\ge 2$. Building on ideas of Fujiki, we prove that $M$ admits a K\\\"ahler metric of constant scalar curvature if and only if $E$ is polystable. We also address the more general existence  problem of  extremal K\\\"ahler metrics on such bundles and prove that the splitting of $E$ as a direct sum of stable subbundles is necessary and sufficient condition for the existence of extremal K\\\"ahler metrics in sufficiently sma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0498","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zyysIGO1JhCO8hcTf1/AzOjFPvZKV8hBxLMRT9pw1DMCf94rUH1Au1rn6PO1gDoL/ynzetZwpZpnD5a8GxHtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T02:01:31.544546Z"},"content_sha256":"8dc064247d47b6855d9b525673ce579b68bc7b951e4e9f2f4c67ba7313c727b6","schema_version":"1.0","event_id":"sha256:8dc064247d47b6855d9b525673ce579b68bc7b951e4e9f2f4c67ba7313c727b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3YDI324AMN3YLMPJERBVK57JN/bundle.json","state_url":"https://pith.science/pith/G3YDI324AMN3YLMPJERBVK57JN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3YDI324AMN3YLMPJERBVK57JN/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T02:01:31Z","links":{"resolver":"https://pith.science/pith/G3YDI324AMN3YLMPJERBVK57JN","bundle":"https://pith.science/pith/G3YDI324AMN3YLMPJERBVK57JN/bundle.json","state":"https://pith.science/pith/G3YDI324AMN3YLMPJERBVK57JN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3YDI324AMN3YLMPJERBVK57JN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:G3YDI324AMN3YLMPJERBVK57JN","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":"d42042a98a6800f0b81b6d0ab20950bcaf096789ee6ed3f3052720d4515eeb5c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T21:41:27Z","title_canon_sha256":"c570f57f7773f645bc99f6da39160a99f572a133eceea654ce8e8bebdfd8acf7"},"schema_version":"1.0","source":{"id":"0905.0498","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0498","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0498v2","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0498","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"G3YDI324AMN3","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_16","alias_value":"G3YDI324AMN3YLMP","created_at":"2026-05-18T12:25:59Z"},{"alias_kind":"pith_short_8","alias_value":"G3YDI324","created_at":"2026-05-18T12:25:59Z"}],"graph_snapshots":[{"event_id":"sha256:8dc064247d47b6855d9b525673ce579b68bc7b951e4e9f2f4c67ba7313c727b6","target":"graph","created_at":"2026-05-18T03:26:39Z","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 $M=P(E)$ be the complex manifold underlying the total space of the projectivization of a holomorphic vector bundle $E \\to \\Sigma$ over a compact complex curve $\\Sigma$ of genus $\\ge 2$. Building on ideas of Fujiki, we prove that $M$ admits a K\\\"ahler metric of constant scalar curvature if and only if $E$ is polystable. We also address the more general existence  problem of  extremal K\\\"ahler metrics on such bundles and prove that the splitting of $E$ as a direct sum of stable subbundles is necessary and sufficient condition for the existence of extremal K\\\"ahler metrics in sufficiently sma","authors_text":"Christina W. T{\\o}nnesen-Friedman, David M. J. Calderbank, Paul Gauduchon, Vestislav Apostolov","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T21:41:27Z","title":"Extremal K\\\"ahler metrics on projective bundles over a curve"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0498","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":"sha256:5d2e4281449d698c52b552e4c99fbac6c848473cc9cdcc7cfc1322216f756f8a","target":"record","created_at":"2026-05-18T03:26:39Z","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":"d42042a98a6800f0b81b6d0ab20950bcaf096789ee6ed3f3052720d4515eeb5c","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T21:41:27Z","title_canon_sha256":"c570f57f7773f645bc99f6da39160a99f572a133eceea654ce8e8bebdfd8acf7"},"schema_version":"1.0","source":{"id":"0905.0498","kind":"arxiv","version":2}},"canonical_sha256":"36f0346f5c031bbc2d8f49221aabbf4b47c8e0322394d0b74c5071e194a4a66e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36f0346f5c031bbc2d8f49221aabbf4b47c8e0322394d0b74c5071e194a4a66e","first_computed_at":"2026-05-18T03:26:39.856568Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:39.856568Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EXdm2x26/HnZO0LmbXoCptIn0ghV5UEKq8RW2GXj7x2Ckwzlu0lz+7JINUxFM1KB69yXE6o4ByisMSx89eu5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:39.857168Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0498","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d2e4281449d698c52b552e4c99fbac6c848473cc9cdcc7cfc1322216f756f8a","sha256:8dc064247d47b6855d9b525673ce579b68bc7b951e4e9f2f4c67ba7313c727b6"],"state_sha256":"0b4af650e3234deffd2430a79430f9a2ec632fdc666e8b4da905474a8ba0ce48"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBJsy3OuCdtWbO3nfnlSGG7q/DgXecM/oXcqog3Y/gMHWjujsQbJltkERHwGa1In/Ifho9g10GXJZKFSih+LBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T02:01:31.546482Z","bundle_sha256":"b0eec640014ccb3b988ba0946ec1c59258ae426d71448b28701b87047261a155"}}