{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4QZ77UIQHTDC2IS4LTEHU7XCWT","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":"f67b50efb02efb0c7559fea37594f27708ec973fc47e846d0e4fd26ed9b62870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-29T20:19:27Z","title_canon_sha256":"52d4de6997be076f512a385c9422ce09ad8f739862a174b3cc8df1ef73e783d6"},"schema_version":"1.0","source":{"id":"1301.7045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.7045","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"1301.7045v1","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.7045","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"4QZ77UIQHTDC","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4QZ77UIQHTDC2IS4","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4QZ77UIQ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:9f75095d6c9046497d9bc8571f4085322246a3e83d5bf6bf882c953fac32a150","target":"graph","created_at":"2026-05-18T01:28:15Z","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 prove the existence of extremal, non-csc, K\\\"ahler metrics on certain unstable projectivised vector bundles $\\P (E) \\to M$ over a cscK-manifold $M$ with discrete holomorphic automorphism group, in certain adiabatic K\\\"ahler classes. In particular, the vector bundles $E \\to M$ under consideration are assumed to split as a direct sum of stable subbundles $E=E_1 \\oplus \\dots \\oplus E_s$ all having different Mumford-Takemoto-slope, e.g. $\\mu(E_1) > \\dots > \\mu(E_s)$.","authors_text":"Till Br\\\"onnle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-29T20:19:27Z","title":"Extremal K\\\"ahler metrics on projectivised vector bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.7045","kind":"arxiv","version":1},"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":"sha256:05453d6c602eb77a8dd3a246ac9c1788e2375490460f571b900a96a9b0e8f408","target":"record","created_at":"2026-05-18T01:28:15Z","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":"f67b50efb02efb0c7559fea37594f27708ec973fc47e846d0e4fd26ed9b62870","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-29T20:19:27Z","title_canon_sha256":"52d4de6997be076f512a385c9422ce09ad8f739862a174b3cc8df1ef73e783d6"},"schema_version":"1.0","source":{"id":"1301.7045","kind":"arxiv","version":1}},"canonical_sha256":"e433ffd1103cc62d225c5cc87a7ee2b4d007297653fdebb0850e24c7ce3113f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e433ffd1103cc62d225c5cc87a7ee2b4d007297653fdebb0850e24c7ce3113f0","first_computed_at":"2026-05-18T01:28:15.406254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:15.406254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xhPCDnZVpSFrtR7RIxLanCxgcTpvU6DsFPIIFNLj8kJYqYirbIqJPRjFNK/WNJyaTL5NEacb23kgEoq+pGNwAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:15.406892Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.7045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05453d6c602eb77a8dd3a246ac9c1788e2375490460f571b900a96a9b0e8f408","sha256:9f75095d6c9046497d9bc8571f4085322246a3e83d5bf6bf882c953fac32a150"],"state_sha256":"2094128aaedc547b4aa76b4d4c40c1be75a4b90599630bc30aaa0add26c30488"}