{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DBFDM6PQ32NWSMOUHJVJRVUOEZ","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":"08c10a19950ac2c0e90daf806dc0910979f9f9531cddf0415302ac9a667c28d8","cross_cats_sorted":["math.AG","math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-05T20:41:56Z","title_canon_sha256":"c4a0acabb61a0ed9402775344e9e5593993fe0d78ed0e01c274e5a0f4288d065"},"schema_version":"1.0","source":{"id":"1102.1097","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.1097","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"arxiv_version","alias_value":"1102.1097v2","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1097","created_at":"2026-05-18T01:27:05Z"},{"alias_kind":"pith_short_12","alias_value":"DBFDM6PQ32NW","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DBFDM6PQ32NWSMOU","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DBFDM6PQ","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:f95ffb9b581d53e173925d39be79ff321db7a715f134e2fe9f49c640df3bd12d","target":"graph","created_at":"2026-05-18T01:27:05Z","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 us consider a projective manifold and $\\Omega$ a volume form. We define the gradient flow associated to the problem of $\\Omega$-balanced metrics in the quantum formalism, the \\Omega$-balacing flow. At the limit of the quantization, we prove that the $\\Omega$-balacing flow converges towards a natural flow in K\\\"ahler geometry, the $\\Omega$-K\\\"ahler flow. We study the existence of the $\\Omega$-K\\\"ahler flow and proves its long time existence and convergence towards the solution to the Calabi problem of prescribing the volume form in a given K\\\"ahler class. We derive some natural geometric co","authors_text":"H. -D. Cao, Julien Keller","cross_cats":["math.AG","math.CV","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-05T20:41:56Z","title":"About the Calabi problem: a finite dimensional approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1097","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":"sha256:02b938a4a60e63f6c36d1b21e69fff33f6e07a429c00ea9b9920047a4c137656","target":"record","created_at":"2026-05-18T01:27:05Z","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":"08c10a19950ac2c0e90daf806dc0910979f9f9531cddf0415302ac9a667c28d8","cross_cats_sorted":["math.AG","math.CV","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-02-05T20:41:56Z","title_canon_sha256":"c4a0acabb61a0ed9402775344e9e5593993fe0d78ed0e01c274e5a0f4288d065"},"schema_version":"1.0","source":{"id":"1102.1097","kind":"arxiv","version":2}},"canonical_sha256":"184a3679f0de9b6931d43a6a98d68e266d26c7e215c4d4e416879b69557c6895","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"184a3679f0de9b6931d43a6a98d68e266d26c7e215c4d4e416879b69557c6895","first_computed_at":"2026-05-18T01:27:05.950623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:05.950623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cSEr+HX1+mAu9O3DzX9yuqHBq9cvs/Lsl2vWwpuM2CEUPYL38l8m+PrVfPlcnG8QFpPwSx2y+i0zf/Qx5Y24Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:05.951293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.1097","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:02b938a4a60e63f6c36d1b21e69fff33f6e07a429c00ea9b9920047a4c137656","sha256:f95ffb9b581d53e173925d39be79ff321db7a715f134e2fe9f49c640df3bd12d"],"state_sha256":"fe7540d9da0406b3e7eceb7e3b33788cb094ba605bc2a32c639e7d1325ac176c"}