{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q4TOF3OU7PLA2F2DRCTPJMBYZD","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":"2dc64962b7563e8460edf86122dc9e81cec4c416a337b4ff5d3d577d310bcd0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:17:35Z","title_canon_sha256":"df465465911be8cf520621b8a1a336d714d378f5fe23b78f8b447d38bd7ba2ed"},"schema_version":"1.0","source":{"id":"1207.5969","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5969","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5969v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5969","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"Q4TOF3OU7PLA","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q4TOF3OU7PLA2F2D","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q4TOF3OU","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:d4f0756725c4f9c31b787bb2df5ed97db9bd183a2b7ce42fac5c63a5b8faf7dc","target":"graph","created_at":"2026-05-18T03:50:09Z","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 toric variety and $u$ be a normalized symplectic potential of the corresponding polytope $P$. Suppose that the Riemannian curvature is bounded by 1 and $\n\\int_{\\partial P} u ~ d \\sigma < C_1, $\nthen there exists a constant $C_2$ depending only on $C_1$ and $P$ such that $\\max_P u < C_2$. As an application, we show that if $(X,P)$ is analytic uniform $K$-stable, then the modified Calabi flow converges to an extremal metric exponentially fast by assuming that the Riemannian curvature is uniformly bounded along the Calabi flow. Also we provide a proof of a conjecture of Donaldson. Fi","authors_text":"Hongnian Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:17:35Z","title":"Convergence of the calabi flow on toric varieties and related Kaehler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5969","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:c43ca03957b79c2a37faeab02a435c132b38c9da81674e5b989c96aba56c13c8","target":"record","created_at":"2026-05-18T03:50:09Z","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":"2dc64962b7563e8460edf86122dc9e81cec4c416a337b4ff5d3d577d310bcd0e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:17:35Z","title_canon_sha256":"df465465911be8cf520621b8a1a336d714d378f5fe23b78f8b447d38bd7ba2ed"},"schema_version":"1.0","source":{"id":"1207.5969","kind":"arxiv","version":1}},"canonical_sha256":"8726e2edd4fbd60d174388a6f4b038c8d0ed3e925de720c4d338c1407153b7be","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8726e2edd4fbd60d174388a6f4b038c8d0ed3e925de720c4d338c1407153b7be","first_computed_at":"2026-05-18T03:50:09.765650Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.765650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/74qg9i8SyPq5WhBiSfp0gJKdFuSOfRtaW9Tzcc7eTLqyKjLrxEQ40mOWI9HRQA3rU6/Q7YaUpaXbfDjBr7ZDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.766471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5969","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c43ca03957b79c2a37faeab02a435c132b38c9da81674e5b989c96aba56c13c8","sha256:d4f0756725c4f9c31b787bb2df5ed97db9bd183a2b7ce42fac5c63a5b8faf7dc"],"state_sha256":"e1c6ca2e2e08f785abd72411b1394df7366f6ee5ee4adfebabdbb6d5ac4ee0c9"}