{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:DDUCKA65SINF7LGDCIQ7XYEMU5","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":"8dd07ce120806ba6541361db3a682ec2babd4da311d4e39ea2dd45773d956330","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:13:38Z","title_canon_sha256":"d3d267f894039d2d4c12462b2bda400c391386f59d8ea0effd39d25f30b804dc"},"schema_version":"1.0","source":{"id":"1207.5964","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5964","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5964v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5964","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"DDUCKA65SINF","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_16","alias_value":"DDUCKA65SINF7LGD","created_at":"2026-05-18T12:27:01Z"},{"alias_kind":"pith_short_8","alias_value":"DDUCKA65","created_at":"2026-05-18T12:27:01Z"}],"graph_snapshots":[{"event_id":"sha256:a91c79acd136296a0dec7e970ca90435ff1062a3677a107e0ce9b358de9779e8","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 surface and $u$ be a normalized symplectic potential on the corresponding polygon $P$. Suppose that the Riemannian curvature is bounded by a constant $C_1$ and $\\int_{\\partial P} u ~ d \\sigma < C_2, $ then there exists a constant $C_3$ depending only on $C_1, C_2$ and $P$ such that the diameter of $X$ is bounded by $C_3$. Moreoever, we can show that there is a constant $M > 0$ depending only on $C_1, C_2$ and $P$ such that Donaldson's $M$-condition holds for $u$. As an application, we show that if $(X,P)$ is (analytic) relative $K$-stable, then the modified Calabi flow conve","authors_text":"Hongnian Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:13:38Z","title":"Toric Surfaces, K-Stability and Calabi Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5964","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:e12b7462a192c1cf5d51fbfc79d535cceea942577b925f586ee0d91d29f06ac0","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":"8dd07ce120806ba6541361db3a682ec2babd4da311d4e39ea2dd45773d956330","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-07-25T12:13:38Z","title_canon_sha256":"d3d267f894039d2d4c12462b2bda400c391386f59d8ea0effd39d25f30b804dc"},"schema_version":"1.0","source":{"id":"1207.5964","kind":"arxiv","version":1}},"canonical_sha256":"18e82503dd921a5facc31221fbe08ca742e1ced94d97e9c6c41ee781471c6152","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18e82503dd921a5facc31221fbe08ca742e1ced94d97e9c6c41ee781471c6152","first_computed_at":"2026-05-18T03:50:09.802771Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.802771Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TxTwcE6vQGQDrnFfgr1J/PmxlTkBMhs0AW4wX2T4u1FYaprGba8W7O0vlzi9ND2Z7mqreswKWW3/I7SIg3lPBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.803553Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5964","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e12b7462a192c1cf5d51fbfc79d535cceea942577b925f586ee0d91d29f06ac0","sha256:a91c79acd136296a0dec7e970ca90435ff1062a3677a107e0ce9b358de9779e8"],"state_sha256":"4169602de0858f5c7d82218223a9532ca2dd03aaff501fd15ce6a3f570d838b0"}