{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HEPTAL6ID4QCNUTVRITOUB7YYG","short_pith_number":"pith:HEPTAL6I","canonical_record":{"source":{"id":"1302.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-07T01:59:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"76c2fb754bfb329b96d79bbfde783c855e3f4613a1199d5cfd551e9586089962","abstract_canon_sha256":"e4db1099448e77667716e4b6639a9653c369737aaede11c47eec52f956612f30"},"schema_version":"1.0"},"canonical_sha256":"391f302fc81f2026d2758a26ea07f8c196bdace12396d0be94ae358543c4b7b3","source":{"kind":"arxiv","id":"1302.1627","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1627","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1627v1","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1627","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"HEPTAL6ID4QC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HEPTAL6ID4QCNUTV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HEPTAL6I","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HEPTAL6ID4QCNUTVRITOUB7YYG","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1627","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-07T01:59:48Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"76c2fb754bfb329b96d79bbfde783c855e3f4613a1199d5cfd551e9586089962","abstract_canon_sha256":"e4db1099448e77667716e4b6639a9653c369737aaede11c47eec52f956612f30"},"schema_version":"1.0"},"canonical_sha256":"391f302fc81f2026d2758a26ea07f8c196bdace12396d0be94ae358543c4b7b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:15.245437Z","signature_b64":"eaIU5ljGjlTn7LqDQyAF9satM9MVeZfBaWK6DzktmoDVjxVxodER/Ag9zi8FmiVPZgyvfC5ampV5NkRI0qHzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"391f302fc81f2026d2758a26ea07f8c196bdace12396d0be94ae358543c4b7b3","last_reissued_at":"2026-05-18T03:34:15.244670Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:15.244670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1627","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgrBLTail0687UA6RMzFLcvvWLAIhhkIxw+dRW3nv9mgkKjkV6YB/tZKjTLo/R+SDtg8wh7hVTPt3uX7pVO8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:27:18.132748Z"},"content_sha256":"15bca799d91c16a06b8d76989573105d4175b912ff5cc64be0c0538d5f82cf19","schema_version":"1.0","event_id":"sha256:15bca799d91c16a06b8d76989573105d4175b912ff5cc64be0c0538d5f82cf19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HEPTAL6ID4QCNUTVRITOUB7YYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The interior regularity of the Calabi flow on a toric surface","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Hongnian Huang, Li Sheng, Xiuxiong Chen","submitted_at":"2013-02-07T01:59:48Z","abstract_excerpt":"Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t < T."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1627","kind":"arxiv","version":1},"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":"2026-05-18T03:34:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X2q013MWJRea7N0lpfdpUdqQKvD2XW3QtXlZSmUeVnE6cMxyS/arezwmHMUoEYVVIAKIjIjZ9OM8wj+cFApuCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T21:27:18.133438Z"},"content_sha256":"7224ca2927aaf0b00d98c17d76ea0bf05f1dd8a19cce0b98e79f3b4ac07fc1d0","schema_version":"1.0","event_id":"sha256:7224ca2927aaf0b00d98c17d76ea0bf05f1dd8a19cce0b98e79f3b4ac07fc1d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/bundle.json","state_url":"https://pith.science/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/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":"2026-06-06T21:27:18Z","links":{"resolver":"https://pith.science/pith/HEPTAL6ID4QCNUTVRITOUB7YYG","bundle":"https://pith.science/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/bundle.json","state":"https://pith.science/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HEPTAL6ID4QCNUTVRITOUB7YYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HEPTAL6ID4QCNUTVRITOUB7YYG","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":"e4db1099448e77667716e4b6639a9653c369737aaede11c47eec52f956612f30","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-07T01:59:48Z","title_canon_sha256":"76c2fb754bfb329b96d79bbfde783c855e3f4613a1199d5cfd551e9586089962"},"schema_version":"1.0","source":{"id":"1302.1627","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1627","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1627v1","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1627","created_at":"2026-05-18T03:34:15Z"},{"alias_kind":"pith_short_12","alias_value":"HEPTAL6ID4QC","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HEPTAL6ID4QCNUTV","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HEPTAL6I","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:7224ca2927aaf0b00d98c17d76ea0bf05f1dd8a19cce0b98e79f3b4ac07fc1d0","target":"graph","created_at":"2026-05-18T03:34:15Z","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":"Let X be a toric surface with Delzant polygon P and u(t) be a solution of the Calabi flow equation on P. Suppose the Calabi flow exists in [0, T). By studying local estimates of the Riemann curvature and the geodesic distance under the Calabi flow, we prove a uniform interior estimate of u(t) for t < T.","authors_text":"Hongnian Huang, Li Sheng, Xiuxiong Chen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-07T01:59:48Z","title":"The interior regularity of the Calabi flow on a toric surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1627","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":"sha256:15bca799d91c16a06b8d76989573105d4175b912ff5cc64be0c0538d5f82cf19","target":"record","created_at":"2026-05-18T03:34:15Z","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":"e4db1099448e77667716e4b6639a9653c369737aaede11c47eec52f956612f30","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-02-07T01:59:48Z","title_canon_sha256":"76c2fb754bfb329b96d79bbfde783c855e3f4613a1199d5cfd551e9586089962"},"schema_version":"1.0","source":{"id":"1302.1627","kind":"arxiv","version":1}},"canonical_sha256":"391f302fc81f2026d2758a26ea07f8c196bdace12396d0be94ae358543c4b7b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"391f302fc81f2026d2758a26ea07f8c196bdace12396d0be94ae358543c4b7b3","first_computed_at":"2026-05-18T03:34:15.244670Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:15.244670Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaIU5ljGjlTn7LqDQyAF9satM9MVeZfBaWK6DzktmoDVjxVxodER/Ag9zi8FmiVPZgyvfC5ampV5NkRI0qHzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:15.245437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1627","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:15bca799d91c16a06b8d76989573105d4175b912ff5cc64be0c0538d5f82cf19","sha256:7224ca2927aaf0b00d98c17d76ea0bf05f1dd8a19cce0b98e79f3b4ac07fc1d0"],"state_sha256":"210e27c0e53da35bc9b241dd933292a3dd27a3825595f7a176451f9a4b6da874"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"reLzJPJ3jua3eOhOfhy86gz+50KMNh1UgnfTmJUfBIcazbVur1wy2O387X3qiTcYuBbFDmJF2d+T7Aft1veuCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T21:27:18.137024Z","bundle_sha256":"b721cba553c7cb74791fff819cd90e3f773b8be25c5b14ee455f5b026177d866"}}