{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NED2D3RCW7OYYYOBF4YNQ2GGB6","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":"3cee8f959ad314b6e63a729d12cd9538d9336a308b5f583c1ca5dc523e3b3fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-19T05:44:11Z","title_canon_sha256":"0ae64d726d01ef71aa99cada5d0d5c8b9f0e7332899feb7800dd0c23b8c02fec"},"schema_version":"1.0","source":{"id":"1303.4492","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4492","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4492v1","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4492","created_at":"2026-05-18T01:29:59Z"},{"alias_kind":"pith_short_12","alias_value":"NED2D3RCW7OY","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NED2D3RCW7OYYYOB","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NED2D3RC","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:63771ef99bf28e4b391cb1ff9658876c83cf252aa3a342bf3dc885732759d2e0","target":"graph","created_at":"2026-05-18T01:29:59Z","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":"This paper concerns conditions related to the first finite singularity time of a Ricci flow solution on a closed manifold. In particular, we provide a systematic approach to the mean value inequality method, suggested by N. Le and F. He. We also display a close connection between this method and time slice analysis of B. Wang. As an application, we prove several inequalities for a Ricci flow solution on a manifold with nonnegative isotropic curvature.","authors_text":"Hung Tran, Xiaodong Cao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-19T05:44:11Z","title":"Mean Value Inequalities and Conditions to Extend Ricci Flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4492","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:caf15de39c164179f8ecde6dd88493550352b312f563d9b070586bed7b884d7e","target":"record","created_at":"2026-05-18T01:29:59Z","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":"3cee8f959ad314b6e63a729d12cd9538d9336a308b5f583c1ca5dc523e3b3fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-03-19T05:44:11Z","title_canon_sha256":"0ae64d726d01ef71aa99cada5d0d5c8b9f0e7332899feb7800dd0c23b8c02fec"},"schema_version":"1.0","source":{"id":"1303.4492","kind":"arxiv","version":1}},"canonical_sha256":"6907a1ee22b7dd8c61c12f30d868c60fb786af8b21ff3d1741d4b5bd7e41c2d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6907a1ee22b7dd8c61c12f30d868c60fb786af8b21ff3d1741d4b5bd7e41c2d6","first_computed_at":"2026-05-18T01:29:59.859463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:59.859463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYoYeOTVegWKZ+Pnjjgal2x9swrUJU/wzGsxInmqrKOgDGn5Js5zhocteQotoUx2JkI+zsX2m9jQgRaj5WB5Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:59.859971Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4492","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caf15de39c164179f8ecde6dd88493550352b312f563d9b070586bed7b884d7e","sha256:63771ef99bf28e4b391cb1ff9658876c83cf252aa3a342bf3dc885732759d2e0"],"state_sha256":"b9ebd71f939b1b59221c230298c283c9abe5dddcaa4c56ef2da1c50191f7228e"}