{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AGKNU5OKLVCITANXO5YOA4IHEW","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":"5873910b7f76a186fe274b08a095075845e25a1a536362c7cbdac5eda0965722","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-01T06:40:16Z","title_canon_sha256":"5d5b71fd8be1d2888ebbbe1a74894bacb0b5f5abcef5d2a405e90360a9b5bb7f"},"schema_version":"1.0","source":{"id":"1108.0247","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1108.0247","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1108.0247v1","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.0247","created_at":"2026-05-18T04:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"AGKNU5OKLVCI","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AGKNU5OKLVCITANX","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AGKNU5OK","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:b453c8e7ad59db1e701e5b14750302ba762d13879bc12d20dee94091f6dd330e","target":"graph","created_at":"2026-05-18T04:16:31Z","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":"We provide a direct proof of a non-collapsing estimate for compact hypersurfaces with positive mean curvature moving under the mean curvature flow: Precisely, if every point on the initial hypersurface admits an interior sphere with radius inversely proportional to the mean curvature at that point, then this remains true for all positive times in the interval of existence.","authors_text":"Ben Andrews","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-01T06:40:16Z","title":"Non-collapsing in mean-convex mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.0247","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":"sha256:2b481de5ef75a67e677933e63c9561947db04900e0163891f527041341336a54","target":"record","created_at":"2026-05-18T04:16:31Z","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":"5873910b7f76a186fe274b08a095075845e25a1a536362c7cbdac5eda0965722","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-08-01T06:40:16Z","title_canon_sha256":"5d5b71fd8be1d2888ebbbe1a74894bacb0b5f5abcef5d2a405e90360a9b5bb7f"},"schema_version":"1.0","source":{"id":"1108.0247","kind":"arxiv","version":1}},"canonical_sha256":"0194da75ca5d448981b77770e071072583bbba3816f776d46e8e840d22b71579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0194da75ca5d448981b77770e071072583bbba3816f776d46e8e840d22b71579","first_computed_at":"2026-05-18T04:16:31.417621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:31.417621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HLMgheb3vjCPvvWF+lPBgh3d7of0CLf3r+UryWL8hj8+CGcaRhdjMMoR4uTJxlYa+ZUALjaZy/6ND4nVjpGbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:31.418056Z","signed_message":"canonical_sha256_bytes"},"source_id":"1108.0247","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b481de5ef75a67e677933e63c9561947db04900e0163891f527041341336a54","sha256:b453c8e7ad59db1e701e5b14750302ba762d13879bc12d20dee94091f6dd330e"],"state_sha256":"77abe74500c85a6ecbe4f64e375e1a39e1a9b80434e5161b58ffb88def9e36af"}