{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EGQQCSW4EID2V4RMFRYXQD3SVS","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":"e2a629aceeff7cfdf953160fba17e4719c01fefbd5d81c64311b3680ba34f6a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-30T04:52:39Z","title_canon_sha256":"cbba95c22eec93925b6cd69547c1889e1bf85be93a9bfc15f9a792aa0740227c"},"schema_version":"1.0","source":{"id":"1405.7774","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.7774","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"arxiv_version","alias_value":"1405.7774v1","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7774","created_at":"2026-05-18T02:50:49Z"},{"alias_kind":"pith_short_12","alias_value":"EGQQCSW4EID2","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EGQQCSW4EID2V4RM","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EGQQCSW4","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:b00b3a324114d70a8da6d7848a95321e178df3659e5ace719cc7fa4f06571986","target":"graph","created_at":"2026-05-18T02:50:49Z","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":"The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and secondly, to illustrate the application of Killing vector fields in the preservation of graphicality for the mean curvature flow with free boundary. To this end we focus on the mean curvature flow of a topological annulus with inner boundary meeting a standard n-sphere in \\R^{n+1} perpendicularly and outer boundary fixed to an (n-1)-sphere with radius R>1 ","authors_text":"Glen Wheeler, Valentina-Mira Wheeler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-30T04:52:39Z","title":"Mean curvature flow with free boundary outside a hypersphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7774","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":"sha256:0b9e624ffebe17ce9ffef66b1bf07ca1aec430f22acf8fe1da5d91a7786cad9f","target":"record","created_at":"2026-05-18T02:50:49Z","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":"e2a629aceeff7cfdf953160fba17e4719c01fefbd5d81c64311b3680ba34f6a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-30T04:52:39Z","title_canon_sha256":"cbba95c22eec93925b6cd69547c1889e1bf85be93a9bfc15f9a792aa0740227c"},"schema_version":"1.0","source":{"id":"1405.7774","kind":"arxiv","version":1}},"canonical_sha256":"21a1014adc2207aaf22c2c71780f72ac9fbb78e96659762ea45c02d2de421f46","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"21a1014adc2207aaf22c2c71780f72ac9fbb78e96659762ea45c02d2de421f46","first_computed_at":"2026-05-18T02:50:49.876872Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:49.876872Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3c7p2OxZMFY/vRZatDI87tXSvY2jvmGCHuG/zKtO1xuCV1OFHhiMm/CRI+yKiYm3fMmzFHqSSe5HPbNNgK4YDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:49.877455Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.7774","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b9e624ffebe17ce9ffef66b1bf07ca1aec430f22acf8fe1da5d91a7786cad9f","sha256:b00b3a324114d70a8da6d7848a95321e178df3659e5ace719cc7fa4f06571986"],"state_sha256":"f40278e61f8935b20b5dfc443cea4bcecf41d99ed8443d08b59cbf5ccce86ef2"}