{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4JBX55DCIAVXRMPKYNQ2SZIS37","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":"7f57c83065a1310beb15df8d3c2c336e39fa8fa4a086005784d0dcbbc81a6c69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T15:09:07Z","title_canon_sha256":"9b50193699ec21b51517fa06caa45e1959edf37fd7350465d06e01a107199481"},"schema_version":"1.0","source":{"id":"1304.2627","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.2627","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"arxiv_version","alias_value":"1304.2627v2","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.2627","created_at":"2026-05-18T03:03:21Z"},{"alias_kind":"pith_short_12","alias_value":"4JBX55DCIAVX","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4JBX55DCIAVXRMPK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4JBX55DC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:cf2b23ad6f94d9b81b7590d8ac372dcfe3fddfcf586ead634d711ed3edf909eb","target":"graph","created_at":"2026-05-18T03:03:21Z","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":"In this paper, we prove that if $M_t\\subset \\mathbb{R}^{n+1}$, $2\\leq n\\leq 6$, is the $n$-dimensional closed embedded $\\mathcal{F}-$stable solution to mean curvature flow with mean curvature of $M_t$ is uniformly bounded on $[0,T)$ for $T<\\infty$, then the flow can be smoothly extended over time $T$.","authors_text":"Cheng Liang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T15:09:07Z","title":"On the extension to mean curvature flow in lower dimension"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.2627","kind":"arxiv","version":2},"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":"sha256:455766789e1f596b7859c3ef033293ab9a990ca991c52fc09ba906623902deff","target":"record","created_at":"2026-05-18T03:03:21Z","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":"7f57c83065a1310beb15df8d3c2c336e39fa8fa4a086005784d0dcbbc81a6c69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-09T15:09:07Z","title_canon_sha256":"9b50193699ec21b51517fa06caa45e1959edf37fd7350465d06e01a107199481"},"schema_version":"1.0","source":{"id":"1304.2627","kind":"arxiv","version":2}},"canonical_sha256":"e2437ef462402b78b1eac361a96512dfd0bee2102d7b238710a085735a01e654","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e2437ef462402b78b1eac361a96512dfd0bee2102d7b238710a085735a01e654","first_computed_at":"2026-05-18T03:03:21.035587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:21.035587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eaYs9yfY1QxyVE/8lpL3EpAJMpl3h7mK3toVKiTe+IKBk1l6jDSNkDmTA7FUJG7zGdQNRfHB4OQKS1UuBnUNAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:21.036261Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.2627","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:455766789e1f596b7859c3ef033293ab9a990ca991c52fc09ba906623902deff","sha256:cf2b23ad6f94d9b81b7590d8ac372dcfe3fddfcf586ead634d711ed3edf909eb"],"state_sha256":"d2f13822f1c03c7fabf47753f9dca04ef49d05528518f67e07865e7c5c3b5bf9"}