{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OLY2LIR43T7GTUNYPGHSNURB6E","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":"1d9aeca596665dbf48331b6d9bdb1419354b0ed1120810e6898277ce7263a271","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T05:06:31Z","title_canon_sha256":"4fb3965497ebe9a8fa4d1e1b462f5801cd5d1d71ec582471a717e6da08014ec4"},"schema_version":"1.0","source":{"id":"1211.0764","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.0764","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"arxiv_version","alias_value":"1211.0764v1","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0764","created_at":"2026-05-18T03:41:31Z"},{"alias_kind":"pith_short_12","alias_value":"OLY2LIR43T7G","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OLY2LIR43T7GTUNY","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OLY2LIR4","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:d19552b1b0948eba53f2fc2091f7bbd6a7429639c3b5e35a8494cb0e8c651a58","target":"graph","created_at":"2026-05-18T03:41:31Z","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 show that the surface area preserving mean curvature flow in Euclidean space exists for all time and converges exponentially to a round sphere, if initially the L^2-norm of the traceless second fundamental form is small (but the initial hypersurface is not necessarily convex).","authors_text":"Longzhi Lin, Zheng Huang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T05:06:31Z","title":"Stability of the surface area preserving mean curvature flow in Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0764","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":"sha256:760388f3627963ea7bb2124602efbbe21bf338d48dddc69a7164a19cfe7cb1fc","target":"record","created_at":"2026-05-18T03:41:31Z","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":"1d9aeca596665dbf48331b6d9bdb1419354b0ed1120810e6898277ce7263a271","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T05:06:31Z","title_canon_sha256":"4fb3965497ebe9a8fa4d1e1b462f5801cd5d1d71ec582471a717e6da08014ec4"},"schema_version":"1.0","source":{"id":"1211.0764","kind":"arxiv","version":1}},"canonical_sha256":"72f1a5a23cdcfe69d1b8798f26d221f11b6f8d2f8e6166d5542a3cfa0160f7aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72f1a5a23cdcfe69d1b8798f26d221f11b6f8d2f8e6166d5542a3cfa0160f7aa","first_computed_at":"2026-05-18T03:41:31.633926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:31.633926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VOHul48MkUaxYE/WgCVDQ7p8S2rFIE2WE7aABeTKcMYj/4fzVs1xAV4wM3UWE1MmE5amRtn6OOAmWN1PjKBHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:31.634503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.0764","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:760388f3627963ea7bb2124602efbbe21bf338d48dddc69a7164a19cfe7cb1fc","sha256:d19552b1b0948eba53f2fc2091f7bbd6a7429639c3b5e35a8494cb0e8c651a58"],"state_sha256":"de6bbe59d6623795cd96ee4e3b94912c7615e2aee518ae0bff5b84e22a74fbb2"}