{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:OLY2LIR43T7GTUNYPGHSNURB6E","short_pith_number":"pith:OLY2LIR4","schema_version":"1.0","canonical_sha256":"72f1a5a23cdcfe69d1b8798f26d221f11b6f8d2f8e6166d5542a3cfa0160f7aa","source":{"kind":"arxiv","id":"1211.0764","version":1},"attestation_state":"computed","paper":{"title":"Stability of the surface area preserving mean curvature flow in Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Longzhi Lin, Zheng Huang","submitted_at":"2012-11-05T05:06:31Z","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)."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1211.0764","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-11-05T05:06:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4fb3965497ebe9a8fa4d1e1b462f5801cd5d1d71ec582471a717e6da08014ec4","abstract_canon_sha256":"1d9aeca596665dbf48331b6d9bdb1419354b0ed1120810e6898277ce7263a271"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:31.634503Z","signature_b64":"VOHul48MkUaxYE/WgCVDQ7p8S2rFIE2WE7aABeTKcMYj/4fzVs1xAV4wM3UWE1MmE5amRtn6OOAmWN1PjKBHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72f1a5a23cdcfe69d1b8798f26d221f11b6f8d2f8e6166d5542a3cfa0160f7aa","last_reissued_at":"2026-05-18T03:41:31.633926Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:31.633926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stability of the surface area preserving mean curvature flow in Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Longzhi Lin, Zheng Huang","submitted_at":"2012-11-05T05:06:31Z","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)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.0764","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.0764","created_at":"2026-05-18T03:41:31.634021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.0764v1","created_at":"2026-05-18T03:41:31.634021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.0764","created_at":"2026-05-18T03:41:31.634021+00:00"},{"alias_kind":"pith_short_12","alias_value":"OLY2LIR43T7G","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_16","alias_value":"OLY2LIR43T7GTUNY","created_at":"2026-05-18T12:27:16.716162+00:00"},{"alias_kind":"pith_short_8","alias_value":"OLY2LIR4","created_at":"2026-05-18T12:27:16.716162+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E","json":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E.json","graph_json":"https://pith.science/api/pith-number/OLY2LIR43T7GTUNYPGHSNURB6E/graph.json","events_json":"https://pith.science/api/pith-number/OLY2LIR43T7GTUNYPGHSNURB6E/events.json","paper":"https://pith.science/paper/OLY2LIR4"},"agent_actions":{"view_html":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E","download_json":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E.json","view_paper":"https://pith.science/paper/OLY2LIR4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.0764&json=true","fetch_graph":"https://pith.science/api/pith-number/OLY2LIR43T7GTUNYPGHSNURB6E/graph.json","fetch_events":"https://pith.science/api/pith-number/OLY2LIR43T7GTUNYPGHSNURB6E/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E/action/storage_attestation","attest_author":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E/action/author_attestation","sign_citation":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E/action/citation_signature","submit_replication":"https://pith.science/pith/OLY2LIR43T7GTUNYPGHSNURB6E/action/replication_record"}},"created_at":"2026-05-18T03:41:31.634021+00:00","updated_at":"2026-05-18T03:41:31.634021+00:00"}