{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:LCQOGQMTNQ2YGRVPI4IVOE2DR2","short_pith_number":"pith:LCQOGQMT","schema_version":"1.0","canonical_sha256":"58a0e341936c358346af47115713438ebbd4c2130994e7513decc993b540fe6b","source":{"kind":"arxiv","id":"1204.5010","version":1},"attestation_state":"computed","paper":{"title":"$\\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ben Andrews, Haizhong Li, Yong Wei","submitted_at":"2012-04-23T09:28:55Z","abstract_excerpt":"In this paper, we formulate the notion of the $\\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\\mathcal{F}$-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's results."},"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":"1204.5010","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2012-04-23T09:28:55Z","cross_cats_sorted":[],"title_canon_sha256":"cc0f557bff15c09e9d9aa666e0c2b75351544e47fa8abf343272e0e12f7e6997","abstract_canon_sha256":"e153d93f29aaef0148cdcb95e2ef48bed67cc118261054613f416c03507e89c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:14.899288Z","signature_b64":"CqH3YEOxeVATgSYKZ+0Y3Sv0u4ElBTxqayjbcwKm87eezlgMopm5tWnaIWDDfgc9VzLJEAR1uUf8s0Ou2sXTDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58a0e341936c358346af47115713438ebbd4c2130994e7513decc993b540fe6b","last_reissued_at":"2026-05-18T03:57:14.898840Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:14.898840Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$\\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Ben Andrews, Haizhong Li, Yong Wei","submitted_at":"2012-04-23T09:28:55Z","abstract_excerpt":"In this paper, we formulate the notion of the $\\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\\mathcal{F}$-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5010","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":"1204.5010","created_at":"2026-05-18T03:57:14.898904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1204.5010v1","created_at":"2026-05-18T03:57:14.898904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5010","created_at":"2026-05-18T03:57:14.898904+00:00"},{"alias_kind":"pith_short_12","alias_value":"LCQOGQMTNQ2Y","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_16","alias_value":"LCQOGQMTNQ2YGRVP","created_at":"2026-05-18T12:27:14.488303+00:00"},{"alias_kind":"pith_short_8","alias_value":"LCQOGQMT","created_at":"2026-05-18T12:27:14.488303+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/LCQOGQMTNQ2YGRVPI4IVOE2DR2","json":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2.json","graph_json":"https://pith.science/api/pith-number/LCQOGQMTNQ2YGRVPI4IVOE2DR2/graph.json","events_json":"https://pith.science/api/pith-number/LCQOGQMTNQ2YGRVPI4IVOE2DR2/events.json","paper":"https://pith.science/paper/LCQOGQMT"},"agent_actions":{"view_html":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2","download_json":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2.json","view_paper":"https://pith.science/paper/LCQOGQMT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1204.5010&json=true","fetch_graph":"https://pith.science/api/pith-number/LCQOGQMTNQ2YGRVPI4IVOE2DR2/graph.json","fetch_events":"https://pith.science/api/pith-number/LCQOGQMTNQ2YGRVPI4IVOE2DR2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2/action/storage_attestation","attest_author":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2/action/author_attestation","sign_citation":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2/action/citation_signature","submit_replication":"https://pith.science/pith/LCQOGQMTNQ2YGRVPI4IVOE2DR2/action/replication_record"}},"created_at":"2026-05-18T03:57:14.898904+00:00","updated_at":"2026-05-18T03:57:14.898904+00:00"}