{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:LZNBSR7Y2RPGUUZ5CSSNCRFBT7","short_pith_number":"pith:LZNBSR7Y","schema_version":"1.0","canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","source":{"kind":"arxiv","id":"1710.00433","version":2},"attestation_state":"computed","paper":{"title":"A strong stability condition on minimal submanifolds and its implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chung-Jun Tsai, Mu-Tao Wang","submitted_at":"2017-10-01T23:13:02Z","abstract_excerpt":"We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a C^1 neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem [arXiv:1605.03645] which applies only to calibrated"},"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":"1710.00433","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-10-01T23:13:02Z","cross_cats_sorted":[],"title_canon_sha256":"a368c03e11bcb5b9c86b923de24ea3650f64e9f11af5282eca818733097ffabf","abstract_canon_sha256":"3bc5bb3a55ff2e0694b16938c54f0895aaa9af0b04c610add91828eae6371dc8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:56.220433Z","signature_b64":"kaa858h7lsh3jymL265va+7GG1AqBQ03V/lPLxK9CxjZERKMZNWFgAFYxXcQJVdwZYU61V8D9Wsen0QwwnD8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e5a1947f8d45e6a533d14a4d144a19fcc525ccbb81eaee1d1831416874dca24","last_reissued_at":"2026-05-17T23:58:56.220011Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:56.220011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A strong stability condition on minimal submanifolds and its implications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Chung-Jun Tsai, Mu-Tao Wang","submitted_at":"2017-10-01T23:13:02Z","abstract_excerpt":"We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for minimal submanifolds that satisfy this condition. The latter theorem states that the mean curvature flow of any other submanifold in a C^1 neighborhood of such a minimal submanifold exists for all time, and converges exponentially to the minimal one. This extends our previous uniqueness and stability theorem [arXiv:1605.03645] which applies only to calibrated"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00433","kind":"arxiv","version":2},"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":"1710.00433","created_at":"2026-05-17T23:58:56.220077+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.00433v2","created_at":"2026-05-17T23:58:56.220077+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00433","created_at":"2026-05-17T23:58:56.220077+00:00"},{"alias_kind":"pith_short_12","alias_value":"LZNBSR7Y2RPG","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_16","alias_value":"LZNBSR7Y2RPGUUZ5","created_at":"2026-05-18T12:31:28.150371+00:00"},{"alias_kind":"pith_short_8","alias_value":"LZNBSR7Y","created_at":"2026-05-18T12:31:28.150371+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/LZNBSR7Y2RPGUUZ5CSSNCRFBT7","json":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7.json","graph_json":"https://pith.science/api/pith-number/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/graph.json","events_json":"https://pith.science/api/pith-number/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/events.json","paper":"https://pith.science/paper/LZNBSR7Y"},"agent_actions":{"view_html":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7","download_json":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7.json","view_paper":"https://pith.science/paper/LZNBSR7Y","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.00433&json=true","fetch_graph":"https://pith.science/api/pith-number/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/graph.json","fetch_events":"https://pith.science/api/pith-number/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/action/storage_attestation","attest_author":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/action/author_attestation","sign_citation":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/action/citation_signature","submit_replication":"https://pith.science/pith/LZNBSR7Y2RPGUUZ5CSSNCRFBT7/action/replication_record"}},"created_at":"2026-05-17T23:58:56.220077+00:00","updated_at":"2026-05-17T23:58:56.220077+00:00"}