{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QHV6OASD3BHA5GKNOGNIUMJK5D","short_pith_number":"pith:QHV6OASD","schema_version":"1.0","canonical_sha256":"81ebe70243d84e0e994d719a8a312ae8e31b2f422b1aa0911ec08bea807e9ceb","source":{"kind":"arxiv","id":"2405.15577","version":3},"attestation_state":"computed","paper":{"title":"Closed mean curvature flows with asymptotically conical singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Tang-Kai Lee, Xinrui Zhao","submitted_at":"2024-05-24T14:06:01Z","abstract_excerpt":"In this paper, we prove that for any asymptotically conical self-shrinker, there exists an embedded closed hypersurface such that the mean curvature flow starting from it develops a singularity modeled on the given shrinker. The main technique is the Wa\\.zewski box argument, used by Stolarski in the proof of the corresponding theorem in the Ricci flow case. As a corollary, our construction, combined with the works of Angenent--Ilmanen--Vel\\'azquez and Chodosh--Daniels-Holgate--Schulze, implies the existence of fattening level set flows starting from smooth embedded closed hypersurfaces. These "},"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":"2405.15577","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-05-24T14:06:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"4f6952fce51fab154250c2aac4e07c35825a3c4c657482eebcd55b750c9d0571","abstract_canon_sha256":"ff9c8c969c4cba03aebab26b8fbaa7d82ab63eb19ac6f65082f450edf57c9751"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:54:51.399418Z","signature_b64":"IRHpsmpfFQqm9CtNbckO4+xKC5PPKzO1QJmR7ddAXOPVlVWnd6fp/vfZb1HFnKEcEwyzYF7jOX6MiQiS0B6WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81ebe70243d84e0e994d719a8a312ae8e31b2f422b1aa0911ec08bea807e9ceb","last_reissued_at":"2026-07-05T08:54:51.398885Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:54:51.398885Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Closed mean curvature flows with asymptotically conical singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Tang-Kai Lee, Xinrui Zhao","submitted_at":"2024-05-24T14:06:01Z","abstract_excerpt":"In this paper, we prove that for any asymptotically conical self-shrinker, there exists an embedded closed hypersurface such that the mean curvature flow starting from it develops a singularity modeled on the given shrinker. The main technique is the Wa\\.zewski box argument, used by Stolarski in the proof of the corresponding theorem in the Ricci flow case. As a corollary, our construction, combined with the works of Angenent--Ilmanen--Vel\\'azquez and Chodosh--Daniels-Holgate--Schulze, implies the existence of fattening level set flows starting from smooth embedded closed hypersurfaces. These "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.15577","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.15577/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2405.15577","created_at":"2026-07-05T08:54:51.398940+00:00"},{"alias_kind":"arxiv_version","alias_value":"2405.15577v3","created_at":"2026-07-05T08:54:51.398940+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.15577","created_at":"2026-07-05T08:54:51.398940+00:00"},{"alias_kind":"pith_short_12","alias_value":"QHV6OASD3BHA","created_at":"2026-07-05T08:54:51.398940+00:00"},{"alias_kind":"pith_short_16","alias_value":"QHV6OASD3BHA5GKN","created_at":"2026-07-05T08:54:51.398940+00:00"},{"alias_kind":"pith_short_8","alias_value":"QHV6OASD","created_at":"2026-07-05T08:54:51.398940+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2506.23359","citing_title":"The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow","ref_index":38,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D","json":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D.json","graph_json":"https://pith.science/api/pith-number/QHV6OASD3BHA5GKNOGNIUMJK5D/graph.json","events_json":"https://pith.science/api/pith-number/QHV6OASD3BHA5GKNOGNIUMJK5D/events.json","paper":"https://pith.science/paper/QHV6OASD"},"agent_actions":{"view_html":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D","download_json":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D.json","view_paper":"https://pith.science/paper/QHV6OASD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2405.15577&json=true","fetch_graph":"https://pith.science/api/pith-number/QHV6OASD3BHA5GKNOGNIUMJK5D/graph.json","fetch_events":"https://pith.science/api/pith-number/QHV6OASD3BHA5GKNOGNIUMJK5D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D/action/storage_attestation","attest_author":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D/action/author_attestation","sign_citation":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D/action/citation_signature","submit_replication":"https://pith.science/pith/QHV6OASD3BHA5GKNOGNIUMJK5D/action/replication_record"}},"created_at":"2026-07-05T08:54:51.398940+00:00","updated_at":"2026-07-05T08:54:51.398940+00:00"}