{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:FNSK7YMKHXVLSYSNFVAUZKIU4M","short_pith_number":"pith:FNSK7YMK","schema_version":"1.0","canonical_sha256":"2b64afe18a3deab9624d2d414ca914e32b7ac518da9dec689ae38febcb17da36","source":{"kind":"arxiv","id":"1304.6356","version":2},"attestation_state":"computed","paper":{"title":"Rigidity of generic singularities of mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Tobias Holck Colding, Tom Ilmanen, William P. Minicozzi II","submitted_at":"2013-04-23T17:28:17Z","abstract_excerpt":"Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, [CM1] showed that the only generic are round cylinders $\\SS^k\\times \\RR^{n-k}$. We prove here that round cylinders are rigid in a very strong sense. Namely, any other shrinker that is sufficiently close to one of them on a large, but compact, set must itself be a round cylinder.\n  To our knowledge, this is the first general rigidity theorem for singularities of a nonlinear geometric flow. We expect that the techniques and ideas de"},"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":"1304.6356","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-04-23T17:28:17Z","cross_cats_sorted":["math.AP","math.GT"],"title_canon_sha256":"856c4a11f2001dc44560ce30784f1583f1b7242761adae3870d91a2f6736e006","abstract_canon_sha256":"62d4598751eeeaa2a5269313fe82026058399f3b71966adfc172ba9af9827c8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:19.088767Z","signature_b64":"5CY67trRM8N3hm+Q1N2H9Cfcn4p+HcAVx5tmL2Ulb8ZmIZLQoTjKNPkFRK7rvT82aWG+91A2HDKAsPzJqPOjCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b64afe18a3deab9624d2d414ca914e32b7ac518da9dec689ae38febcb17da36","last_reissued_at":"2026-05-18T02:27:19.088008Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:19.088008Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rigidity of generic singularities of mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Tobias Holck Colding, Tom Ilmanen, William P. Minicozzi II","submitted_at":"2013-04-23T17:28:17Z","abstract_excerpt":"Shrinkers are special solutions of mean curvature flow (MCF) that evolve by rescaling and model the singularities. While there are infinitely many in each dimension, [CM1] showed that the only generic are round cylinders $\\SS^k\\times \\RR^{n-k}$. We prove here that round cylinders are rigid in a very strong sense. Namely, any other shrinker that is sufficiently close to one of them on a large, but compact, set must itself be a round cylinder.\n  To our knowledge, this is the first general rigidity theorem for singularities of a nonlinear geometric flow. We expect that the techniques and ideas de"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6356","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":"1304.6356","created_at":"2026-05-18T02:27:19.088132+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.6356v2","created_at":"2026-05-18T02:27:19.088132+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6356","created_at":"2026-05-18T02:27:19.088132+00:00"},{"alias_kind":"pith_short_12","alias_value":"FNSK7YMKHXVL","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"FNSK7YMKHXVLSYSN","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"FNSK7YMK","created_at":"2026-05-18T12:27:45.050594+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/FNSK7YMKHXVLSYSNFVAUZKIU4M","json":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M.json","graph_json":"https://pith.science/api/pith-number/FNSK7YMKHXVLSYSNFVAUZKIU4M/graph.json","events_json":"https://pith.science/api/pith-number/FNSK7YMKHXVLSYSNFVAUZKIU4M/events.json","paper":"https://pith.science/paper/FNSK7YMK"},"agent_actions":{"view_html":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M","download_json":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M.json","view_paper":"https://pith.science/paper/FNSK7YMK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.6356&json=true","fetch_graph":"https://pith.science/api/pith-number/FNSK7YMKHXVLSYSNFVAUZKIU4M/graph.json","fetch_events":"https://pith.science/api/pith-number/FNSK7YMKHXVLSYSNFVAUZKIU4M/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M/action/storage_attestation","attest_author":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M/action/author_attestation","sign_citation":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M/action/citation_signature","submit_replication":"https://pith.science/pith/FNSK7YMKHXVLSYSNFVAUZKIU4M/action/replication_record"}},"created_at":"2026-05-18T02:27:19.088132+00:00","updated_at":"2026-05-18T02:27:19.088132+00:00"}