{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:PAO3N2CFJSB5PSMMCW7P7JHMF6","short_pith_number":"pith:PAO3N2CF","schema_version":"1.0","canonical_sha256":"781db6e8454c83d7c98c15beffa4ec2fa2e0ea49765351866cde587c96938262","source":{"kind":"arxiv","id":"2208.14280","version":2},"attestation_state":"computed","paper":{"title":"A nonexistence result for rotating mean curvature flows in $\\mathbb{R}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Robert Haslhofer, Wenkui Du","submitted_at":"2022-08-30T13:59:39Z","abstract_excerpt":"Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at $-\\infty$ is a cylinder $\\mathbb{R}^k\\times S^{n-k}$ and that are rotating within the $\\mathbb{R}^k$-factor. We note that while the $\\mathbb{R}^k$-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the $\\mathbb{R}^k$-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flow"},"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":"2208.14280","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-08-30T13:59:39Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"59f8d84fa140f9954061ee88609be70661a23c6ad3963e160e7e14f317161856","abstract_canon_sha256":"4617c5f0b6a96ff2643b344401f542840ee5e3e955f4cc07747dfcb24a347a72"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:17:01.240495Z","signature_b64":"RWGxZLOUb/ozqJs3GqlA3S9l5CMeFoNe3u5MK03f+ak9DnbqX9Xf5VITnZ07Beo8pvbd+bVbB0DZ4DoNy4GwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"781db6e8454c83d7c98c15beffa4ec2fa2e0ea49765351866cde587c96938262","last_reissued_at":"2026-07-05T06:17:01.240147Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:17:01.240147Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A nonexistence result for rotating mean curvature flows in $\\mathbb{R}^{4}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Robert Haslhofer, Wenkui Du","submitted_at":"2022-08-30T13:59:39Z","abstract_excerpt":"Some worrisome potential singularity models for the mean curvature flow are rotating ancient flows, i.e. ancient flows whose tangent flow at $-\\infty$ is a cylinder $\\mathbb{R}^k\\times S^{n-k}$ and that are rotating within the $\\mathbb{R}^k$-factor. We note that while the $\\mathbb{R}^k$-factor, i.e. the axis of the cylinder, is unique by the fundamental work of Colding-Minicozzi, the uniqueness of tangent flows by itself does not provide any information about rotations within the $\\mathbb{R}^k$-factor. In the present paper, we rule out rotating ancient flows among all ancient noncollapsed flow"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.14280","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2208.14280/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":"2208.14280","created_at":"2026-07-05T06:17:01.240209+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.14280v2","created_at":"2026-07-05T06:17:01.240209+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.14280","created_at":"2026-07-05T06:17:01.240209+00:00"},{"alias_kind":"pith_short_12","alias_value":"PAO3N2CFJSB5","created_at":"2026-07-05T06:17:01.240209+00:00"},{"alias_kind":"pith_short_16","alias_value":"PAO3N2CFJSB5PSMM","created_at":"2026-07-05T06:17:01.240209+00:00"},{"alias_kind":"pith_short_8","alias_value":"PAO3N2CF","created_at":"2026-07-05T06:17:01.240209+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/PAO3N2CFJSB5PSMMCW7P7JHMF6","json":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6.json","graph_json":"https://pith.science/api/pith-number/PAO3N2CFJSB5PSMMCW7P7JHMF6/graph.json","events_json":"https://pith.science/api/pith-number/PAO3N2CFJSB5PSMMCW7P7JHMF6/events.json","paper":"https://pith.science/paper/PAO3N2CF"},"agent_actions":{"view_html":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6","download_json":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6.json","view_paper":"https://pith.science/paper/PAO3N2CF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.14280&json=true","fetch_graph":"https://pith.science/api/pith-number/PAO3N2CFJSB5PSMMCW7P7JHMF6/graph.json","fetch_events":"https://pith.science/api/pith-number/PAO3N2CFJSB5PSMMCW7P7JHMF6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6/action/storage_attestation","attest_author":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6/action/author_attestation","sign_citation":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6/action/citation_signature","submit_replication":"https://pith.science/pith/PAO3N2CFJSB5PSMMCW7P7JHMF6/action/replication_record"}},"created_at":"2026-07-05T06:17:01.240209+00:00","updated_at":"2026-07-05T06:17:01.240209+00:00"}