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Near the center the appropriately-rescaled pointed Cheeger-Gromov limits are round cylinder solutions $S^J \\times \\mathbb{R}^{n-J}$, $1 \\leq J \\leq n-1$. These results are the analog of the corresponding results in Ricci flow ($J=n-1$) and mean curvature 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":"1812.04926","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.DG","submitted_at":"2018-12-12T13:07:58Z","cross_cats_sorted":[],"title_canon_sha256":"7e1a6a0053293be91a287bfeec6135fd2c6f112b3760c4badb6cd968e219c775","abstract_canon_sha256":"141b860db327cf84c4a1680fd073764be68ced1a6cda36f332f6d7df0dd543c9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:26.903966Z","signature_b64":"nMK/WbO5wsF0Vax0z71NVdJ7JaAZ8L6GaXCZMEL963YEuvyMjWTiM6sKYiPf2N0b3+GDL7RYaRYyiZTJvVe+Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5ebe45a592e3a83b3449cd4fadf4e4f82bf5573609d6006eb594bb4d7138c64","last_reissued_at":"2026-05-17T23:58:26.903266Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:26.903266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ancient solutions for Andrews' hypersurface flow","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Jiuru Zhou, Peng Lu","submitted_at":"2018-12-12T13:07:58Z","abstract_excerpt":"We construct the ancient solutions of the hypersurface flows in Euclidean spaces studied by B. 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