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This answers a question of Bru\\`e-Pigati-Semola [arXiv:2405.03839] about the topological obstructions of $4$-dimensional non-collapsed tangent cones. Combining this result with a recent work of Bru\\`e-Pigati-Semola [arXiv:2405.03839], one can classify the $4$-dimensional non-collapse"},"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":"2406.02279","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-06-04T12:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"b39d386aa478e3762a0894e31244c40d186b8ab790677439d2619591139a399a","abstract_canon_sha256":"e9c35fade04b13d9c4f0164e5b723212f474715bf1ad953387396405610e7d94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:27:17.442533Z","signature_b64":"YLMD/63UFXTBtZ923z2ZoOI5LnWeF8tvbXi15BKYWXU2eRk08Y4j3efRzVZiMVJy19Q9I97INtEhUDZmPm6eDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4578527475d3ea83d9ea43ec79fbecf1fc3a23f20ac7846773c4141629f7d706","last_reissued_at":"2026-07-05T08:27:17.442044Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:27:17.442044Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A family of $4$-manifolds with nonnegative Ricci curvature and prescribed asymptotic cone","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Shengxuan Zhou","submitted_at":"2024-06-04T12:52:50Z","abstract_excerpt":"In this paper, we show that for any finite subgroup $\\Gamma < O(4)$ acting freely on $\\mathbb{S}^3$, there exists a $4$-dimensional complete Riemannian manifold $(M,g)$ with ${\\rm Ric}_g \\geq 0 $, such that the asymptotic cone of $(M,g)$ is $C(\\mathbb{S}_\\delta^3 /\\Gamma )$ for some $\\delta = \\delta (\\Gamma ) >0$. This answers a question of Bru\\`e-Pigati-Semola [arXiv:2405.03839] about the topological obstructions of $4$-dimensional non-collapsed tangent cones. 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