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The main result in this paper asserts that if $\\mathcal{R}_1\\ne \\emptyset$, then $Y$ is a one dimensional topological manifold. Our result improves the Handa's result \\cite{Honda}"},"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":"1508.07105","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-28T06:22:06Z","cross_cats_sorted":[],"title_canon_sha256":"3309e7885c59eb47b585c34cc4b589162145645f14007c3d854ca8b368eab070","abstract_canon_sha256":"7b08c491017c3f3cfbdfd046322ceda984f03adb66120419756d5d8f1b892c74"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:36.685915Z","signature_b64":"xfbtALWJ9bRJcUQNE48DlI9sOOPT7AVJiad5hSsHLTRrajPXWjBd1l9630AGZIt5GLwXmzOci9ALu7prbfHTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d89d8f30802ce08de32118a0d6e29b71e7744889078e1101f4f8acc1475389a8","last_reissued_at":"2026-05-18T01:22:36.685488Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:36.685488Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Remark on Regular Points of Ricci Limit Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Lina Chen","submitted_at":"2015-08-28T06:22:06Z","abstract_excerpt":"Let $Y$ be a Gromov-Hausdorff limit of complete Riemannian n-manifolds with Ricci curvature bounded from below.\n  A point in $Y$ is called $k$-regular, if its tangent is unique and is isometric to an $k$-dimensional Euclidean space.\n  By \\cite{B5}, there is $k>0$ such that the set of all $k$-regular point $\\mathcal{R}_k$ has a full renormalized measure.\n  An open problem is if $\\mathcal{R}_l=\\emptyset$ for all $l<k$? 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