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A pretangent space to $X$ at $p$ is a metric space consisting of some equivalence classes of convergent to $p$ sequences $(x_n), x_n \\in X,$ whose degree of convergence is comparable with a given scaling sequence $(r_n), r_n\\downarrow 0.$ A scaling sequence $(r_n)$ is normal if this sequence is eventually decreasing and there is $(x_n)$ such that $\\mid d(x_n,p)-r_n\\mid=o(r_n)$ for $n\\to\\infty.$ Let $\\mathbf{\\Omega_{p}^{X}(n)}$ be the set of pretangent spaces to $X$ at $p$ with normal scaling sequences. We prove that $\\mathbf{\\Omega_{p}^{X}(n)}$ is unifo"},"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":"1409.3418","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-09-11T12:46:35Z","cross_cats_sorted":[],"title_canon_sha256":"01dea7afe8f0424a0ba29d3224528314adf22c132080cf493417687d697144dc","abstract_canon_sha256":"5cb1ad79d6ae2eff203f4710d5bcd46949a367d1f7452ebeb209a37ffa6cb21c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:01.410995Z","signature_b64":"ufQSRgVci7FOGHCsMraWJ9edyzaqJw9fD417zqGb99LrrGjR1SIKdO8XcwHGJbqTip10jkuewxMnJAtwxapeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1c1d83e47c81a8407c61e98309f35cc1919202a47912741ec4c8f6d411fb403","last_reissued_at":"2026-05-18T02:43:01.410463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:01.410463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform boundedness of pretangent spaces, local constancy of metric derivatives and strong right upper porosity at a point","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Mehmet Kucukaslan, Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2014-09-11T12:46:35Z","abstract_excerpt":"Let $(X,d,p)$ be a pointed metric space. A pretangent space to $X$ at $p$ is a metric space consisting of some equivalence classes of convergent to $p$ sequences $(x_n), x_n \\in X,$ whose degree of convergence is comparable with a given scaling sequence $(r_n), r_n\\downarrow 0.$ A scaling sequence $(r_n)$ is normal if this sequence is eventually decreasing and there is $(x_n)$ such that $\\mid d(x_n,p)-r_n\\mid=o(r_n)$ for $n\\to\\infty.$ Let $\\mathbf{\\Omega_{p}^{X}(n)}$ be the set of pretangent spaces to $X$ at $p$ with normal scaling sequences. 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