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We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\\to\\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\\in X}is a so-called completely strongly porous set."},"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":"1302.4599","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-02-19T13:07:41Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"573495a66aa103ae128b871d6e6413281769f5236bc22ab0cf0e6fdc60f64246","abstract_canon_sha256":"2fb93ee0ae330831cd115ab60c96cfd06ed9600a66653625e5f086c185caaaae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:12.791033Z","signature_b64":"vIrZCcxHE2x3cnWVojnyhnFVdZrbJ4Mp36G4HTn1IceMBygw9GgIRSmEocoKWI0ahaLsBcagR+111ekj91apCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2748d2cfde657af1961c561973c08b744982874db67e1a727580391cb8e0fe36","last_reissued_at":"2026-05-18T03:33:12.790150Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:12.790150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Uniform boundedness of pretangent spaces and local strong one-side porosity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"Oleksiy Dovgoshey, Viktoriia Bilet","submitted_at":"2013-02-19T13:07:41Z","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. We say that (r_n) is normal if there is (x_n) such that |d(x_n,p)-r_n|=o(r_n) for n\\to\\infty. Let Omega_{p}^{X}(n) be the set of pretangent spaces to X at p with normal scaling sequences. We prove that the spaces from Omega_{p}^{X}(n) are uniformly bounded if and only if {d(x,p:x\\in X}is a so-called completely strongly porous set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4599","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1302.4599","created_at":"2026-05-18T03:33:12.790306+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.4599v1","created_at":"2026-05-18T03:33:12.790306+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4599","created_at":"2026-05-18T03:33:12.790306+00:00"},{"alias_kind":"pith_short_12","alias_value":"E5ENFT66MV5P","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"E5ENFT66MV5PDFQ4","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"E5ENFT66","created_at":"2026-05-18T12:27:43.054852+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/E5ENFT66MV5PDFQ4KYMXHQELOR","json":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR.json","graph_json":"https://pith.science/api/pith-number/E5ENFT66MV5PDFQ4KYMXHQELOR/graph.json","events_json":"https://pith.science/api/pith-number/E5ENFT66MV5PDFQ4KYMXHQELOR/events.json","paper":"https://pith.science/paper/E5ENFT66"},"agent_actions":{"view_html":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR","download_json":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR.json","view_paper":"https://pith.science/paper/E5ENFT66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.4599&json=true","fetch_graph":"https://pith.science/api/pith-number/E5ENFT66MV5PDFQ4KYMXHQELOR/graph.json","fetch_events":"https://pith.science/api/pith-number/E5ENFT66MV5PDFQ4KYMXHQELOR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/action/storage_attestation","attest_author":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/action/author_attestation","sign_citation":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/action/citation_signature","submit_replication":"https://pith.science/pith/E5ENFT66MV5PDFQ4KYMXHQELOR/action/replication_record"}},"created_at":"2026-05-18T03:33:12.790306+00:00","updated_at":"2026-05-18T03:33:12.790306+00:00"}