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We prove that each self-similar arc of Hausdorff dimension $s>1$ in $\\mathbb{R}^N$ is a strict Whitney set with criticality $s$. We also study a special kind of self-similar arcs, which we call \"regular\" self-similar arcs. We obtain necessary and sufficient conditions for a regular self-similar arc $\\Lambda$ to be a $t$-quasi-arc, and for the Hau"},"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":"1703.10665","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-03-30T20:33:39Z","cross_cats_sorted":["math.DS","math.GN"],"title_canon_sha256":"8adc68db17aedb1effa4d666b71d6f24e0947bcb0a5c8cd31033f49397e5430c","abstract_canon_sha256":"ef3f1e1fc55cb4160a9a8eee641f1e1f230aad5a0f34fe21b0cf220141d5adcd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:01.212059Z","signature_b64":"OwS6yzstzNFTDNK3f+/z8Spw4LB4i8g9MI5WERExEqkjBiGC00G6ngSK/DkDxujj7aQH+feSCT0/kmFyrqhfDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e1b381a03bf517787e94c2410f47e61e8524ee55ad5cbefeadfef2080660728","last_reissued_at":"2026-05-18T00:14:01.211519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:01.211519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On strict Whitney arcs and $t$-quasi self-similar arcs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GN"],"primary_cat":"math.MG","authors_text":"Daowei Ma, Xin Wei, Zhiying Wen","submitted_at":"2017-03-30T20:33:39Z","abstract_excerpt":"A connected compact subset $E$ of $\\mathbb{R}^N$ is said to be a strict Whitney set if there exists a real-valued $C^1$ function $f$ on $\\mathbb{R}^N$ with $\\nabla f|_E\\equiv 0$ such that $f$ is constant on no non-empty relatively open subsets of $E$. 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