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We prove that this is equivalent to saying that $X$ contains a sequence $\\{x_i\\}$ whose Frenet $k$-frame $(u_1,\\ldots,u_k)$ is an outgoing Severi-Bouligand ta"},"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":"1308.0662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-08-03T06:10:49Z","cross_cats_sorted":[],"title_canon_sha256":"d64541080c1a32f3204590f012d2e7ee5e8139a182778b32209d6e4452513e41","abstract_canon_sha256":"8256fa690a2412eb220c6baa40558d88abaa42c23d7619f3e0151568423ad0e5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:46.319221Z","signature_b64":"4zBJffg9As2lKex2AgzaTuEbPNgmGE9YLo2OCUgX7ocFvaIEHXN/ZMYJtn6yWIxm9Gl4gLOr5GC5dMXAaqZ2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b20d518501d1e9fc989340fca7d17590df1678db6624bfdd4dfce168bd39e68e","last_reissued_at":"2026-05-18T03:01:46.318617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:46.318617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Severi-Bouligand tangents, Frenet frames and Riesz spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Daniele Mundici, Leonardo Manuel Cabrer","submitted_at":"2013-08-03T06:10:49Z","abstract_excerpt":"It was recently proved that a compact set $X\\subseteq \\mathbb R^2$ has an outgoing Severi-Bouligand tangent vector $u\\not=0$ at $x\\in X$ iff some principal ideal of the Riesz space $\\mathcal R(X)$ of piecewise linear functions on $X$ is not an intersection of maximal ideals. \"Outgoing\" means $X\\cap [x,x+u]=\\{x\\}$.\n  Suppose now $X\\subseteq \\mathbb{R}^n$ and some principal ideal of $\\mathcal R(X)$ is not an intersection of maximal ideals. 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