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We first obtain general upper bounds for the Hausdorff dimension of these sets $E_f(h)$, for all convex functions $f$ and all $h\\geq 0$. We prove that for typical/generic (in the sense of Baire) continuous convex functions $f:[0,1]^{d}\\to \\mathbb{R} $, one has $\\dim E_f(h) =d-2+h$ for all $h\\in[1,2],$ and in addition, we obtain that the set $ E_f({h} )$ is empty if $h\\in (0,1)\\cup (1,+\\infty)$. Also, whe"},"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":"1704.02816","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2017-04-10T11:58:52Z","cross_cats_sorted":[],"title_canon_sha256":"5ed0876d8b57bbf6f8023abb55aba7943cdac7d21d01b863d87464ab5a4a4a3d","abstract_canon_sha256":"912b4f13e61cc35ca83be48a30a694625c64aff0598de7ff6065565be6675a45"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:59.612761Z","signature_b64":"vZ7z/kZURk6j8yfE5HVugj/IRTdL3zXjfmIh2gShumCAnr/NaR6fXC5/Ty3sPn/DUJTiBmK8E7tkBNF/PxhuDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2c79e9a99792d26b7394044e7c269ed61d47203e6b0033265e1ac23974b8ff75","last_reissued_at":"2026-05-18T00:31:59.612358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:59.612358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Multifractal properties of typical convex functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"St\\'ephane Seuret, Zolt\\'an Buczolich","submitted_at":"2017-04-10T11:58:52Z","abstract_excerpt":"We study the singularity (multifractal) spectrum of continuous convex functions defined on $[0,1]^{d}$. Let $E_f({h}) $ be the set of points at which $f$ has a pointwise exponent equal to $h$. We first obtain general upper bounds for the Hausdorff dimension of these sets $E_f(h)$, for all convex functions $f$ and all $h\\geq 0$. We prove that for typical/generic (in the sense of Baire) continuous convex functions $f:[0,1]^{d}\\to \\mathbb{R} $, one has $\\dim E_f(h) =d-2+h$ for all $h\\in[1,2],$ and in addition, we obtain that the set $ E_f({h} )$ is empty if $h\\in (0,1)\\cup (1,+\\infty)$. 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