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The main purpose of this article is to characterize the set of points at which $F_a$ has an infinite derivative. We compute the Hausdorff dimension of this set for the case $a\\leq 1/2$, and estimate it for $a>1/2$. For all $a$, we determine the Hausdorff dimension of the sets of points where: (i) $F_a'=0$; and (ii) $F_a$ has neither a finite nor an inf"},"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":"1502.03374","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-02-11T17:00:46Z","cross_cats_sorted":[],"title_canon_sha256":"9dcb59d879624951502747008131659c26c3f32b6d29d06e89d0aab1c70c841c","abstract_canon_sha256":"a7741b7c922baa126be6d738ae8ef17d5cd97ea0086dd4e8fc8197e592d042cb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:55.227612Z","signature_b64":"EkDj24ZRKTukjZhTSxT49GePBACabo1pm5uF9uj3PJ4HzDrZDOC4vyf9T5nwn7eZt421BZfRfi3UBkpFPWAFCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af576e3425eca4fe8deab26f1a6cf540563a1a09f6a83a378293f640f9813632","last_reissued_at":"2026-05-18T01:11:55.227266Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:55.227266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The infinite derivatives of Okamoto's self-affine functions: an application of beta-expansions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Pieter C. 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