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On the other hand the set of real numbers $v$ that can be written in the form $v=xy$ with $x$ and $y$ in $C$ is a closed subset of $[0,1]$ with Lebesgue measure strictly between $\\tfrac{17}{21}$ and $\\tfrac89$. We also describe the structure of the quotient of $C$ by itself, that is, the image of $C\\times (C \\setminus \\{0\\})$ under the function $f(x,y) = x/y$."},"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":"1711.08791","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-11-23T17:59:59Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"00d729d21fbb67bb58813943e17f24a1447055be3cc11f667f236b89c88c6654","abstract_canon_sha256":"4b8c1f708594965f564193c876670383606474e9a7465cc0fad3d666ec155b11"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:44.085686Z","signature_b64":"GqaF7OUyx1W1AsSZ/zF3LWSWL7HeKwu/3tSsNysbd3ynDxNfMwaFVRprSZONgeSzRO7Zztu2OgPPoWj7ebbbBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79b71aa63278d079fad68db96a4287d97522bdf402178bc9d964f1bd1331fe77","last_reissued_at":"2026-05-18T00:29:44.085158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:44.085158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cantor set arithmetic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.MG","authors_text":"Bruce Reznick, Jayadev S. 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