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The smallest Kakeya sets have size $\\left\\lfloor\\frac{3q^{2}+2q}{4}\\right\\rfloor$, and all Kakeya sets with weight less than $\\left\\lfloor\\frac{3(q^{2}-1)}{4}\\right\\rfloor+q$ are classified: there are approximately $\\sqrt{\\frac{q}{2}}$ types."},"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":"1601.03539","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-14T10:12:45Z","cross_cats_sorted":[],"title_canon_sha256":"81bcdaa04665095c11161940c7a7060b3555e80da60ce171df27591d56cf3e26","abstract_canon_sha256":"cba6bcbd12e8d43a7e0097074333b73862491f4531da3b38fb2984d57a8c4732"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:53.211260Z","signature_b64":"krOHPZearQ+G3dFwgRSF3dOiQxu4uN5DcFB1/mQ1ZSoHeCv5Rex+NXC3dLlgrPzaAm0s7cj80Ic/rkVHN0qKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40b71247fe367a29957d4b6aaa8544946788709b46f5ad1f203e4607589a2ed3","last_reissued_at":"2026-05-18T01:22:53.210647Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:53.210647Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The small Kakeya sets in $T^{*}_{2}(\\mathcal{C})$, $\\mathcal{C}$ a conic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maarten De Boeck","submitted_at":"2016-01-14T10:12:45Z","abstract_excerpt":"A Kakeya set in the linear representation $T^{*}_{2}(\\mathcal{C})$, $\\mathcal{C}$ a non-singular conic, is the point set covered by a set of $q+1$ lines, one through each point of $\\mathcal{C}$. 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