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For $d \\ge 3$ we prove upper bounds for $\\alpha(\\mathbb{F}_q^d,p)$ that are essentially tight within certain ranges for $p$.\n  We establish the upper bound $2^{(1+o(1))q}$ for the number of general position sets in $\\mathbb{F}_q^d$, which matches the triv"},"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":"2309.07744","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2023-09-14T14:30:47Z","cross_cats_sorted":[],"title_canon_sha256":"6351a5a975d2a881fa1fc7d55c7026a161b654bf4d0225e5dc73ef1c587c0337","abstract_canon_sha256":"60528f6769b41ddb334f241096a2ae59da9099e5911400f34ddc27d8207e30bb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:17:05.227407Z","signature_b64":"vOjEuafQfZSe66csNNF3C+/WrVupLblmgUyyi5BvUM2nwRgTSkpCEcZ3//OopSvwWEiUBXqvJ/GcKrmPz4TIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"293aa72cbf3ff356a2c6323cf9e8f5bdedfabc91f103d48e6357da477b823385","last_reissued_at":"2026-07-05T10:17:05.226848Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:17:05.226848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Tur\\'an and counting results for general position sets over finite fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiaxi Nie, Ji Zeng, Xizhi Liu, Yaobin Chen","submitted_at":"2023-09-14T14:30:47Z","abstract_excerpt":"Let $\\alpha(\\mathbb{F}_q^d,p)$ denote the maximum size of a general position set in a $p$-random subset of $\\mathbb{F}_q^d$. 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