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Given $E\\subset \\mathbb F_q^d$ and an integer $k\\ge 2$, the $k$-resultant modulus set, denoted by $\\Delta_k(E)$, is defined as $$ \\Delta_k(E)=\\{\\|x^1\\pm x^2 \\pm \\cdots \\pm x^k\\|\\in \\mathbb F_q: x^j\\in E, ~j=1,2,\\ldots, k\\},$$ where $\\|\\alpha\\|=\\alpha_1^2+\\cdots+ \\alpha_d^2$ for $\\alpha=(\\alpha_1, \\ldots, \\alpha_d) \\in \\mathbb F_q^d.$ In this setting, the $k$-resultant modulus set problem is to determine the minimal cardinality of $E\\subset \\m"},"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":"1508.02688","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-11T19:00:02Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"9a92adde11909f6a8755517d5e83c6464383385d4964b033eba094b242aedf30","abstract_canon_sha256":"9ea637bfd48e74484f08f38e594423f510d521ca959e3e74e6193bdc0ebf5692"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:28.536461Z","signature_b64":"4fhdzD0rWus1uzANsB+wSo+xzNy5AyD/qGqi0fqWyHj5OF58lhdKDFV6I0E1djt6apn75buWe7HTtHNQXZlVCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eda6c4f4839e7c58fa15b29170507914eb6ca7e213519029617df06e772b62fb","last_reissued_at":"2026-05-18T01:35:28.535981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:28.535981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $k$-resultant modulus set problem on algebraic varieties over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.CO","authors_text":"David Covert, Doowon Koh, Youngjin Pi","submitted_at":"2015-08-11T19:00:02Z","abstract_excerpt":"We study the $k$-resultant modulus set problem in the $d$-dimensional vector space $\\mathbb F_q^d$ over the finite field $\\mathbb F_q$ with $q$ elements. 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