Integer Circulant Determinants of Order 28

Abstract

This preprint gives a complete effective classification of the determinants of 28 by 28 circulant matrices with integer entries. Writing |D| = 2^a 7^b m with gcd(m,14)=1, it proves the exact local floors, identifies (a,b)=(5,0) and (0,2) as the only exceptional faces, and proves that 32m belongs to S_28 if and only if 49m belongs to S_28. Both faces are governed by one exact prime-packet condition in C_4 x C_2 x C_2 with target (2,0,0). The deposit includes matching manuscript source, a constructive decision-and-witness implementation, frozen quotient data, exact-arithmetic certificates, independent audits, an expected transcript, and SHA-256 verification data.