Integer Circulant Determinants of Order 20

Abstract

For F in Z[X], set M_20(F) = Res(X^20 − 1, F) and S_20 = {M_20(F) : F in Z[X]}. This preprint determines S_20 completely. Write a nonzero integer as D = ±2^a 5^b m, where m ≥ 1 and gcd(m,10) = 1. The local conditions a = 0 or a ≥ 4 and b = 0 or b ≥ 2 are sufficient except on exactly two faces. On the 25m face, occurrence is characterized by explicit minimum prime-packet weights depending on the residue class modulo 20. On the 32m face, occurrence is characterized by residue-class thresholds, a cross-prime cancellation in the class 11 modulo 20, and a Kummer square condition for primes congruent to 1 modulo 20. The proof uses exact conductor squares, cyclotomic norms, explicit ray-class packet extensions, finite defect groups, Galois norm operators, and a split-row Kummer refinement. The release includes the matching source, an independent verification supplement, and an eight-program exact-arithmetic certificate suite.