arf-invariant

Part IV of "Prime polynomials in Legendre intervals over F_{2^k}[t]": hexad formula and trace parity for Z/4 Gauss sums; the sign law is proved in all 11 Frobenius classes (v2: classes 3 2 1 and 6); X = q^6 + q^5 now depends only on the class counts. Paper, Python code, data for q = 8, 32, 128. DOI 10.5281/zenodo.23308682

Genus-4 Gold family y²+y = λ9x⁹+λ5x⁵+λ3x³+λ1x over F_{2^k}: the canonical degree-28 polynomial B with L' = x⁸B²+B+1, the coset-sum theorem for Z/4 Gauss sums, the quadratic-form torsor on K = F₂⁶ (28 Arf-1 + 36 Arf-0 points), trace parity, Sp6(F2) Frobenius types. Paper, Python code, data. DOI 10.5281/zenodo.23306002