A distinct covering system with minimum modulus 7 and least common multiple 10080 exists (Zhang & Zhang 2026, §7) — kernel-decided construction half: the 66 exhibited congruence classes cover every n ≥ 0, their moduli are distinct, the least is 7 and their lcm is exactly 10080. The paper's MINIMALITY claim (L_min(7) = 10080), which rests on complete Gurobi computations, is NOT amplified here and is not implied by this law.
an integer n ≥ 0 lying in none of the 66 classes — equivalently a residue mod 10080 left uncovered