Removing the binary and ternary factors from cyclic Weyl rank uncertainty

For a nonzero complex matrix in the cyclic Weyl basis, let u_d(s) be the minimum rank under a support budget of s coefficients. We give exact formulas reducing u_d to the profile in the part of the dimension coprime to 6. Removing a factor 2^k uses a minimum over binary subgroup costs. Removing a factor 3^k uses products of the three costs 1, 2, 3, with rank multipliers 3, 2, 1. Lower bounds follow from residue-sector compressions and central Fourier blocks; the ternary two-residue case uses a triangular minor on two sectors of a directed three-cycle. Upper bounds are attained by scalar cyclic projectors and binomials, combined with the Chinese remainder theorem. In every even dimension whose only prime factors are 2 and 3, the exact minimum is d/max{q: q divides d, q <= s}. Sharp uniform coefficient-erasure budgets follow for arbitrary complex low-rank matrices. Residual profiles with prime factors at least 5, efficient recovery and numerical stability are not determined.