 Bounded nonconvergent Fourier partial sums

A continuous complex-valued function can have uniformly bounded Fourier partial sums which fail to converge at one point. Normalize harmonic sine polynomials by their harmonic coefficient sums, modulate them into disjoint high-frequency intervals and choose their degrees so that the complete norms are summable. At zero, complete blocks vanish while their midpoint prefixes have a common nonzero value. The frequency-separated Fourier block series gives a uniform bound on every partial sum as well as two distinct subsequential values.