= 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.
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