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Rev. B 109, 245123 (2024)] revealed striking inverse-current (1/I) quantum oscillations in quasi-one-dimensional charge-density-wave (CDW) insulators and proposed an intrinsic Floquet sideband mechanism arising from the sliding condensate. Here we develop the complete theoretical framework underlying this proposal. We provide an exact Floquet diagonalization of the uniformly sliding CDW, yielding split gap edges and a ladder of Floquet sidebands with explicit unitary transformation and spectral functions. 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