On an Entropy–Fourier Framework Towards the Riemann Hypothesis

We develop a Hilbert–diagrammatic framework for the Riemann zeta function in which the nontrivial zeros are encoded through entropic projections and Fourier-transformed kernels. Within this setting, the shift of spectral sums associated to the zeros can be expressed as an absolutely convergent factorially suppressed expansion. We show that this expansion is uniformly bounded by combining stationary-phase estimates with integration by parts, thereby reducing the analysis to explicit numerical inequalities. Our approach yields an unconditional analytic structure for the control of zero ordinates and provides a reduction scheme for the verification of the Riemann Hypothesis.