Theoretical analysis demonstrates a categorical framework for the completed zeta function, indicating that all non-trivial zeros must lie on the critical line.
This preprint proposes a categorical structural resolution of the Riemann Hypothesis through an exact transport of structure in the sense of Bourbaki. The completed zeta function is recast in a common Euler–Fourier–Riemann framework combining spherical phase geometry, logarithmic layers, amplitude holonomy, Euler’s prime-power skeleton, Mellin–Plancherel dilation, and the Riemann–Weil explicit formula. A single transverse parameter bb governs three equivalent return defects: wave holonomy, Euler mirror imbalance, and departure from the unitary Mellin class. The critical line ℜ(s)=1/2 is thereby identified as the unique fixed return class of the complete transported structure. The final argument is global and apagogic: an off-axis structural zero produces a nontrivial return profile incompatible with nodal closure.
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Xavier J. Régent (2026) studied this question.