The Riemann Hypothesis: A Categorical Structural Resolution by Spherical Transport In the Sense of Bourbaki
Year: 2025
Type: preprint
Abstract: 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.
Author: Régent, Xavier J.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077515233
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