Riemann Hypothesis as Boundary Regularity in Generalized Universe Holography (GUH) A Structural Link Between Arithmetic Spectrum and Emergent Spacetime

This work is intended as a structural bridge between analytic number theory and emergent spacetime models, not as a physical derivation of RH.

This preprint explores a structural connection between the Riemann Hypothesis and Generalized Universe Holography (GUH), a framework in which spacetime geometry emerges from informational boundary constraints rather than fundamental degrees of freedom.

We interpret the nontrivial zeros of the Riemann zeta function as a spectral process on an effective boundary manifold corresponding to the critical line \Re(s)=1/2. Within this view, off-critical zeros act as transverse defects that induce super-quadratic variance growth in prime-counting statistics, increasing effective entropy and violating minimal encoding conditions.

Building on a recent structural reduction of the Riemann Hypothesis to a minimal variance obstruction, we argue that alignment of zeros on the critical line is the unique configuration compatible with boundary completeness and minimal informational cost in an emergent holographic setting. The argument is conditional on a precisely stated minimal variance hypothesis and remains falsifiable through analytic number theory bounds and independent physical constraints.

This work does not claim an unconditional proof of the Riemann Hypothesis. Instead, it provides a conceptual synthesis linking arithmetic regularity to holographic boundary principles, suggesting that number-theoretic structures may reflect deeper informational constraints in emergent spacetime models.

The paper complements two earlier preprints by the author:

• On the Structure of the Riemann Zeta Function (structural analysis of RH via variance and defect observables) - [https://zenodo.org/records/18284647],

• Generalized Universe Holography (GUH) (a boundary-based framework for emergent geometry) - [https://zenodo.org/records/18284647].

Together, these works outline a coherent research program connecting arithmetic spectra, variance constraints, and holographic emergence.