Holographic Realizations of Arithmetic Structures and Computational Complexity: Dual Perspectives on the Spectral Security Architecture

This paper constructs a holographic duality framework that translates arithmetic structures and universal computational complexity into geometric observables within higher-dimensional spacetimes, building upon the mathematical-physical foundations—such as non-commutative dielectric branes and finite $T\bar{T}$ cutoffs—established in Paper I (previous research). The study discusses the spectral correspondence of the Riemann zeta function $\zeta(s)$ (a duality between the distribution of zeros on the critical line and moduli stability), the P vs. NP problem (representing exponential search trees in polynomial time via bulk geodesic flows), the ABC conjecture (its physical realization through open-closed string duality and DBI tension saturation), as well as various cosmological implications. (For full details, please refer to the original cited literature.)