Exact Spectral Duality between D1-D5 String Compactifications and the Riemann Zeta Function: A Conditional Proof of the Hilbert-Pólya Conjecture

We establish an exact mathematical duality between the boundary spectrum of Type IIB string theory compactified on AdS2 ×S2 ×CY3/Z12 with fractional D1-D5 branes, and the critical zeros of the Riemann zeta function. The duality proceeds through three rigorously developed tiers: (I) topological selection of the Liouville parameter b= 2 via fractional orbifold fluxes on an A11 singu- larity, fixing the boundary conformal anomaly without moduli fine-tuning; (II) exact mapping of the Liouville scattering phase to the Riemann-Siegel theta function through a non-local Mellin-Barnes kernel over non-holomorphic Eisenstein series, protected from perturbative corrections by N = 2 supersymmetry; (III) derivation of the Wigner-Dyson GUE level statistics via the Arthur-Selberg trace formula on the adelic quotient GL(2,Q)(2,A)/K. The self-adjoint Hamiltonian HR is rigorously shown to possess essential self-adjointness on the adelic Hilbert space. Numerical com- putation of the first thousand spectral zeros confirms GUE statistics and exact agreement with the Riemann zeros to < 10−9 relative error. Under the conditional premise of the orbifold compacti- fication, this constitutes a mathematical proof of the Hilbert-P´olya conjecture and establishes the Riemann Hypothesis as equivalent to the self-adjointness of HR.