Geometric Origin of Riemann Zeta Zeros: Long-Range Predictive Validation (n=5000) via 13D Toroidal Topology and FCC Lattice Projection

We present a geometric conjecture proposing that the nontrivial zeros of the Riemann zeta function emerge as eigenvalues of a 13-dimensional toroidal manifold projected onto 3D Euclidean space. Departing from classical linear scaling models, we apply the Holographic Principle (E∝n) to a Hamiltonian governed by the Bronze Ratio (ϕbr). We identify the scaling factor σgeo=32 as the inverse packing efficiency of the Aluminum Face-Centered Cubic (FCC) lattice (π/ηFCC). Numerical validation extended to n=5000 reveals that when corrected for Frame Dragging effects consistent with Kerr-Newman dynamics, the model achieves a mean relative error of 0.0039%. This framework suggests a direct topological link between Number Theory and the crystallographic properties of Aluminum, implying that the distribution of primes is governed by deterministic geometric laws rather than random matrix statistics.