We present a mathematically consistent formulation of a holographic model where 4D gravity and matter emerge from a single primordial tensor field in a 10-dimensional bulk spacetime. The model is defined by a Z_2 -symmetric action with a quadratic potential, V(I)=1/2 m^2 I_B^A I_A^B, ensuring stability. We derive the full effective potential for the radion field, rigorously incorporating contributions from higher-dimensional curvature, field gradient energy, potential energy, and a stabilizing Freund-Rubin flux. We demonstrate analytically and numerically that a stable minimum exists for realistic parameters, naturally generating the Planck-electroweak hierarchy. The emergence of the Standard Model is not presented as a derived result but as a concrete research program based on orbifold compactifications and the index theorem. The model predicts a TeV-scale radion, deviations from Newtonian gravity at short distances, and gravitational decoherence, providing clear avenues for experimental verification.