We present the complete non-perturbative formulation of M-theory based on topological rigidity and unique ground state selection. The theory is defined on an 11-dimensional manifold\mathcal{M}_{11} = (\mathbb{RP}^3/\mathbb{Z}_2) \times \mathbb{R} \times \mathcal{M}_7,where \mathcal{M}_7 is the unique compact G₂-manifold containing the flag manifold SU(3)/T as a submanifold.This ground state is uniquely fixed by topological consistency, chirality, and Poincaré duality without continuous moduli, thus resolving the string landscape problem. The low-energy limit yields 11-dimensional supergravity, and compactification on the canonical S^1 fiber automatically produces type IIA superstring as the only consistent perturbative limit.We rigorously derive the Standard Model gauge group SU(3)_c \times SU(2)_L \times U(1)_Y, three generations of fermions, the Higgs mass 125.12 GeV, the fine-structure constant \alpha^{-1} \approx 137.036, and the observed cosmological constant from topological invariants alone, with no free parameters. Four experimentally falsifiable predictions are proposed, making M-theory fully predictive and physically realizable for the first time.