Five Dimensional Universe: Gauge Groups, Coupling Constants, Dynamics, and the Gravitational Hierarchy from a Five-Dimensional Quotient Manifold

No existing framework derives quantum mechanics, general relativity, and the full Standard Model — gauge groups, coupling constants, particle masses, and the Lagrangian — from a single geometric object. This paper shows that the five-dimensional quotient manifold M = (Im(ℍ) × Sp(1))/U(1) ≅ ℝ³ × S² does so. The fiber connection curvature yields Einstein's equations; KK decomposition on the compact fiber yields the Schrödinger equation, the linearity of quantum mechanics, and energy quantization; the base topology determines the gauge groups SU(3) × SU(2) × U(1); and the complete tree-level SM Lagrangian with all coefficients predicted follows from the derived gauge groups, matter content, and coupling constants — with every coefficient given by Φ(g) and none fitted. A single zero-parameter function Φ(g) = exp(−g^(6/5)/ln 3) determines every coupling constant and mass scale. From one dimensionful input (v = 246.22 GeV), three data inputs, one partially derived structural constant (θ = 2/9), and zero fitted coefficients, the framework produces 53 scored quantities: 26 within 1%, 41 within 5%. The cosmological constant — a 56-order-of-magnitude hierarchy that no other framework explains quantitatively — is reproduced at +1.77%. Fifteen blind predictions are stated with kill conditions, including Σm_ν = 3.0 meV and a permanent null in dark matter direct detection.