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.