The $Lambda$CDM model successfully accounts for cosmic expansion and large-scale structure but treats dark matter, dark energy, and the fine-structure constant $alpha$ as independent inputs. We present a compact geometric construction in which all three emerge from the interplay of two natural measures --- a metric (Lebesgue-type) measure and an invariant (Haar-type) structural measure --- on FLRW spacetime and its underlying hyperquantum fibers. A single crossover scale $r^* = e^{-1}$ and a unified visibility kernel $K(x) = Sigma(x) cdot Pi_{m time}$ (with $Pi_{m time} = 1/2$ from the arrow-of-time projection) simultaneously produce the observed baryon-to-dark-matter ratio $Omega_{m DM}/Omega_b approx 5.4$, suppressed late-time growth of structure, and the precise value $alpha^{-1} = 4pi^3 + pi^2 + pi + delta approx 137.036$ (where $delta$ is the explicit higher-order vista correction). The framework requires no new particles, no free parameters, and makes concrete, falsifiable predictions for current and upcoming surveys and precision measurements of the fine-structure constant $alpha$.