The Euler ensemble is a discrete statistical manifold of regular star polygons that emerges as a fixed point of the momentum loop equation in the Navier-Stokes formulation. It provides an exactly solvable model of decaying turbulence, replacing heuristic scaling laws with universal functions derived from number theory.

Unlike Kolmogorov's K41 model, which assumes a universal energy cascade with power-law scaling, the Euler ensemble produces non-trivial universal functions for turbulence decay. These functions match experimental and numerical data, demonstrating that decaying turbulence does not follow a simple power law but a more intricate spectrum dictated by number-theoretic structures.

The theory reveals an unexpected duality between turbulence and a quantum system, where the loop functional satisfies an equation analogous to the Schrödinger equation in loop space. This correspondence allows the use of quantum mechanical tools to solve classical turbulence in quadrature.

The statistical structure of the Euler ensemble is deeply linked to prime numbers and Euler totient functions. The universal decay spectrum involves discrete sums over rational fractions, making turbulence one of the few physical systems directly governed by number-theoretic distributions.

The predicted energy decay follows $E(t) \sim t^{-5/4}$, which aligns with grid turbulence experiments and DNS data within a 1% margin of error. The energy spectrum also exhibits oscillations correlated with Riemann zeta function zeros, an effect observed in large-scale numerical simulations.

Future experiments should focus on measuring the predicted non-trivial decay spectra and testing the oscillatory corrections linked to number theory. Large-scale DNS and controlled laboratory experiments will be key to validating the finer details of this theory.