  This paper presents a recent advancement that transforms the problem of
decaying turbulence in the Navier-Stokes equations in $3+1$ dimensions into a
Number Theory challenge: finding the statistical limit of the Euler ensemble.
We redefine this ensemble as a Markov chain, establishing its equivalence to
the quantum statistical theory of $N$ fermions on a ring, interacting with an
external field associated with random fractions of $\pi$. Analyzing this theory
in the turbulent limit, where $N \to \infty$ and $\nu \to 0$, we discover the
solution as a complex trajectory (instanton) that acts as a saddle point in the
path integral over the density of these fermions.
  By computing the contribution of this instanton to the vorticity correlation
function, we obtain an analytic formula for the observable energy spectrum -- a
complete solution of decaying turbulence derived entirely from first principles
without the need for approximations or fitted dimensionless parameters. Our
analysis reveals the full spectrum of critical indices in the velocity
correlation function in coordinate space, determined by the poles of the Mellin
transform, which we prove to be a meromorphic function. Real and complex poles
are identified, with the complex poles reflecting dissipation and uniquely
determined by the famous complex zeros of the Riemann zeta function.
  Universal functions of the scaling variables supersede the traditional
turbulent scaling laws (K41, Heisenberg, and multifractal). These functions for
the energy spectrum, energy decay rate, and velocity correlation significantly
deviate from power laws but closely match the results from grid turbulence
experiments \cite{GridTurbulence_1966, Comte\_Bellot\_Corrsin\_1971} and recent
DNS data \cite{SreeniDecaying} within experimental error margins.
