Certificate summary

The executed Python construction validates a finite-dimensional invariant fluid model on $E_{47}$:

$\partial_tu+\nu Au+PB(u,u)=0,\qquad u(t)\in E_{47}.$

With $A=A^\dagger\ge0$ and $B(u,u)=G(u)u$, $G(u)^\dagger=-G(u)$,

$\operatorname{Re}\langle u,B(u,u)\rangle=0$

and therefore

$\frac{d}{dt}\frac12\lVert u\rVert^2=-\nu\langle u,Au\rangle\le0.$

Machine results: kernel leakage $1.47\times10^{-13}$; energy increase $0$; energy-balance residual $2.78\times10^{-17}$.

Boundary: finite-dimensional projected closure only. No continuum Millennium-Prize claim is inherited.