  We propose to define $\mathbb{F}_1$-algebras as integral bi-rings with the
co-ring structure being the descent data from $\mathbb{Z}$ to $\mathbb{F}_1$.
The coordinate bi-ring of $\mathbf{Spec}(\mathbb{Z})/\mathbb{F}_1$ is then the
co-ring of integral linear recursive sequences equipped with the Hadamard
product.
  We associate a noncommutative moduli space to this setting, show that it is
defined over $\mathbb{F}_1$, and has motive $\prod_{n \geq 0} \frac{s-n}{2
\pi}$.
