  In this paper, we describe a mathematical formalism for a
$(D_\tau,D_x)$-dimensional manifold with $N$-correlators of $N_t$ types of
objects, with cross correlations and contaminants. In particular, we build this
formalism using simple notions of mathematical physics, field theory, topology,
algebra, statistics n-correlators and Fourier transform. We discuss the
applicability of this formalism in the context of cosmological scales, i.e.
from astronomical scales to quantum scales, for which we give some intuitive
examples.
