A $(D_{\tau },D_x)$-manifold with $N$-correlators of $N_t$-objects

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.