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

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