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In this paper a new small parameter associated with the density matrixdeformation (density pro-matrix)studied in previous works of the author isintroduced into the Generalized Quantum Mechanics (GQM), i.e. quantum mechanicsinvolving description of the Early Universe. It is noted that this parameterhas its counterpart in the generalized statistical mechanics. Both parametersoffer a number of merits: they are dimensionless, varying over the intervalfrom 0 to 1/4 and assuming in this interval a discreet series of values.Besides, their definitions contain all the fundamental constants. Theseparameters are very small for the conventional scales and temperatures, e.g.the value of the first parameter is on the order of $\approx 10^{-66+2n}$,where $10^{-n}$ is the measuring scale and the Planck scale $\sim 10^{-33}cm$is assumed. The second one is also too small. It is demonstrated that relativeto the first of these parameters the Universe may be considered as a nonuniformlattice in the four-dimensional hypercube with dimensionless finite-length(1/4)edges. And the time variable is also described by one of theabove-mentioned dimensions due to the second parameter and generalizeduncertainty relations in thermodynamics. In this context the lattice isunderstood as a deformation rather than approximation.Comment: 15 pages, no figure

THE UNIVERSE AS A NONUNIFORM LATTICE IN FINITE-VOLUME HYPERCUBE I: FUNDAMENTAL DEFINITIONS AND PARTICULAR FEATURES