Dimensionality of space of the early universe as a consequence of the second law of thermodynamics

Preliminary analytical calculations show that if one assumes fermions (quarks or electrons) generated by superstrings in the early Universe to have existed as a degenerate, nonrelativistic, ideal quantum gas, then the entropy of such a system will have local maxima in spaces with number of dimensions n = 5, 9, 13, … . Thus there are reasons to assume that the Universe was formed in a space with specifically such a number of dimensions. With further evolution of the Universe, if we continue to adhere to the ground-laying principle of the second law of thermodynamics, in connection with ongoing changes in the temperature and composition, it appears that space with n = 3 began to correspond to an entropy maximum. Whatever the case may be, the latter assertion is only a hypothesis, whose proof at the given stage of knowledge is not possible.