Let us initially consider one given arbitrary mass-bearing cohesive set of discrete energy quanta, as taken over the course of one given arbitrary iteration of group-related instanton. For all of those individually taken superstrings of discrete energy permittivity that work to comprise such an implied tense of a cohesive set of discrete energy quanta, each of such said strings are to work to bear the exhibition of the same Betti Number going Into the earlier mentioned iteration of group-related instanton, (as being either "0," or as being of a "positive" integer here); as well as that each of such individually taken superstrings of discrete energy permittivity that are here to work to comprise such an implied tense of a cohesive set of discrete energy quanta, are to work to bear the exhibition of the same Betti Number going Out of the earlier mentioned iteration of group-related instanton (as being either "0," or as being of a "negative" integer here). If the Betti Number is here to be "0" during both the general process of both going Into the said respective iteration of group-related instanton, as well as if the Betti Number is also to be "0" during the general process of going Out of the said respective iteration of group-related instanton, then, both each of the given arbitrary individually taken respective superstrings of such case , as well as the entire mass-bearing cohesive set of discrete energy quanta, will remain of as working to continue to display the same number of spatial dimensions, in the general process of this to be occurring. SAM ROACH.
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