Compact Manifolds

If an orbifold eigenset is to be of a cotangent bundle of phenomenology, that is here to be of a given arbitrary number of spatial dimensions, then, such an orbifold eigenset that is consequently to be moving via the general manner of Noether Flow, is said to work to maintain -- during the course of the correlative evenly-gauged Hamiltonian eigenmetric, in which it is here to be of a compact nature -- then, the  general Ward-Cauchy-related condition, of remaining as a manifold of a discrete overall quanta of energy, that is here to be of one specific number of spatial dimensions, will then be at what is here to be at the vantage point of a relatively respective internal reference-frame.  This will then mean, -- that if an orbifold eigenset is to be of what is to here to be of a compact nature, -- that, as this is to be in the process of being the general case -- that, for each of such so-eluded-to iterations of group-related instantons, that the Beti number that is here to be of the individually taken superstrings of discrete energy permittivity, that are here to work to help at comprising the earlier mentioned orbifold eigenset -- as it is to be just about to enter the Ward-Cauchy-related process of group-related instanton, is to be of the same absolute value of such a correlative Beti number, that is here to be of the individually taken superstrings of discrete energy permittivity that are here to work to help at comprising the earlier mentioned orbifold eigenset -- as it is to be entering the ensuing general gauge-action of the Regge Action.  This will then mean -- that the Beti number for all of the individually taken superstrings that are here to work to comprise the said orbifold eigenset, at a vantage-point of such a respective eigenset, as it is to be just about ready to enter its correlative iteration of group-related instanton, is to be of an even positive integer (for compactification), as well as the Ward-Cauchy-condition, that all of the individually taken superstrings that are here to work to comprise the said orbifold eigenset, at a vantage-point of such a respective eigenset -- as it is to be working to enter its ensuing iteration of the Regge Action, is to be of an even negative integer (for decompactification) (to where the earlier mentioned positive integer is to bear the same scalar matgnitude from zero as the earlier mentioned negative integer), to where such said superstrings of such a given respective case, are to here to not vary in the number of spatial dimensions that these are here to have, over the correlative so-eluded-to sequential series of the directly corresponding iterations of BRST.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.