Homotopic Waves -- Homotopic Residue

 Homotopic waves may often help at working to describe metric(al)-related associations of dimensional-related pulsations.  So; when a given arbitrary physical entity, that is here to be exhibiting the general characteristic of acting as a topological manifold, in which it is here to be considered in lieu of its Ward-Cauchy-Based nature, is thence to change or alter in its respective physical attribute of dimensional-related pulsation, then, not only will the given arbitrary entity of topological manifold, of such a respective case, tend to work to form a metric-based Chern-Simons singularity -- at the covariant "point" in duration, at which such an inferred set of discrete energy quanta, is here to have phased into such a said change in its dimensional-related pulsation, yet, in the process of doing so, -- this general process that has just been eluded-to here, will also tend to work to involve, the eminent proximal adjutant flow, in the dispensation of its directly associated tense of energy-related indices, over a discrete increment of time. (That is, as this is taken over the course of a directly corresponding Fourier Transformation.) Such a general genus of an eminent adjutant flow, in the dispensation of a tense of energy-related indices, as taken over a Fourier Transformation, is directly associated with the general Ward-Cauchy-related concept, of what I term of as being the physical condition of "homotopic residue." To Be Continued! Sincerely, SAM ROACH. (1989).