Compounded Homotopic Residue — Asymptotic Divergence

 The more that the homotopic residue of an escalating Lagrangian, that is here to be of a Euclidean expansion, is to be compounded, over a given arbitrary proscribed duration, that is here to be of a sequential series of group-related instantons, the more that the corresponding pertinent Euclidean tangential bundle(s) directly involved, will consequently result, in tending to diverge in more of an asymptotic manner. The more that the homotopic residue of an escalating Lagrangian, that is here to be of a Clifford expansion, is to be compounded, over a given arbitrary proscribed duration, that is of a sequential series of group-related instantons, the more that the corresponding pertinent hyperbolic tangential bundle(s) directly involved, will consequently result, in tending to diverge in more of an asymptotic manner. I will continue with the suspense later! Sincerely, SAM ROACH. (1989).

Scattering And Cotangent Bundle

When Ward-Cauchy-related phenomenology are to scatter -- in so as to work to converge upon a substringular cotangent bundle of some given arbitrary spatial dimensionality, -- then, this is one general genus of a Reimman Scattering; Whereas, -- when Ward-Cauchy-related phenomenology are to scatter -- in so as to work to diverge from a substringular cotangent bundle of some given arbitrary spatial dimensionality, -- then, this is one general genus of a Rayleigh Scattering.  Samuel Roach.

Majorana-Weyl-Invariant-Mode And Homotopic Residue

The higher that the tense is of the correlative condition, that is appertaining to a Majorana-Weyl-Invariant-Mode -- that an individually taken superstring of discrete energy permittivity is to be of -- the more that homotopic residue is to then to tend to Converge Upon the proximal locus of the just mentioned superstring of discrete energy permittivity -- at a reference-frame that is Poincare to the topological stratum of the said individually taken string.  Consequently, the lower that the tense is of the correlative condition, that is appertaining to a Majorana-Weyl-Invariant-Mode -- that an individually taken superstring of discrete energy permittivity is to be of -- the more that homotopic residue is to then to tend to Diverge From the proximal locus of the just mentioned superstring of discrete energy permittivity -- at a reference-frame that is Poincare to the topological stratum of the said individually taken string.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Homotopic Residue And Rates Of Speed

Let us initially consider one given arbitrary orbifold eigenset.  The Slower that the said orbifold eigenset is to travel in one given direction -- the more that homotopic residue is to tend to Converge upon those individually taken superstrings, that work to comprise the said orbifold eigenset.  Consequently, the Faster that the said respective orbifold eigenet is to travel in that same one given direction -- the more that homotopic residue is to Diverge from those individually taken superstrings, that work to comprise the said orbifold eigenset.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

First Discussion As to Flow Of Partition-Related Discrepancies

The higher that the Beti number is, during a dimensional compactification, of which is to here to happen right before any one given arbitrary iteration of BRST -- the more partition-related discrepancies will tend to flow out of or diverge from a correlative superstring just before the said iteration of BRST.  Furthermore, -- the higher that the absolute value of the Beti number is, during a dimensional decompactification, which is here to happen during any one iteration of the Regge Action -- the more partition-related discrepancies will tend to flow into or converge upon a correlative superstring, during the so-stated iteration of the Regge Action.  Compactification of dimensions tends to work to involve a tangential flow of exchanged homotopic residue, whereas, decompactification of dimensions tends to work to involve a cotangent-related flow of exchanged homotopic residue. 
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach. 

Extra Stuff About Cyclic Permutations

Let us initially consider a phenomenology that goes through a state of a Fourier-related activity,  that is repeated over and over again -- yet, to where such a so-eluded-to general tendency of a cycle is to work to bear one or more slight changes, over the course of the iterations of each of such a so-eluded-to process or processes of cyclical states.  If the pattern of the cyclical changes, is never symmetrically completed -- in such a manner to where the overall pattern of such a general condition of a cycle is not equivalently iterative, then, such a cyclical pattern is said to diverge.  Yet, if the pattern of the cyclical changes, is to instead, be symmetrically completed in such a manner -- to where the overall pattern of such a general condition of a cycle is to be equivalently iterative, then, such a cyclical pattern is said to converge.  For instance -- let us consider an elliptical pattern, that is cyclical in permutation.  Let us say -- within a here considered tendency of time constraints -- that one physical phenomenology is to orbit around another physical phenomenology, in such a manner to where the tense of such an orbit, per each adjacent iteration of orbit, is to be slightly different is its precise Lagrangian-based contour, -- yet, let us say that in this given arbitrary case scenario, that after one thousand iterations of such an elliptical tendency of orbit, that the whole overall general pattern of a cyclical tendency is to be repeated in the exact same manner again, to where the second set of one thousand iterations of such an elliptical orbital-based tendency is to be exactly the same as the first set of one thousand iterations of such an elliptical orbital-based tendency.  In this just mentioned tense of a condition of cyclical permutation, the cycle is to here be symmetrical in its behavior, and thus, such a so-stated tense of a condition of cyclical permutation is to here be convergent, -- at least over the course of the first two thousand iterations of such a pattern of a cyclical-based permutation-related tense of elliptical orbit.  Furthermore, there are three general genre of Fourier-related cyclical permutations -- of which may sometimes be combined. There are Lagrangian-based cyclical-based permutations, and/or there are metrical-based cyclical permutations, and/or there are contour-based cyclical-based permutations.  I will later discuss what is meant by a Laplacian-related state of conditions, that would work to bear a tense of cyclical permutation.

I will continued with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.