Homotopic Transfer -- i*PI(del) Action

 The greater the absolute value of the homotopic transfer, the greater the absolute value of the i*PI(del) Action. The lower the absolute value of the homotopic transfer, the lower the absolute value of the  i*PI(del) Action. TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH.(1989). 

Diminishing Ricci Flow -- Logarithmic Attenuation Of Directly Corresponding Ricci Curvature

 The larger that the absolute value of a diminishing Ricci Flow is to be, the greater that the logarithmic attenuation of its directly corresponding Ricci Curvature will consequently tend to be. SAM ROACH.

Part Three As To Solitons

Let us initially consider one given arbitrary Ward-Cauchy-related phenomenon, that is here to be a soliton.  Let us consider the condition, that, in order for it to be a "soliton," it is to not be compact -- to where it is here to conform to the Ward-Cauchy-related condition, that it is to bear a tense of diffeomorphisrm.  Since the said soliton is to work to bear diffeomorphisrm, it is to bear a manifold, complex here if you will, that is to have both a smooth and an isomorphic homeomorphic topological contour -- to where one could theoretically try to here, act in so as to extrapolate a Laplacian-related cohomological mappable-tracing, along the Minkowski-related plane of its external topological surface, at the Poincare level -- in such a manner, to where there would here be the condition of one to not to have any Lagrangian-based Chern-Simons spurs to be detected.  This would then work to mean here, in this given arbitrary general case,  that the absolute value of the Beti number would not vary, and, in so long as such a soliton is here to be of a Noether-related tense of phenomenology, such a consistent absolute value of the Beti number, would be of the same absolute value of an even integer per group-related instanton, in so long as both the constraints as to being -- that such a said phenomenon is to be a soliton, as well as the constraint, that the said phenomenon does not become tachyonic here at all.  Yet, if the absolute value of the Beti number is to either decrease or to increase spontaneously, then, the soliton will no longer be a soliton -- it will then be of a compact nature, that will to be either losing or to be gaining a certain number of spatial dimensions, spontaneously.  If such an initially stated soliton, that is to change into not being a soliton, in such a manner -- to where there is not only a change in the compactification of its correlative dimensionality, yet also to where -- the topological strands of the said superstring are to expand, in terms of the scalar amplitude of their Ward-Neumman bounds, over a relatively transient evenly-gauged Hamiltonian eigenmetric, -- then, there is then to be a Clifford-Expansion in the size of the core-field-density of such a phenomenon, that is here to have perturbated from being a soliton into Not being a soliton.  Furthermore, if such a change is here to work to convert an initial Legendre homology into a symplectic homology, over time -- then, such a change will almost certainly work to alter the initial complex manifold M, -- into then being of a Real Reimman manifold, instead.  If such an alteration in the type of phenomenon that is being discussed, is to work to bear a set of one or more Laplacian-based Chern-Simons Lagrangian-related topological spurs, then, the said phenomenon is to no longer be of a flat Ricci curvature.  Let us still stay, though, that the flow of such so-eluded-to phenomenon will work to displace a holomorphic vector field.  Such A Change In Ward-Cauchy-Conditions Is One General Manner Of How One Given Arbitrary Eigenstate Of A Nijenhuis Holographic Spacing, May Work To Convert Into A Real Reimman Hilbert Space, Thus Working To Convert The Soliton Into A Cohomological-Based Compact Calabi-Yau Space, Which Is Then No Longer A Soliton.  This may often be able to happen, when there is a significant dissonance of the tendencies of the push and tug of gravitational waves, in such a manner -- to where the "best-fit-curve" as to how such a phenomenon as to what was initially a soliton -- is to behave, is then to bear a perturbative alteration, in both the display and in the scalar amplitude of its "phenotypical" correlative proximal local altering cotangent bundle.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Open Strings And "Swivel-Shaped" Phenomenology

The higher that the Absolute Value is of the Bette Number, that is here to be directly corresponding to either an open-looped or an open-strand related superstring of discrete energy permittivity, during any one given arbitrary respective iteration of instanton -- the more "swivel- shaped" that such an either respective open-looped or open-strand related superstringular phenomenology will tend to be -- during the directly corresponding iteration of BRST that is correlative to the said iteration of instanton.  The more "swivel-shaped" that such a so-eluded-to open string or fermionic superstring of discrete energy permittivity is to be -- during any one given arbitrary respective iteration of BRST, (which is during a majority of the directly corresponding iteration of instanton), the more likely that such a said superstring is to ensue in so as to become of a tachyonic nature -- as opposed to, instead, of being of a Noether-related nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Net Exchange Of Partition-Related Discrepancies

If the Lorentz-Four-Contraction of a phenomenology of mass-bearing superstrings is to be maintained over time -- to where the correlative Polyakov Action eigenstate, that is of the self-same phenomenology of mass-bearing superstrings, is here as well to be maintained over that same period of time, -- the number of partition-related discrepancies that the said phenomenology of mass-bearing superstrings is to gain per each individually taken instanton, will tend to equal the number of partition-related discrepancies that the so-stated phenomenology of mass-bearing superstrings will lose per each individually taken instanton -- over the said duration of time.  This will then mean, that the directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional compactification, will here tend to be equal to that directly corresponding absolute value of the Beti number per instanton -- that is here to be correlative to the directly corresponding scalar amplitude of spatial dimensional decompactification, -- over the so-eluded-to evenly-gauged Hamiltonian eigenmetric, that is here to correspond to the said time period of such a said case.
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. 

The Beti Number And Dimensional Compactification

When a superstring compactifies in the number of spatial dimensions that it expresses -- its correlative Beti number is positive.  When a superstring decompactifies in the number of spatial dimensions that it expresses -- its correlative Beti number is negative.  A positive Beti number works to express the number of spatial dimensions that a superstring has just compactified in.  The absolute value of a negative Beti number works to expresses the number of spatial dimensions that a superstring has just decompactified in.  If the Beti number is +2 -- the correlative superstring of discrete energy permittivity has just decreased in its spatial dimensionality by two dimensions, -- it has just compactified by two dimensions.  However, if the Beti number is -2 -- the correlative superstring of discrete energy permittivity has just increased in its spatial dimensionality by two dimensions, -- it has just decompactified by two dimensions.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.