Metric-Based Chern-Simons Singularities -- Incursion Of Lowered Isotropic Stability

 When a given arbitrary initially isotropically stable Noether-Based mass-bearing cohesive set of discrete energy quanta, is to ensue, in so as to spontaneously go into the general process, by which it is then to end-up working to bear, a set of one or more proximally local attributable metric-based Chern-Simons singularities, it will thereby consequently follow, that this general type of a case scenario, will often tend to result, in the general incursion of a lowered tense of isotropic stability, when this is in terms of the general resultant type of behavior, in which the initially inferred homomorphic characteristic, that is thence to be of the herein stated Noether-Based mass-bearing cohesive set of discrete energy quanta, is thereby to consequentially be decreased, in its scalar amplitude of effectual import. SAM ROACH. (PINCKNEY HIGH SCHOOL, 1989).

The Polyakov Action And Gauge-Invariance

 When any given arbitrary Noether-Based mass-bearing superstring of discrete energy permittivity, is to be gauge-invariant, both the scalar amplitude/magnitude, AND, the delineation of its directly corresponding Polyakov Action, will tend to be maintained -- of which is to happen, when the relative motion of such an earlier stated respective given arbitrary superstring of discrete energy permittivity, is to remain the same, while in its relation to both the motion and presence of electromagnetic energy. TO BE CONTINUED! SAM (1989).

Attenuated/Augmented Ricci Curvature

The given arbitrary covariant proximal local presence, of a cohesive set of inverted gravitational waves, often tends to be directly associated, with a Ricci Curvature, that is here to be attenuated, from a heuristically flat Ricci Curvature. Whereas; The given arbitrary covariant proximal local presence, of a cohesive set of amplified heuristic gravitational waves, often tends to be directly associated, with a Ricci Curvature, that is here to be augmented, from a heuristically flat Ricci Curvature. SAM ROACH. (1989).

Isotropic Stability And Structural Integrity

 Individually taken cohesive sets of discrete energy quanta, that work to bear a high scalar amplitude of isotropic stability, have a "habit" of tending to work to bear a greater structural integrity, -- than if such said cohesive sets of discrete energy quanta, were, instead, to not work to bear such a tense of isotropic stability. I will continue with the suspense later! To Be Continued! Sincerely, SAM ROACH. (1989).

Group Action And Magnetism

 Let us initially consider two different unique mass-bearing cohesive sets of discrete energy quanta.  Both of which are here to be of the same quantum of mass; as well as the given arbitrary physical condition, that both of such said sets of discrete energy quanta, are, as well, to work to bear the same innate tendency of working to exhibit a De Rham cohomology.  Furthermore; both of such respective mass-bearing cohesive sets of discrete energy quanta,  are also to tend to work to bear both the same charge, as well as working to bear the same basic means, of translating the exhibition of the externalized transversal component of their Fourier-related spatial delineation, over a fairly transient covariant relativistic duration of time, that is here to be simultaneous in comparison to one another — as this is to occur, via the vantage-point of a central coni-point.  The main difference in the behavior of these two said cohesive sets of discrete energy quanta, is that one of such sets of cohesive discrete energy, is to bear a reductional tense of group action — by working to bear a tense of isotropic stability; whereas, the other of such said respective given arbitrary mass-bearing cohesive sets of discrete energy quanta, is to work to bear a tense of isotropic instability. That stated set of discrete energy quanta (mass-bearing cohesive set), that is here to be of a tense of isotropic stability, will tend to result in working to display a relatively higher scalar amplitude of a fractal of magnetism, than the other of such said mass-bearing cohesive sets of discrete energy quanta, — of which, instead, is consequently to result in working to bear a lower scalar amplitude of a fractal of magnetism. I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach.

Abelian Nature Of Thought Waves

 Let us consider here, that one were to have two different thought waves.  Each of such said thought waves, is here to be in the process of transmitting the same frequency, -- as well as the general condition, being here, that both of such said thought waves, are otherwise to be of basically the same nature, except that one of these two different mentioned thought waves, is here to bear a smaller scalar amplitude of wavelength, than the other of these two different said thought waves. That thought wave of the two, that is here to be of a smaller scalar amplitude of wavelength, will tend to work to bear a greater scalar attribute of an abelian nature -- than the other of the two different said thought waves.  SAMUEL DAVID ROACH.

Scalar Amplitude Of The Kinematic Translation Of Correlative Chern-Simons Invariants

The higher that the scalar amplitude of that correlative tense of physical magnetism is to be, that is here to be directly associated with the physical charge of any one given arbitrary Noether-based mass-bearing orbifold eigenset, over time, -- the greater that the directly corresponding scalar amplitude will then tend to be, of the correlative rate that is of the kinematic translation of those correlative Chern-Simons Invariants, that are here to be most directly associated with the externalized radial/(transversal) transfer of such a said given arbitrary Noether-based mass-bearing orbifold eigenset, over an implied correlative evenly-gauged Hamiltonian eigenmetric. To Be Continued! Sam Roach.

The Polyakov Action And Hyperbolic Approach

The slower that the rate is, of any given arbitrary superstring of discrete energy permittivity, when this is here to be taken in its relationship to the motion of electromagnetic energy, the lower that its directly corresponding Lorentz-Four-Contraction will consequently tend to be.  The lower the Lorentz-Four-Contraction is to be, for any given superstring of discrete energy permittivity -- the higher that its directly corresponding Polyakov Action will then tend to be.  The higher that the respective Polyakov Action will tend to be, for any given superstring of discrete energy permittivity -- the greater that the scalar amplitude will tend to be, of the hyperbolic approach of the correlative respective second-order light-cone-gauge eigenstates, that are of the proximal local self-same discrete quantum of energy, -- as such said respective second-order light-cone-gauge eigenstates, are here to work to interconnect the directly corresponding Fadeev-Popov-Trace eigenstate that is of the self-same discrete quantum of energy, To the initially stated superstring of discrete energy permittivity, of such a particular given arbitrary case scenario.  To Be Continued!  Sincerely, Samuel David Roach.

Even Cotangential Flow

When the Lorentz-Four-Contraction is here to be maintained, for any one given arbitrary superstring of discrete energy permittivity -- consequently, -- those first-order point particles that work to comprise such a said string, are here to work to bear just as much of a net hyperbolic cotangential flow of an ebbing of mini-stringular segmentation, that is here to be converging upon it , over any one proscribed evenly-gauged Hamiltonian eigenmetric, over which such a said Lorentz-Four-Contraction is here to be staying at the same scalar amplitude; as there is here to be a net hyperbolic tangential flow of an ebbing of mini-stringular segmentation, that is here to be diverging from it, over any one proscribed evenly-gauged Hamiltonian eigenmetric, over which such a said Lorentz-Four-Contraction is here to be staying at the same scalar amplitude.  To Be Continued! Samuel David Roach.

Some Stuff As To Amplitude Of Metrics

The higher that the amplitude of that given arbitrary metric, that is here to be most directly associated with a depiction of the path integral of a respective given arbitrary Lagrangian-based expression -- the higher that the Hamiltonian-related wave-tug will then tend to be, -- as to that respective given arbitrary motion of the overall energy of a system, that is here to be depicted as I have done -- in this so-eluded-to just mentioned respective case.  Sincerely, Samuel David Roach.

An Ellaboration Of Quotients Of A Certain Genus Of Expressions

Let's say that there is here to be the progression of three dividends or quotients, that may be determined by working to divide the euclidean expression of four different resultant dilatino-related functions, (the second to the first, the third to the second, and the fourth to the third), which is here to result in a Bianchi-related scalar curvature, that may be extrapolated into a four-spatial-dimensional Bianchi-curvature , that works to help at determining the scalar Lagrangian-related path of an ulterior particle, -- to where such a resultant scalar flow, that is to be extrapolated by the so-eluded-to respective quotients, is to work to bear the flow of an overall continuous function.  Once the four-spatial dimensional curvature is extrapolated, one may then attach directorals in an arbitrary yet consistent manner to the variable-related attributes, that are of the determined Bianchi-related scalar curvature.  The chirality is not altered over the said progression, and the pulse is here to remain unchanged per quotient -- to where the resultant integrative cohomology that such a so-eluded-to ulterior particle is here to traverse, would then here be able to be of a De Rham nature, over time, when this is taken as one whole.  The progression of the three consecutive quotients is to dampen, from the first quotient-determined path to the second quotient-determined path to the third quotient-determined path.  This means that the integrative cohomological expansion of the trajectory of the second quotient is of a lower amplitude of proximal divergence than the first one, and that the cohomological expansion of the trajectory of the third quotient is of a lower amplitude of proximal divergence than the second one.  Each of such quotients takes place, over a span of one million consecutive iterations of group-related instantons -- as an evenly-gauged Hamiltonian eigenmetric.  This will then mean that the overall Fourier Transformation that is here to be directly associated with the three consecutive quotients -- is to occur over an evenly-gauged Hamiltonian eigenmetric that is to span a duration of 3 millions consecutive group-related instantons. This dampening is an exponential decay in the rate of the expansion of the directly associated Lagrangian-related path, -- of which may be described of here as a natural logarithmic action -- that is taken in so as to work to decrease the rate of the expansion of the directly associated Lagrangian-based path.  One may then say that an inverse Clifford Expansion had happened to the general flow of the Ward-Cauchy-related eigenstate or Hamiltonian operator, that is here to had undergone the traversal of the three said consecutive quotients -- in so as to decrease the divergence of the said eigenstate or Hamiltonian operator, from propagating out of the adjacent general locus spontaneously.  Hint:  Each of the three directoral-related dependant variables are to be equidistant from the origin, at each endpoint of the three different quotient-based functions!  Such an eigenstate or Hamiltonian operator would here happen to be a Ward-Cauchy-related holonomic substrate, other than a superstring.  (It could, though however, be an orbifold eigenset -- that may act as one perturbating Hamiltonian operator.)
I will continue with the suspense later!  To Be Continued!  To Be Continued!  Sincerely, Samuel David Roach.