Detectable Frequencies

 Frequencies, that may be detected by a physical mechanism, may often tend to be reverberative vibrational oscillations, that are thenceforth to be propagated along the Rarita Structure, that resound along the interconnecting sub string-related fields, of which work to comprise the general multiplicity of the homotopic basis, by which the net respective Clifford vibrational index, is to be subtended in a covariant manner, via the net perturbative Fourier-Related-Progression, by the net respective Euclidean vibrational index.

The deeper that the Kahler-Based Quotient is to be, the more spontaneously resonant, that the eminently corroborative frequency, that is here to be of the respective Kahler Hamiltonian Topological Manifold, will consequently tend to be. 

The more dimensionally compact, that a Calabi-Yau Manifold is to be, the spontaneously deeper, that its eminently corroborative Kahler-Based Quotient, will consequently tend to be. This is to where, relatively compact Calabi-Yau Manifolds, dimensional-wise, tend to exhibit, relatively deep, Kahler-Based Quotients. Calabi-Yau Manifolds, tend to be of the same number of spatial dimensions. So; If two different and distinct Calabi-Yau spaces, of which are here to be exhibiting the same number of spatial dimensions, are to be covariant and co-differentiable, and one is to be more of a compact Hamiltonian Topological Manifold than the other, than the more compact one of the two, will consequently tend to work to spontaneously bear a deeper Kahler-Based Quotient, than the other of the two. 

Two different and distinct kinematically propagated Kahler Hamiltonian Topological Manifolds, are to work, in this particular case scenario, to be exhibiting the same spatial dimensionality. One of which, is more of a compact Ward-Cauchy-Related phenomenology, than the other one. The more compact implicit Hamiltonian Topological differentiable space, of kinematic propagational import, will tend to work to exhibit a relatively stronger resonant frequency, and a stronger resonant pulsation, than the less compact kinematically propagated Kahler Hamiltonian Topological Manifold, will tend to exhibit, if every other physical factor was otherwise fairly analogous here. 

If two different and distinct Kahler Hamiltonian Topological Manifolds, are here to be exhibiting the same spatial dimensionality, yet, one of these two respective implicit teams of mass-bearing discrete energy quanta, is here to be of a more compact Ward-Cauchy-Related nature, than the other of the two Kahler Hamiltonian Topological Manifolds, then it will thereby consequently tend to spontaneously occur, that the more compact kinematically propagated space of discrete energy quanta, will work to express a more resolute tense, of a Fourier-Related-Progression, than the other of the two spaces.

A heuristic, kinematically propagated, Kahler Hamiltonian Topological Manifold, that is relatively more compact, than an otherwise analogous spatially translated implicit team, of mass-bearing discrete energy quanta, will not only tend to be more resolute, than the ulterior team of mass-bearing discrete energy quanta, yet, it will also tend to be more succinct in its motion, than even another kinematically propagated Kahler Hamiltonian Topological Manifold, that is instead, to eminently bear a metric-gauge behavior, even though such an implicit third tense of an implicit team of energy, is otherwise analogous.

The proximal local presence of anti gravitational force, tends to facilitate the permeability, that an eminently regional, kinematically propagated, Kahler Hamiltonian Topological Manifold, is to be exhibiting, as it is here to be traveling through, such an implicit anti gravitational field. 

Anti Gravitational Force -- Depth Of Kahler-Based Quotients

 As a general tendency; It may often occur -- that the stronger the incursion of an anti gravitational force, as it is to be imparted upon a given arbitrary correlative Noether-Based mass-bearing Hamiltonian Operator, the deeper that its directly associated Kahler-Based quotient, may often tend to become. SINCERELY, SAMUEL DAVID ROACH. (PHS -- 1989).

Fourier-Related-Progression

 The Fourier-Related-Progression of a given arbitrary Hamiltonian Operator, may often tend to be perceived of, as being, the quotient that is here to exist, between the respective Fourier-Transformation of the said Hamiltonian Operator, as divided by the directly associated Lagrangian of that self-same inferred "team" of discrete energy quanta. (To where; Such a stated "team" of discrete energy quanta, may be thought of as being a means of working to describe, the herein mentioned "Hamiltonian Operator.") SINCERELY, SAMUEL DAVID ROACH. TO BE CONTINUED LATER!!!

Wave-Tug Of Hamiltonian Operator Frequency

 A Hamiltonian Operator that expresses a relatively deep Kahler-Based Quotient, often tends to exhibit a frequency, that is eminently associated with a relatively strong wave-tug, that is here to be directly corresponding, to the expression of its correlative angular momentum. 

Greater Kahler-Based Quotient -- Deeper Resonant Vibration

 The greater that the Kahler-Based quotient is to be, for a given arbitrary Noether-Based Hamiltonian Operator, the deeper of a resonant vibration, that such a stated Hamiltonian Operator will thereby often consequently tend to work to express. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. 

Deeper Kahler-Based Quotient -- Greater Permittivity

 The deeper that the Kahler-Based quotient is to be, for a superstring of discrete kinetic energy, the more permittivity that such a stated superstring, will consequently tend to express. SAMUEL ROACH.

Kahler-Based Quotient -- Gauge-Invariant Hamiltonian Operator -- Stronger Tendency Of Isotropic Stability

 The deeper that the Kahler-Based quotient is to be, for a gauge-invariant Hamiltonian Operator, the stronger that its resultant tendency will thereby consequently tend to be, for exhibiting the display, of a general tense of isotropic stability. SAM.

Inertia Of Hamiltonian Operators

 A given arbitrary Noether-Based Hamiltonian Operator, that works to bear a binary Kahler-Based quotient, tends to be more inert, than an otherwise analogous Noether-Based Hamiltonian Operator, that works to bear a unitary Kahler-Based quotient. A given arbitrary Noether-Based Hamiltonian Operator, that works to bear a tertiary Kahler-Based quotient, tends to be more inert, than an otherwise analogous Noether-Based Hamiltonian Operator, that works to bear a binary Kahler-Based quotient; etc... . SAM.

High Scalar Amplitude Of Kahler-Based Quotient -- Deep Resonant Vibration

 It is often the case, to where -- The greater the scalar amplitude of the Kahler-Based quotient, the deeper that the directly associated resonant vibration will therefore consequently tend to be. I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SINCERELY, SAMUEL DAVID ROACH.

Scalar Amplitude Of Kahler-Based Quotient -- Relative Tense Of Inertia

 In general, for a Noether-Based mass-bearing cohesive set of discrete energy quanta: The stronger that the scalar amplitude of the Kahler-Based quotient is here to be, the greater that the relative tense of inertia that will tend to be exhibited, by the inferred "team" of mass-bearing discrete energy quanta. SINCERELY, SAM.

Scalar Amplitude Of Kahler-Based Quotients -- Correlative Intensity Of Wave-Tug

 Let us initially consider two different Noether-Based mass-bearing cohesive sets of discrete energy quanta, that are here to be of basically the same general nature. Both of these two different inferred individually taken "teams" of discrete energy, are here to be exhibiting the mappable-tracing, of a "congruent" tense of a Lagrangian-Based path, as this is here to be taken into consideration, over the durational course of a relatively brief covariant Fourier-Transformation, that is here to work to bear the span of the same sequential series of group-related instantons. (As the inferred covariant duration that is to be considered here, in which these two different inferred "teams" of energy, are here to have had worked to map-out their correlative Lagrangian-Based paths, is to be indicated by a monomial tense, of an evenly-gauged relativistic Hamiltonian eigenmetric.) Next; The kinematic motion of one of these two said cohesive sets of discrete energy quanta, is here to work to mathematically bear a greater scalar amplitude of a Kahler-Based quotient, than the other indicated cohesive set of discrete energy quanta, as this is here to be taken, over the covariant span of time, in which these two earlier inferred sets of discrete energy quanta, have worked to map-out their "congruent" individually taken Lagrangian-Based traces. As a result; that cohesive set of discrete energy quanta of the two, that is here to have worked to mathematically bear a greater scalar amplitude of a Kahler-Based quotient, -- in the process of working to map-out its correlative Lagrangian-based path, -- will consequently tend to work to bear a higher relativistic intensity of a wave-tug, upon its immediately external environment, than that other cohesive set of discrete energy quanta of the two, that was instead, to mathematically bear a lower scalar amplitude of a Kahler-Based quotient. I will continue with the suspense later! To Be Continued! 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.