Altered Dimensional Settings

Let us first consider in this given arbitrary case, an electron that is differentiating here, in a Fourier-based manner -- in nine spatial dimensions plus time -- through a discrete Lagrangian, over a relatively transient duration of time.  An electron exists in a d-field -- of which is a subatomic field, that exists in a minimum of six spatial dimensions plus time, in any minimally considered given arbitrary respective Fourier Transformation -- by which such a said electron is moving as a Hamiltonian operator through, in its correlative Hamiltonian operand, over time.  So, since the so-stated electron of such a respective given case is here moving in two more so-eluded-to spatial dimensions, than the minimum number of spatial dimensions in which such a said particle such as an electron must be going through, as it is moving through space over time -- the so-stated electron of such a given case must then work to bear the Laplacian-based condition as to having two Njenhuis-based tensors, that are Yukawa to the topology of the said electrons core-field-density.  Let us say that the said electron is, in this said given case, moving in a tertiary Lagrangian -- as it is moving as the holonomic substrate of a given d-field, which is in the case of working here to bear the condition of interacting directly with eight spatial dimensions plus time -- instead of  working to bear the condition of interacting directly with six spatial dimensions plus time -- over the directly correlative Fourier-based transformation in which the said electron, as a respective orbifold eigenset, is moving in such a manner in so as to have a respective hermitian flow, -- by which one would thereby not have any overt Chern-Simons singularities.  This would then mean, that, although such an electron would bear, in such a case, an intrinsic Njenhuis "platitude" -- since it works to bear in this case two added spatial dimensions than it would if it were of simply of a Real Reimmanian-based nature -- it would work to bear a Doubolt cohomology that would be of a partially Yau-Exact nature, since it would be basically completely hermitian in a Li Algebra-based manner, yet, the Njenhuis topological sway of the wave-tug/wave-pull of the electron, as it is moving here in two added spatial dimensions than it usually would go through over its correlative Fourier Transformation that would make the Lagrangian-based path of the said Hamiltonian operand through which the said electron is moving through to be as a hermitian-based Hamiltonian operation that is off of the Real Reimmanian Plane.  Let us say that the so-stated electron of such a case is then pulled completely back into a simply Real Reimmanian-associated  Rham-based cohomology, that is as well of a hermitian based nature (the Fourier-based cohomology of such a case would then change in a maximum of only six derivatives here, instead of in a maximum of eight derivatives -- since the directly corresponding electron that is to form the correlative cohomology is to then to be only moving in six spatial dimensions plus time instead of in eight spatial dimensions plus time)  -- after a set sequential series of group-related instantons, after it has been pulled-out of being as a Doubolt-based Hamiltonian operator, that had initially worked to bear the two so-stated Njenhuis tensors that it had started-out by having at the beginning of this said scenario.  This would work to involve the process of what may here be termed of as the compactification of the dimensionality of the cohomological substrate of the so-mentioned electron -- by the projection of the trajectory of the electron, as a Hamitonian operator, being converted from existing as a GSO ghost that would have two Njenhuis coniaxials, to existing as a GSO ghost that would instead have only Real Reimmanian-based coniaxials.  The so-stated electron will then be back to moving in a kinematic manner as a Hamiltonian operator that is differentiating through a Fourier Transformation that is of purely a Yau-Exact nature.  This is a compactification of the dimensionality of an integrative Fourier-based ghost-based Hamiltonian operator -- that is as the physical memory in the substringular of a metrical-gauge-based nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some More As To The Fractal Of The Kahler-Metric

Here is some additional information, as to the manner in which the wobble-like tendencies of discrete quanta of energy -- as such wobbling happens during each succeeding iteration of group-related instanton -- happens in some ways, to kind of act like a fractal of the kinematic-based activity of the Kahler-Metric.  When any respective given arbitrary Fadeev-Popov-Trace eigenstate wobbles, in so as to work at bearing a topological sway -- over the course of any correlative iteration of BRST (during the main part of any respective given arbitrary iteration of instanton) -- such a so-eluded-to discrete quanta of energy impedance (specifically here, the particle-based physical holonomic substrate, that acts as a discrete physical unit of energy impedance) will tend to bear a covariant, codeterminable, and a codifferentiable back-and-forth angling motion, that will bear a subtension, that is of the relative scalar amplitude of 1.104735878*10^(-81)I degrees -- relative to all of the other adjacent Fadeev-Popov-Trace eigenstates that are encoded as being of the exact same universe, during the simultaneous iteration of group-related instanton, of any respective given arbitrary case scenario.  However, depending upon what other universal setting that other adjacent Fadeev-Popov-Trace eigenstates of a respective case belong to -- such an angling will vary -- as an interdependent condition, that is involved with both the manner and the degree that the two different individually taken Fadeev-Popov-Trace eigenstates are encoded as being -- of a specific scalar amplitude of divergence from being of the same universal setting.  So, if two spaces are of the same universe -- then, these will be of a Gaussian-based nature, the one towards the other, over the course of one specifically entailed iteration of group-related instanton, in which the two said given spaces are here being compared of as such.  Yet, if two spaces are not of the same universe -- then, these will only be able to be compared to one another through a Gaussian-based Transform -- via the involvement of certain Njenhuis-based mathematics, or, in other words, via a tense of a manner of Li Algebra.  Thereby, if two respective Fadeev-Popov-Trace eigenstates are not of the same universe -- then, the correlative covariant-based wobbling, that these so-eluded-to discrete quanta of energy impedance will work to bear- - will then involve a different topological sway of wobbling, relative to one another, depending upon both the manner and the scalar amplitude of the differences that these discrete quanta of holonomic substrate would here work to bear -- over each individually taken iteration of group-related instanton, in which the different said individual quanta of discrete energy impedance -- that are here of different universal settings -- are here to remain in the same relative general tense of codifferentiability.  Furthermore and specifically (more in terms of discrete energy impedance than with discrete energy permittivity) -- the covariant topological sway as to the wobbling of one genus of a Fadeev-Popov-Trace eigenstate towards another of such a genus of Fadeev-Popov-Trace eigenstate -- works to define the general format as to the differences in Li Algebra-based indices of the discrete energy impedance -- of the one discrete quanta of related energy towards the other discrete quanta of related energy -- during any respective given arbitrary iteration of group-related instanton, in which any given arbitrary comparison that is taken between two of such particle-based discrete quanta of energy are being compared in the substringular.  This may act as a fractal as to the condition in which the Kahler-Metric tends to bear those correlative Klein Bottle eigenstates -- that, unless perturbated -- tend to work only upon discrete quanta of energy, that are of the same universal setting.  To Be Continued!  Sincerely, Sam Roach.

Activity Associated With Chern-Simmons Genus

The higher the genus of a Chern-Simmons Lagrange-based singularity is, the more likely that the directly corresponding superstring, or, orbifold of one or more superstrings, is at being pulled out of its initial spatiality of Gaussian-based format.  So, if an orbifold moves through a Lagrangian in a kinematic manner over time in such a manner in so that  there is a change in eight more derivatives than the dimensionality of its initial euclidean Real Reimmanian arc, then, the said given arbitrary orbifold is more likely to become of a Li Algebra-based pretense -- subsequent to the eluded to metric of Chern-Simmons-based perturbation that would be along what is here then its Njenhuis-based Lagrangian kappa scattering -- than an orbifold that only changes in one more derivative than the number of spatial dimensions that it is traveling through over time, to become of a different universal setting of Gaussian format and/or of a different layer of reality.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

Li Algebra Co-Relations Between Physical Spaces

Different orbifolds and/or different orbifold eigensets that are, respectively, belonging to different universes, involve a Li Algebra co-relation -- when in terms of the physical spaces that these given arbitrary respective orbifolds and/or orbifold eigensets belong to in terms of their corelative Real Reimmanin spaces.  Orbifolds and/or orbifold eigensets that are of the same universe bear spaces that are Real Reimmanian relative to one another.  Whereas, spaces that are of different universes when in terms of their relationship to one another -- spaces that are here represented by orbifolds and/or orbifold eigensets -- are considered here to be Njenhuis when in relationship to one another.  Spaces that are Njenhuis when considered in co-relation to one another are of different Gaussian formats when in terms of their Real Reimmanian spatial-basis.  Spaces that are not Real Reimmanian when in co-relationship to one another may be compared in terms of a Li Algebra basis.  Li Algebra is linear algebra that involves an Imaginary Gaussian Format.  Spaces that are existent in realtiy -- although these said spaces are Njenhuis when in co-relationhip to one another -- yet, here, involve an Imaginary Gaussian correspondence in terms of the mathematical and therefore in terms of the physical relationhips that these work to bear towards each other, may be compared in such a type of case by using Li Algebra. Physically speaking, Li Algebra may be applied by comparing orbifolds and/or orbifold eigensets that covariantly corelate -- even though such orbifolds and/or orbifold eigensets are here, in such a given arbitrary case, respectively belonging to different univeres.  I will continue with the suspense later!  Sincerely, Samuel David Roach.