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.

An Interim In-Between Parts to Session 11 of Course 19 -- The Klein Bottle and Orbifold Differentiation

The overall degrees of freedom that exist in two spatial parameters of dimensionality is 2pi.  The overall degrees of freedom that exist in three spatial parameters of dimensionality is 4pi.  The overall degrees of freedom that exist in four spatial parameters of dimensionality is 4piI. ... The overall degrees of freedom that exist in 96 spatial parameters of dimensionality is 96piI.  On account of this so-stated set of conditions -- if the relative tense of a Njenhuis basis of orphoganation, in a comparison of two different distinct substringular phenomena -- that are here to be extrapolated, in terms of the correlative degree of the wobbling of their respective given arbitrary correlative Fadeev-Popov-Trace eigenstates, that work to comprise the said two different distinct phenomena, is of a higher scalar amplitude -- the more of a tendency that there will then be, of the two respective distinct different substringular entities, that are here being compared, to be of more of a relatively remote nature -- over any respective given arbitrary time period, in which the two so-eluded-to physical phenomena that are here to be compared, in a Fourier-based manner.  This is given as a comparison -- in terms of their relative covariant, codifferentiable, and codeterminable Ward-Caucy conditions, in the process of the said comparison of the so-mentioned Fourier Transformations -- that are of the two said distinct and differing so-stated substringular physical phenomena, that are here to be contrasted.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of the Test Solutions to Test Two of Course 17

1)  A hermitian singularity is one in which there is either no Chern-Simmons singularities  -- in one or more manners of working to determine this.

2)  A Chern-Simmons singularity is a change in the derivative, as to either the kinematic flow and/or the mappable tracing of a substringular phenomenon, that would here, either:  change in more derivatives than the number of spatial dimensions that it is traveling through -- in its directly corresponding Lagrangian path -- , and/or bear either an enharmonic extension or an enharmonic attenuation of its substringular pulse, and/or, if it is of a cohomological tracing, move as a Njenhuis projection that is pulsating off of the relative Real Reimmanian Plane.

3)  The two basic superstringular-based Chern-Simmons topological singularities, are either a Lagrangian-based singularity or a metrical-based singularity.

4)  The three basic cohomological-based Chern-Simmons singularities are either a Lagrangian-based singularity, a metrical-based singularity, and/or a Njenhuis cohomological tracing of a ghost-based indical pattern -- the latter of which may be described of as hermitian off of the Real Reimmanian Plane (a tense of being partially hermitian).

5)  A heritian-based orbifold -- if it is completely hermitian, to where it works to describe a tense of superstringular phenomena that are Yau-Exact, will be in reference to the direct existence of a mass.  It is the phenomena of mass that work most succinctly to influence the interactivity of gravity.  The Ricci Scalar is the eigenbase of that mechanism that works to drive the activity of gravity itself.

6)  Cohomologies are the mappable tracing of both the activity and the existence of substringular phenomena.  If a cohomology is completely hermitian, then, not only is it Yau-Exact, yet, it bears only Real Reimmanian-based tensors -- when under these said eigenconditions.  This will then mean that we are talking about phenomena of mass that are here able to make viable Yakawa Couplings with each other.  This would work to indicate the format of Calabi-Yau manifolds that interact as Real Reimmanian eigenstates, that bear no unattenuated Njenhuis residue.  This would then involve a relatively more Hodge-based  index, in terms of the given arbitrary genus of Ricci Scalar eigenbase -- in terms of the directly involved inter-activity  -- than if one would instead have an added clause of Njenhuis-based tensors.  (Since we would here have purely Rham-based cohomologies instead of Doubolt-based cohomologies.)

I will continue with the solutions later! Sincerely, Sam Roach.