Homologies And Norm-State-Projection Strike

 A superstring that works to bear a symplectic homology -- tends to form a Yukawa Coupling upon those norm-state-projections that these are to strike in a Gliosis-related manner, that is of more of an orthogonal manner, than the general tense of a Yukawa-based Coupling that a superstring that works to bear a Legendre homology is to bear upon those norm-state-projections that these are to strike in a Gliosis-related manner, -- because superstrings that work to bear a symplectic homology, tend to interact with less topological slippage upon the stratum that these are to work to bear a Yukawa-related coupling upon,  than superstrings that are to instead to work to bear a Legendre homology are to tug upon the correlative topological stratum that these are to come into a direct contact with.  This is, in part, because, superstrings that are of a symplectic homology, are of a closed-looped nature, that thereby work to interact with the norm-state-projections that these are to interact with, in a manner that is to tend to bear a stronger direct wave-tug-related angular drive in their directly corresponding holomorphic direction, whereas, superstrings that are of a Legendre homology, are of an open-looped nature, that thereby work to bear a stronger indirect wave-tug-related angular drive in their directly corresponding holomorphic direction.  This helps at working to describe as to why phenomenologies that are of abelian geometries, tend to form cohomology entities around the topological region of closed-looped superstrings of discrete energy permittivity -- whereas, phenomenologies that are of non abelian geometries, tend to form around the topological stratum of superstrings of discrete energy permittivity, -- that are of either of an open-looped or of an open-stand-related nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cohomologies, Ghosts, And Distortions, Part One

Remember back at the condition that I have mentioned in the past -- that the projection of the trajectory of a substringular phenomenology is a world-sheet.  The mappable-tracing of a world-sheet is a cohomology.  That manner of considering a cohomology -- to where this may be viewed of as a relatively transient phenomenology, that is generally not to be apprehended -- is a ghost anomaly.  Cohomologies are initially harmonically scattered into place, via a correlative Reimmanian scattering, into a set of norm-state-projections -- that work in so as to help at indicating the physical memory of both the where, the how, and the when, that any particular given arbitrary respective substringular phenomenon had physically differentiated -- over any correlative proscribed sequential series of instantons.  The initiation of such a general genus of Reimmanian-based scattering, works to form a harmonic perturbation of those norm-state-projections, that had just been in the Lagrangian-based path of that Ward-Cauchy-related phenomenology, that is here to be forming an integrable set of cohomological eigenindices, as a set of Hamiltonian operand-related eigenstates, -- in so as to work to form a Wess-Zumino distortion of those point commutators that had eminently been in the path of the said substringular phenomenology, that had just formed the said cohomology.  Such a general genus of a Wess-Zumino distortion, is here to be formed by a set of relatively forward-holomorphic tending norm-state-projections -- that are here to have come into contact with that Ward-Cauchy-based phenomenology, that is here to form the so-eluded-to set of the so-stated physical memories.   I will get to the topic, as to the conditions that are related to those Cevita distortions of point particle-related motion -- soon.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little More As To Homology Versus Cohomology

Substringular Ward-Cauchy-related physical memories, that are conical in their mappable-tracing -- tend to be of the nature of being homologies -- that generally tend to be made by open-strands of stringular phenomenology.  Whereas, substringular Ward-Cauchy-related physical memories, that are toroidal in their mappable-tracing -- tend to be of the nature of being cohomologies -- that generally tend to be made by closed-loops of stringular phenomenology.  Furthermore, substringular Ward-Cauchy-related physical memories, that are semi-toroidal in their mappable-tracing -- tend to be of the nature of being homologies -- that generally tend to be made by open-loops of stringular phenomenology. I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Two As To Coupled Cohomologies

Let's initially take into consideration two different distinct orbifold eigensets, to where both of these said eigensets are here to be undergoing their respective Fourier Transforms in a manner, that is both covariant, codifferentiable, and codeterminable -- over an evenly gauged Hamiltonian operation.  Both of these said respective orbifold eigensets, are here to bear two individually taken Rham cohomologies -- as well as the condition that these orbifold eigensets are here to be undergoing their respective tenses of the general processes of a Majorana-Weyl-Invariant-Mode.  Next, let us say here, that there is to soon be the eminent presence of a group-attractor, that is here to be Yukawa to both of the said orbifold-related phenomena.  These orbifold eigensets are here to be proximal local, as well as to here to be consistently of the same layer of reality.  The earlier mentioned group-attractor is here to bring about a certain Cevita interaction upon the two said eigensets, by drawing both of the initially eminent Rham cohomologies out of their respective tenses of Majorana-Weyl-Invariance -- over a transient span of a sequential series of group-related instantons.  Consequently, both of the earlier mentioned Rham cohomologies, will soon alter in so as to then to become of the nature of two initially distinct Doubolt cohomologies.  After an ensuing relatively brief number of instantons after the so-inferred Rayleigh-related cohomological perturbation, the two spurious respective Doubolt cohomologies will then often be of the nature -- in so as to potentially tend to couple into one overall cohomology.  If the activity of such a coupling, is to bring about a Reimman scattering of  cohomological eigenindices -- that are to tug the two initially adjacent Chern-Simons cohomologies into a tense of to then to work in such a manner, in so as to become of one Rham-based cohomological holonomic substrate, then, the resultant Wess-Zumino interaction will then often tend to work to form a dual state of metrical-gauge-related Hamiltonian operators -- that work here to form one overall tense of a Majorana-Weyl-Invariant-Mode. 
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Ghosts And Gravity Waves

The substringular residue that may be derived from the enharmonic scattering of Gliosis-Sherk-Olive ghosts, works to act in the recycling process of norm-state indices, in the balance of the substringular residue that may here be derived from the enharmonic scattering of Neilson-Kollosh ghosts, -- in such a manner, to where the activity of the Rarita Structure is to here to be directly involved with the process of such a recycling-based nature.  Gliosis-Sherk-Olive ghosts are formed by the physical memory of the motion of superstrings of discrete energy permittivity, over time.  Relatively as soon as such physical memories as to the where, the when, and the how that any correlative superstrings that had just acted via a directly corresponding Fourier Transform, that is to here have just recently ended in its respective duration in any one of such respective given arbitrary cases, -- such a so-eluded-to integration of eigenindices of such a directly corresponding Reimman scattering will then be enharmonic scattered into residue, that is to then to be transferred off of the relative Real Reimmanian Plane as norm-state indices.  Likewise, as I have mentioned in earlier posts, the correlative Neilson-Kollosh ghosts are formed by the physical memory of both gravitons and gravitinos -- to where these just mentioned particles of which are innately here, to be off of the Real Reimman Plane.  The soon to be enharmonically scattered Neilson-Kollosh ghosts are to then to be transferred, via the activity of the Rarita Structure, as norm-state-projections that are to then be spatially occupied onto the relative Real Reimmanian  Plane.  Those eigenindices of the Rarita Stucture, that are to here to assist with the transferrence of such ghosts,  are a multiplicit form of Schwinger-Indices, that are to here be an association of gravity waves.   Ghosts in this case are a way of considering the temporal nature of cohomological indices.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

The Terms Cohomologies Versus Ghost Anomalies

That description of the physical memories, as to the where, the when, and the how, that the multiplicit substringular eigenstates have differentiated over time -- as may be described by the term that I call ghost anomalies, -- works to imply the temporal nature of the existence of the so-eluded-to  individually taken cohomological entities.  This is since the presence of an anomaly -- works to imply the existence of something that may rarely be both significantly detected and apprehended as both real and observable, at any specific given arbitrary locus.  Whereas -- the eigenstate of a given arbitrary respective cohomology, may simply refer to the existence of the physical memories as to the where, the when, and the how, that the multiplicit substringular eigenstates have differentiated in the arena of space-time-fabric in general.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Different Genre Of Cohomologies

Any given arbitrary respective eigenstate of cohomology, that may be considered -- when this is taken over a respective Laplacian Transform -- will be of either a Rham-based nature, or, of a Doubolt-based nature.  Any Rham-based cohomology -- when this is taken over a Fourier Transform, over a long enough duration of time -- will eventually be altered into a Doubolt-based cohomology. 
I can think of 13 different types of genre of cohomology, these of which will each be of either a Rham-based nature or of of Doubolt-based nature -- when taken over a respective Laplace Transform.
These would be:
1)  Gliosis-Sherk-Olive cohomologies
2)  Fadeev-Popov-Trace-related cohomologies
3)  Neilson-Kollosh cohomologies
4)  Light-Cone-Gauge eigenstate-related cohomologies
5)  Cohomologies of Schwinger-Indices, via the Rarita Structure
6)  Cohomologies of Campbell-based norm-states
7)  Cohomologies of Hausendorf-based norm-states
8)  Cohomologies of Campbell-Hausendorf-based norm-states
9)  Cohomologies of Campbell-based norm-state-projections
10)  Cohomologies of Hausendorf-based norm-state- projections
11)  Cohomologies of Campbell-Hausendorf-based norm-state-projections
12)  The cohomological mappable-tracings of Klein Bottle eigenstates
&13)  Cohomological mappable-tracings of Higgs Boson eigenstates.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Some More As To Generative Cohomologies

Let us consider an orbifold eigenset -- that is initially to be working to generate a set of cohomological indices, that are to be directly associated with a Doubolt cohomology, that is to here to be associated with a gradual increase in the tendency of working to bear an ellongated pulsation of the metrical eigenindices -- that are here to be correlative to a steadily accelerated orbifold eigenset-related oscillation-based mode.  As the said orbifold eigenset is to be generating cohomological indices at a gradually increasing metrical-based rate, -- it is to here to be in the process of this general activity to here be working to form a resultant tense of metrical-based Chern-Simons singularities, that are here to be extrapolated by a set of complex metrical-based roots.  If the development of the said integrative set of cohomological indices , that are here to be generated by the Fourier-related motion of the said orbifold eigenset over time --  is to be displaced at a kinematic-based "Sterling Approximation," as a unitary Hamiltonian operator, that is to be delineated via a Hamiltonian operand that is to here to work to involve a discrete Lagrangian-based path, that is to be traversed, then, the resultant Doubolt cohomology will not necessarily work to form any Lagrangian-based Chern-Simons singularities.  This is the tendency of this case, (to not work to bear any Lagrangian-based Chern-Simons singularities), in so long as the flow of the homotopic torsional eigenindices is to be hermitian as  a covaraint-based Hamiltonian operator -- that is to bear both a codifferentiable and a codeterminable hermitian-based transversal flow, that is here to be of an overall discrete nature as a wholistic hermitian-based Hamiltonian operator -- as the said orbifold eigenset is to both transversal-wise and torsional-wise, to flow in as many spatial dimensions as the number of derivatives that is is to be changing in, -- as this so-stated orbifold eigenset is to be delineated along the whole translation of the directly associated Lagrangian-based path, --  over the correlative gauged group-metric, that is of this particular genus of a case scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Wave Modulae And Doubolt Cohomologies

Let us say that one was to have an orbifold eigenset -- that was here to work to bear a wave modulus, that would here be of the nature of:  e^(lambda*the wave function), to where "lambda" would here be significantly greater than zero.  This would then mean, that the said orbifold eigenset would then:   1)Be of a Doubolt cohomology.  2)  Tend to work to bear an ellongated pulse.  3)  Work to bear a set of one or more Chern-Simons metrical singularities.  4)  Be generative of its external core-field-density eigenindices.  5)  Bear a Faro wave modulus.  6)  Work to bear spurious iterative Calabi-based singularities.  7)  Has more to do with a Clifford Expansion of its externalized core-field eigenindices.  8)  Will tend to bear an amplification of wave-related eigenvalues, that are of the directly corresponding Hamiltonian operation-based eigenstates.  & 9) Will tend to work to generate a significant scalar magnitude of the cohomological-based eigenindices, that are of the topological stratum that is to be Yukawa to the path of the resultant Fourier-based propagated Hamiltonian operand.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Degenerative Cohomologies

Any one said given arbitrary degenerative cohomology, will tend to be exclusively of a Doubolt nature.  Such a respective said general tense of a degenerative cohomological index, will tend to be both of an attenuated pulsation, as well as the condition that such a general genus of a cohomological metric -- will always tend to bear metrical-based Chern-Simons singularities, in the form of the directly corresponding complex roots, that are to be correlative to the corresponding perturbation in the Fourier translation of those eigenstates -- that have to had here just increased in the scalar magnitude of their metrical instability, over time.  Fourier-based transformations, that are to involve a degenerative cohomological index -- will often tend to also work to bear what would here be the presence of Lagrangian-based Chern-Simons singularities, that will here have more to do with an assymptotic approximation to what would otherwise be of a Rham-based cohomological index, than if the resultant Lagrangian-based path were to instead to be of a hermitian-based nature -- due to the general Ward-Cauchy-based condition, that such a degeneration will often tend to bear such a dampening of the metrical-based singularities -- that will as well help at working to cause the formation of a set of potential complex Lagrangian-based roots, via the resultant space-time translation that would here be imbued upon the holonomic substrate of the correlative Hamiltonian operand, that would thus be potentially formed over time, to where such Njenhuis singularities are here to be formed by the resultant Ward-Supplemental motion of the external core-field-density-related eigenindices of the respective Calabi-based manifold -- that had just been translated into a directly corresponding antiholomorphic Kahler condition, upon what would have initially been the presence of a relatively Njenhuis topological substrate of Hamiltonian operand space-time-fabric phenomenology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Ghost-Inhibitors And Orbifold Eigensets

Let us initially consider a given arbitrary orbifold eigenset, that is to here be moving in what may be termed of as the relatively forward-holomorphic direction.  Let us next, consider that the said orbifold eigenset is to work to form a cohomological mappable-tracing -- over time.  Let us next consider the condition -- that those norm-state-projections, that operate in so as to work to form the cohomological mappable-tracing of the physical memory as to the what, where, and how the here respective given arbitrary orbifold eigenset is to have differentiated in a basically Fourier-based manner over a successive series of group-related instantons -- are to tend to be certain of those proximal localized relatively forward-holomorphic norm-state-projections, that have either moved into and/or have been moved in, the relatively immediate path of the overall Hamiltonian-based momentum of the so-stated orbifold eigenset.  Let us next, consider that there is to soon be certain of what may here be termed of as the relatively reverse-holomorphic bearing norm-state-projections, -- that are to here act in a Fourier-based manner -- in so as to work to form a Rayleigh scattering of the initially stated cohomological mappable-tracing of the said orbifold eigenset, over a relatively transient period of time.  Those norm-state-projections that are to here act in so as to annharmonically scatter the initially so-eluded-to harmonically ordered ghost-based indices of the said cohomological mappable tracing, that is to here be directly corresponding to the initially formed physical memory of the said orbifold eigenset -- may here be described of as being of the general nature of what may be termed of as ghost-based inhibitors.  If that wave-tug that any of such ghost-based inhibitors, that is to here be acting in so as to work to form a Rayleigh scattering of a correlative cohomological stratum -- is to work to push upon the correlative orbifold eigenset in what would here be the respective relatively reverse-holomorphic direction as well, then this general genus of a wave-tug/wave-push -- will then tend to at least work -- in so as to help to slow down the directly corresponding orbifold eigenset of such a case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some Stough As To Doubolt Versus Rham Cohomologies

The general condition of there being the presence of a Rham cohomology, is always a temporary Ward-Caucy-based condition.  Any given arbitrary orbifold eigenset, is going to eventually be tugged into either a Real Reimmanian-based and/or a Njenhuis-based Chern-Simons condition -- that will work to form an antiholomorphic Kahler-based condition, -- of which will form the general ensuing Ward-Caucy-based condition of there then being the proximal localized state of the Kahler-Metric, that will then be implemented upon the said respective given arbitrary orbifold eigenset, in a Yukawa-based manner, over time.  Any "time" that there is the presence of an antiholomorphic Kahler condition -- from the Ward-Caucy-based Laplacian state that is to here exist, from "right before" until "right after" the Fourier-related activity of any respective given arbitrary orbifold eigenset, that is to proceed to go through what is to here involve the presence of a Chern-Simons singularity -- that is to reverse the general directoral-based flow of the said orbifold eigenset, -- this will happen to where there is to then be such a perturbation of the cohomology of such an orbifold eigenset, from initially being of a Rham-based cohomology, to then being of a Doubolt-based cohomology.  Such a general tendency of a directoral-based perturbation, will tend to always work to eventually be Yukawa upon any respective given arbitrary orbifold eigenset, over time.  So, superstrings tend to exist under the Ward-Caucy-based conditions -- of what will here tend to be the existence of what may be called of as the mappable tracings of Doubolt cohomologies.  The state of Rham-based cohomologies will always tend to be temporary.

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclical Reverberations And Reference Frames, Part Two

Let us initially consider a given arbitrary orbifold eigenset, that works to be of a cyclical nature -- that works to reverberate via a relatively rectangular Lagrangian-based path, over time.  Let us say, once again, that such a cyclical reverberation is one that involves the tendency of working to bear a cyclical permutative tense -- to where, seeing that, over the course of each ensuing iteration of such a so-eluded-to reverberation, the relative respective Ward-Caucy-based angling of the said given arbitrary respective orbifold eigenset is mildly perturbative -- in so that the directly corresponding Stoke's-based depth that is here to be involved, will alter when in terms of the directoral-based tense of its correlative angular momentum-based indices, to where, at the so-eluded-to internal-based reference frame, the tense of such a cyclical permutative rectangular reverberation is mildly altered in its specific cohomological-based mappable tracing -- per each succeeding iteration of such a said general genus of this form of a reverberation.  Let us next say that the general motion of the spin-orbital-based momentum, that is to here be directly correlative to the wave-tug/wave-push of the Hamiltonian-based operation of the said orbifold eigenset, is to here be considered of as tending to go in the relative Njenhuis-to-forward-holomorphic directoral wave-based flow -- over the course of the correlative group-metric in which such a said orbifold eigenset is to be in the course of such a so-stated reverberation-based metrical eigenbase of a Fourier-related translation over time.  Next, let's say that -- from an external tense of a reference frame -- that the so-stated reverberating orbifold eigenset of such a case, is to, as well, be oscillating from being pushed initially into the relative norm-to-forward-holomorphic direction into then being pushed into the relative norm-to-reverse-holomorphic direction, over time -- to where such a so-eluded-to orbifold eigenset, from a given arbitrary external vantage-point, is to be oscillating in such a manner, as may be relatively considered of as oscillating in such a way that goes from moving relatively "up," to then moving relatively "downward" -- if the torsioning of the more planar-based kinematic context, that is of the reverberation of the said orbifold eigenset, is one that may be then considered of as to be said to be torquing to the relative "left"-related direction.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Energy Density And Cohomologies, Part Two

Let us here consider two different covariant given arbitrary orbifold eigensets, that are of the same Ward-Caucy mass-based density, over the course of one respective given arbitrary group-metric.  Let us next say, that one of such orbifold eigensets is moving at a faster relative velocity -- in a terrestrial-based manner -- than the other said orbifold eigenset, over the self-same said group-metric.  The faster of the two said orbifold eigensets, will tend to eliminate its cohomologies at a faster rate than the slower of the two said orbifold eigensets.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Energy Density And Cohomologies, Part One

Let us take into consideration two different covariant given arbitrary orbifold eigensets.  Both of such orbifold eigensets are moving at the same velocity, relative to one another -- over the group-metric that is to be considered here.  Both of such orbifold eigensets are, as well, of the same relative Ward-Caucy-based "volume," in this respective given arbitrary case scenario.  One of these so-stated orbifold eigensets has a greater mass than the other of such orbifold eigensets, over the course of the said group-metric.  The orbifold eigenset that is to here have a greater mass-based density (more mass per relative Ward-Caucy-based "volume"), will tend to work to bear a Rayleigh scattering of its ghosts -- that will tend to eliminate its directly corresponding cohomologies, in a quicker manner -- than the orbifold eigenset that is of a lower mass-based density.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Norm-State-Projections And Cohomologies

In general -- a Reimman scattering that works to form ghost-based indices, is caused by the relatively forward-holomorphic interaction of norm-state projections with the holonomic substrate of superstrings, in a Yukawa-based manner that is not necessarily of a Gliosis-based manner, while, a Rayleigh scattering of ghost-based indices -- is caused by the relatively reverse-holomorphic interaction of norm-state-projections with a set of ghost-based indices that have already been formed in the substringular, in a Gliosis-based manner.  The formation of proximal localized ghost-based indices, or, in other words, the formation of proximal localized cohomologies, is formed by a general genus of a Reimman-based scattering.  The elimination of proximal localized  ghost-based indices, or, in other words, the elimination of proximal localized cohomologies, is formed by a general genus of a Rayleigh-based scattering.  The activity of the ordering of ghost-based indices, works to form the Laplacian-based condition of the correlative respective adjacent eigenindices, that work to form the eigenmembers of the said cohomologies to bear an even chirality.  The activity of the Fourier-based activity that works to form the relative disordering of ghost-based indices, works to form the Laplacian-basesd condition of the correlative respective adjacent eigenindices that work to form the eigenmembers of the here entropic state of the so-eluded-to cohomology, that is to here be in the process of being eliminated, to bear an odd chirality.  The so-stated Reimman scattering, is a genus of a harmonic perturbation, -- in which the correlative eigenindices of the then formed ghost-based pattern are, in the process, to be integrated in so as to work to form a cohomological mappable tracing.  Yet, the so-stated Rayleigh scattering, is a genus of an enharmonic perturbation, -- in which the correlative eigenindicies of the then eliminated ghost-based pattern are, in the process, to be broken-down in to a set of relatively unordered eigenstates, as the so-eluded-to cohomological mappable tracing is to here be spontaneously dissolved.  This said general genus of the tendency as to the ordering of first-ordered point particles into at tense of a physical memory of superstrings, via the multiplicit interaction of discrete energy quanta working to bear a viable Yukawa-based interaction upon relatively forward-holomorphic norm-state-projections, may here be considered as a generative process, while the said general genus of the tendency as to the increasing disorder of first-ordered point particles into a tense of an elimination of the physical memory of superstrings, via the multiplicit interaction of relatively reverse-holomorphic norm-state-projections upon a cohomological stratum, may here be considered as a degenerative process.  I will continue with the suspense later!  To Be Continued!  Sincerely,Sam Roach.

Reason For Transmission of Scattered Cohomologies

As I have said before, the residue of the multiplicit scattered GSO cohomologies has the tendency of being pulled off of the multiplicit relative Real Reimmanian Plane into the multiplicit relative Njenhuis Plane -- as the residue of the multiplicit scattered Neilson-Kollosh cohomologies have the tendency of being pulled off of the multiplicit relative Njenhuis Plane into the multiplicit relative Real Reimmanian Plane.  This tendency is on account of the following Laplacian-based set of  conditions:  The genus of the overall general norm-state-projections that are of the multiplicit relative Real Reimmanian Plane work to bear a harmonic even parity with the genus of the overall general norm-state-projections that are off of the multiplicit relative Njenhuis Plane -- in such a manner in so as to bear a multiplicit condition of their being a tendency of the Laplacian-based existence of a mean Lagrangian-based path that is of an even chirality, -- towards each enharmonically scattered GSO ghost that has been broken down by a Rayleigh scattering, and, there is a tendency of the Laplacian-based existence of a mean Lagrangian-based path that is of an even chirality, -- toward each enharmonically scattered Neilson-Kollosh ghost that has been broken down by a Rayleigh scattering. The condition, that, for every action -- there is an equal and opposite reaction -- happening in the opposite direction from the first said action, -- works to elude to the condition in which the antichiral parity of the adjacent eigenmembers of one set of cohomological indices that have just undergone a Rayleigh-based scattering of ghost anomalies, -- will work to cause the then existent condition of a proximal local chiral parity that bears a Hamiltonian operand that works to bear a clear path that is of a mean Lagrangian, to cause the pre-existent condition that the substringular tends to work in so to move in the direction of optimum rest, to cause a wave-tug/wave-pull of what may be thought of as the so-eluded-to just scattered ghost-based indices to recycle in the manner that I have just described of earlier in this post.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Interaction Of Certain Indices

The interaction of  first, second, and third-ordered Schwinger-Indices, works to help in the process of the delineation of the ensuing delineations of discrete energy quanta.  So, that fabric -- that may be here described of as "gravitational-waves," -- works to help in the process of the relative placement, in terms of the pull and push of constituent substringular eigenmembers, of the individually taken discrete quanta of energy, in an interdependent retrospect of each of such eigenmembers towards and amongst each other, over a sequential series of the iterations of group-related instantons.  This is in terms of both the Laplacian-based interactions and the Fourier-based interactions of the so-stated first, second, and the third-ordered Schwinger-Indices amongst each other, over time.  This is in part due to the condition -- that the resultant physical interaction of those vibrational oscillations that are utilized in so as to cause there to be an interaction between discrete energy quanta and the existence and the activity of both gravitons and gravitinos, works to help in the sequential series of the relative covariant distribution of those so-stated discrete energy quanta.  This is in part due to the relative pull of the centralized knotting of the so-eluded-to Rarita Structure eigenstates.  Here's why.  Discrete energy quanta work to form GSO cohomologies.  Such GSO cohomologies are spontaneously broken down into residue that is forced off of the relative Real Reimmanian Plane.  This said residue comes together in so as to work to form what may be termed of as both gravitons and gravitinos.  These just mentioned gravitons and gravitinos form Neilson-Kollosh cohomologies.  Such Neilson-Kollosh cohomologies are spontaneously broken down into residue that is fed back into the initially so-stated Real Reimmanian Plane.  This just mentioned re-aquired residue by the Real Reimmanian Plane, is then in the form of norm-state-projections.  These norm-state-projections that are re-aquired, then act as the holonomic substrate-based template of the multiplicit general entity that discrete quanta of energy act upon -- in so as to form the ensuing GSO cohomologies.  Cohomologies are due to the existence of proximal local point commutators.  Point commutators are needed, in order for both discrete energy quanta and gravitational particles to have a viable venue for constant motion that is quick enough for the activity of the generally unnoticed duration of Ultimon Flow.
To Be Continued!  Samuel David Roach.

An Elaboration As To My Last Post

Let us here, first consider the physical situation of which I ended-up mentioning in my last post.  One will here have a diamond-like shape, that is situated right above an arbitrary horizonal axis -- this just mentioned axis of which is here to be considered arbitrarily as the x axis.  Let us now say that this said diamond-like shape were to have, as well, a trivially isomorphic diamond-like shape -- that is to be situated just below the first so-stated diamond-like shape, on the negative quadrant of what may be termed here as an arbitrary y axis.  Now, let us say -- that one were to bear a Laplacian-based shift of the two said entities that have been mentioned here, as bearing a diamond-like shape -- to where the so-stated relative top diamond-like configuration that is situated in the positive y quadrants, will bear an integration of indices, that are pulled both around and "into the page" from its initial flat-space-like initial configuration, -- while there will, simultaneously, from the vantage-point of the center of the so-eluded-to coniaxion, be the condition of the so-stated relative bottom diamond-like configuration -- that is situated in the negative y quadrants, working to bear an integration of indices, that are pulled both around and "out of the page" from its initial flat-space-like initial configuration.    The annulus that I am about to mention will act as the so-eluded-to "washer." As I have here eluded-to -- the volume-based region that goes Into the page may be considered here as the region for a relative positive z-based region, while, the volume-based region that goes Out of the page may be considered here as the region for a relative negative z-based axial region.  Besides both the x axis, the y axis, and the z axis -- three other spatially-based coniaxial directorals (l hat, m hat, and n hat, arbitrarily) are to be integrated into the coming together of the Laplacian-based picture of this respective given arbitrary situation.  The last two of such so-eluded-to spatially-based coniaxial directorals (directly associated here arbitrarily to m hat and n hat, in this given arbitrary case), are of a curled-up nature.  Consider this spatial integration of indices -- that are integrated as I have suggested -- to work at forming a toroidal-based entity.  The annulus of the toroid may be considered here, to be bearing in a relative holomorphic-based manner -- as is going from just outside of the relatively antiholomorphic end of the very center of the said toroid, on the i hat directoral positioning -- that would here tend to be centered as is going right from a spot proximal to the x axis -- while then going, in a holomorphic and a relatively left-moving manner, until it works to exit the Ward-Neumman bounds of the holonomic substrate of the entity of the so-stated toroidal-based shape, that is of this said given arbitrary Laplacian-based example.  Since this particular example works to include the conical-based edges of the so-stated diamond-like shapes, that I have here mentioned -- the so-stated toroidal-based  structure that I have just mentioned as forming, will be as a theoretical genus of a toroidal-based cohomology, that works to bear certain conical cyclic permutations -- that may be extrapolated in a Laplacian-based manner.  This would be similar but different to the GSO type of a ghost anomaly -- that may be formed by the physical memory of a superstring of a mass-bearing eigenmember, that is from the Ward-Caucy bounds of an electron -- that would be probable as existing in a condition of a respective given arbitrary tense of a Majorana-Weyl-Invariance-Mode -- over a directly corresponding Fourier-Transformation, in which such a superstring that is differentiating in a kinematic manner, over time, is undergoing the general process of conformal invariance.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

Part Two of Session Four of Course 19 -- The Klein Bottle and Orbifold Differentiation

The interior of the cohomological-based pattern that is formed by any respective given arbitrary Klein Bottle --is like a limited contorted "toroid" that contains both forward-holomormphic and reverse-holomorphic-based norm-states.  These multivarious norm-states of which tend to differentiate in a Fourier-based manner that is of a relatively harmonic manner, over time.  Yet, when the interaction of the norm-states, that exist from within the Ward-Neumman boundaries of the interior of the holonomic substrate of any respective given arbitrary Klein Bottle eigenstate, act in so as to differentiate kinematically in a relatively rigorous  annharmonic manner over time, the cohomological-based pattern that is formed by both the existence and the activity of the so-stated given arbitrary Klein Bottle eigenstate, eventually is perturbated into a Rayleigh-based scattering of those norm-state indices that had previously existed within the Ward-Caucy bounds of the said Kliein Bottle eigenstate.  This just mentioned general genus of activity of which may often cause the composition of the specific respective given arbitrary Klein Bottle eigenstate to be indistinguishably replaced, via those immediately surrounding eigenindices that may here work to both antiderivate the previous Klein Bottle eigenstate, while yet re-constructing a newly established Klein Bottle-based construction -- in a manner that works to bear a tendency of an indistinguishable difference.  This just-eluded-to recycling-based tendency of a "worn-out" Klein Bottle eigenstate into a newly established so-stated Klein Bottle eigenstate, works to conform to the overall tendency -- that is directly affiliated with the recycling of norm-state-projections, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.