Extra Stuff About Cyclic Permutations

Let us initially consider a phenomenology that goes through a state of a Fourier-related activity,  that is repeated over and over again -- yet, to where such a so-eluded-to general tendency of a cycle is to work to bear one or more slight changes, over the course of the iterations of each of such a so-eluded-to process or processes of cyclical states.  If the pattern of the cyclical changes, is never symmetrically completed -- in such a manner to where the overall pattern of such a general condition of a cycle is not equivalently iterative, then, such a cyclical pattern is said to diverge.  Yet, if the pattern of the cyclical changes, is to instead, be symmetrically completed in such a manner -- to where the overall pattern of such a general condition of a cycle is to be equivalently iterative, then, such a cyclical pattern is said to converge.  For instance -- let us consider an elliptical pattern, that is cyclical in permutation.  Let us say -- within a here considered tendency of time constraints -- that one physical phenomenology is to orbit around another physical phenomenology, in such a manner to where the tense of such an orbit, per each adjacent iteration of orbit, is to be slightly different is its precise Lagrangian-based contour, -- yet, let us say that in this given arbitrary case scenario, that after one thousand iterations of such an elliptical tendency of orbit, that the whole overall general pattern of a cyclical tendency is to be repeated in the exact same manner again, to where the second set of one thousand iterations of such an elliptical orbital-based tendency is to be exactly the same as the first set of one thousand iterations of such an elliptical orbital-based tendency.  In this just mentioned tense of a condition of cyclical permutation, the cycle is to here be symmetrical in its behavior, and thus, such a so-stated tense of a condition of cyclical permutation is to here be convergent, -- at least over the course of the first two thousand iterations of such a pattern of a cyclical-based permutation-related tense of elliptical orbit.  Furthermore, there are three general genre of Fourier-related cyclical permutations -- of which may sometimes be combined. There are Lagrangian-based cyclical-based permutations, and/or there are metrical-based cyclical permutations, and/or there are contour-based cyclical-based permutations.  I will later discuss what is meant by a Laplacian-related state of conditions, that would work to bear a tense of cyclical permutation.

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

Ghost-Inhibitors And Eigenstates, Next

If the force of any given arbitrary ghost-inhibitor, that works to bear a relatively reverse-holomorphic wave-tug/wave-push upon any respective given arbitrary orbifold eigenset -- is to ease in the scalar magnitude of its Hamiltonian operation that it is to bear, over a successive series of group-related instantons, then, this general tendency of a relaxation of a relatively reverse-holomorphic-based wave-tug/wave-push -- will then tend to work to allow for an acceleration of the Hamiltonian-based pulse of the Fourier-related motion of the here respective given arbitrary orbifold eigenset.  Since the so-stated orbifold eigenset is to here be undergoing a tendency of a Noether-based flow over time, -- then, this general tendency of an accelerated scalar magnitude of either the tranversal and/or of the radial motion of the said eigenset, will then tend to work here in so as to loosen the proximal localized Majorana-Weyl-Invariance that is to here be directly corresponding to the covariance that is to be affiliated with the Hamiltonian momentum of the kinematic flow of the so-eluded-to set of superstrings that are to here operate in so as to perform one specific function.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Ghost-Inhibitors And Orbifold Eigensets, Part Two

If a proximal localized state of relatively reverse-holomorphic norm-state-projections, is to work to act in a reverse-holomorphic-based manner upon a given arbitrary respective orbifold eigenset -- over a successive series of group-related instantons, -- to where such a general genus of activity is to here to work to "slow down" the theoretical rate of the said orbifold eigenset, yet to where the so-stated orbifold eigenset is to here consistently maintain a tense of Noether Flow, then, such a Fourier-related general genus of a slowing rate of a set of cohesive superstrings, is to work at actually acting in so as to tighten the relative tense of the Majorana-Weyl-Invariance of the directly corresponding kimematic motion of the correlative orbifold eigenset, over time.
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.

Again As To Adjacent Light-Cone-Gauge Eigenstates

The more Yukawa that the Kahler-Metric is, upon the topological substrate of any respective given arbitrary bosonic superstring of discrete energy permittivity  -- the more that the holomorphically adjacent second-ordered light-cone-gauge eigenstates, as taken to just to the counterclockwise positioning towards each other, as taken in a Laplacian-based manner -- to where the more that there will then tend to be the bearing of  those correlative gauge-boson eigenstates, that will then be angled in an assymetrical manner, during the course of any respective given arbitrary iteration of BRST.  And as said before, -- the more assymetric that the holomorphically adjacent gauge-boson eigenstates will tend to be distributed as, in a Laplacian-based manner during BRST, -- the more harmonic that the resultant Schwinger-Indices that will then be formed, by the "plucking" of the correlative second-ordered light-cone-gauge eigenstates by the correlative gauge-boson eigenstates, as this will tend to consequently be.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Adjacent Light-Cone-Gauge Eigenstates In Bosonic Strings

Let us initially take one given arbitrary bosonic superstring of discrete energy permittivity.  Let us next consider what is to here exist, when one is to be at the vantage-point of looking, in a Laplacian-based manner, towards the relative holomorphic direction -- by way of to here consider the so-eluded-to Laplacian-based condition of the directly corresponding light-cone-gauge eigenstate.  Next, consider, arbitrarily, the Laplacian-based condition of the delineation-based displacement of the said correlative light-cone-gauge eigenstate -- during one respective given arbitrary iteration of BRST.  In this particular case, consider the here relative counerclockwise direction that is to be considered in this given arbitrary Laplacian-based comparison, as to be considered here as the relative forward-holomorphic direction.  Next, consider a given arbitrary comparison of two second-ordered light-cone-gauge eigenstates -- the here compared eigenstate of the light-cone-gauge is to be considered here as just to the immediate or just to the counterclockwise positioning to the initially so-eluded-to second-ordered light-cone-gauge eigenstate.  The more assymetric that the relative delineatory-based angling of the one of such second-ordered light-cone-gauge eigenstates is to the other, during the so-eluded-to iteration of BRST -- the more that the resultant Schwinger-Indices that are to be formed by such gauge-bosons, is to then tend to be of a harmonic nature -- as such so-eluded-to third-ordered Schwinger-Indices are to then ensue as such, through the correlative Rarita Structure.  I will continue with the suspense later!  To Be Continued!
Sam Roach.

Ensuing Delineations of Superstrings And Gauge-Bosons

In any individual given arbitrary case, that is of one set of gauge-bosons and their directly corresponding discrete quantum of energy, -- both the flow of the ensuing delineations of the directly corresponding discrete energy quantum, as well as the flow of the individually taken scalar amplitude of the directly corresponding Polyakov Action eigenstates, as well as whether or not the directly corresponding superstring is to be orientable or not, -- are some characteristics that work to influence the condition, as to the manner of the Ward-Caucy-based angling of those gauge-boson eigenstates -- that are to here be directly pertinent to certain of both the Laplacian and the Fourier-based conditions, that will here work to influence both the manner and the genus of the ensuing Schwinger-Indices, that will then form by the topological stratum of the so-eluded-to discrete quantum of energy, over the course of the ensuing iteration of group-related instanton.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

More As To Heterotic Strings And Dimensionality

Gauge-Bosons -- over the course of any given arbitrary respective iteration of BRST -- work to bear a general Laplacian-based condition, that is of the general state of initially being placed, in so as to ensue as to work at "plucking" the directly corresponding respective second-ordered light-cone-gauge eigenstates, in such a manner in so as to be distributed in such a delineaetion, in so as to work to bear a best-fit-curve to then being able to form the needed Schwinger-Indices, with the directly pertinent Ward-Caucy-based conditions that will here work to bear an optimum annharmonic pulsation with any immediately adjacent gauge-bosons that are to, as well, be able to form Schwinger-Indices -- with the physical condition of working here in a state of maximum rest-based capacity.  This will then mean, that the respective given arbitrary gauge-bosons -- that are to here be directly affiliated with the Fourier-based translation of any of one given arbitrary respective iteration of BRST -- will then tend to be angled in a potential assortment, that may here work to bear a multifarious litany of Ward-Caucy-based angles.  More later!
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Heterotic Superstrings And Dimensionality

Gauge-Bosons, or E(6)XE(6) superstrings, are the heterotic strings -- that act in so as to work to "pluck" the respective second-ordered light-cone-gauge eigenstates -- in so as to work to form what may be termed of here as Schwinger-Indices.  The Laplacian-based existence of these said E(6)XE(6) strings, works, to an extent, in so as to bring a certain degree or manner of the needed added spatial dimensionality, to the internal Ward-Caucy-based physical bounds of orbifold eigensets.  So, the existence of the those heterotic superstrings that are named of as gauge-bosons -- may be alagorical or metaphorical, to what may be thought of as the reverse-fractal-based tense of "microtubules" in living cells a much higher level.  At a much more macroscopic tense from the substringular -- microtublules act in so as to add additional spatial dimensionality to the existence of  living cells.  Furthermore, those heterotic superstrings that may be termed of as E(8)XE(8) strings, -- act in so as to work at supporting the external Ward-Caucy-based physical bounds of the spatial dimensionality of orbifold eigensets, -- in so as to work to help in the structural continuity of those sets of superstrings, that operate in so as to perform a given arbitrary specific function.  In this said tense, -- those superstrings, that may be termed of as E(8)XE(8) strings -- act in a manner that may be alagorical or metaphorical to the reverse-fractal of the much more macroscopic condition of the microtubules, of which would exist a a much larger level.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Kahler-Metric And Yukawa Coupling

A phenomenology is Gliosis upon another phenomenology, when there is a direct topological contact, that will work here to bear a borne tangency at the relative Poincare level.  A phenomenology is Yukawa upon another phenomenology, when there is either a non-direct or a direct topological contact, that is not necessarily a borne tangency at the relative Poincare level.  Not every superstring is always in a Gliosis-based relationship with the general Ward-Caucy-based condition of the Kahler-Metric, all of the time, yet, -- every superstring is always going to tend to be in a Yukawa-based relationship with the general Ward-Caucy-based condition of the Kahler-Metric, all of the time.  This is due to the condition, that individually taken superstrings do not need to literally be constantly in the process of re-attaining there fractals of discrete energy quanta with no relent, yet, the process of that general-based Fourier-related activity of the re-attaining of the fractals of discrete energy quanta are to be happening "all over the place" in the substringular "all of the time."  The higher the scalar amplitude is of the Yukawa-related wave-tug -- that is to be enacted upon any respective given arbitrary discrete energy quantum by the activity of the Kahler-Metric, the sooner that there is to be that general Fourier-based activity of the said respective discrete energy quantum, to be undergoing the processes of working to re-attain the fractals of its discrete energy.  Once that such a Yukawa-based coupling is to then be of a Gliosis-based nature, then, this so-eluded-to Kahler-Metric-related eigenstate is to then be eminent.  Therefore, there is always the presence of the Kahler-Metric upon the holonomic substrate of the multiplicit array of substringular  eigenstates.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

More As To Real Versus Njenhuis Doubolt Cohomologies

The lower that the genus is, that is to here be directly associated with the Fourier-based activity of a Rham-based cohomology -- that is to then be formed into a Doubolt-based cohomology -- via the kinematic-based formation of a relatively low genus of an eigenstate of a Chern-Simons singularity, the more that there tends to be the proximal local Ward-Caucy-based condition of the state of homotopic torsional eigenindices, -- that are to here to bear Real Reimmanian or euclidean roots, instead of then working to bear Njenhuis or complex roots.  Furthermore -- the higher that the genus is, that is to here be directly associated with the Fourier-based activity of a Rham-based cohomology -- that is to then be formed into a Doubolt-based cohomology -- via the kinematic-based formation of a relatively high genus of an eigenstate of a  Chern-Simons singularity, the more that there tends to be the proximal local Ward-Caucy-based condition of the state of homotopic torsional eigenindices, -- that are to here bear Njenhuis or complex roots, instead of then working to bear Real Reimmanian or euclidean roots.  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.

As To Spaces From Different Universal Settings

Let us here consider two different orbifold eigensets -- one orbifold eigenset of which is to be from one universe, while the other orbifold eigenset is to be from another universe.  These two different given arbitrary respective orbifold eigensets, would then work to belong to two different respective universal settings.  This would then mean, that each of the two said different orbifold eigensets -- would here act as two different spaces -- that would then be of two different universal settings.  This would then mean, that each of the two said eigensets, is to not be of a Real Reimmanian nature towards the other of the two said orbifold eigensets.  This would then, as well, mean, that each of the two said eigensets is to be of a Njenhuis-based nature towards the other of the two said eigensets.  Yet, if there were to be a kinematic group-attractor, that is to be Yukawa upon both of the two said orbifold eigensets -- that is to work as a holonomic substrate that is to be kinematic here upon the so-eluded-to proximal locus, as a physically taken eigenbase -- in relation to what would here be a relative Fourier-initiated Gaussian-based assortment of one of the two so-stated orbifold eigensets when this is in relation to the other of the two so-stated orbifold eigensets, then, this general genus of a Fourier-initiated Gaussian-based assortment, may often act in such a manner in so as to work to cause -- what would here be the equivalent of a physically-based Li-Algebra-related eigenbase, in so as to be able to help in so as to make both of the two so-stated orbifold eigensets, to then be of the same universal setting, over a successive series of group-related instantons -- that would take part in such a so-eluded-to group-metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Next As To Kahler Conditions

When the earlier mentioned orbifold eigenset is to, at a relatively external reference frame, reverberate back-and-forth from going into the relative "down" or in the relative norm-to-reverse-holomorphic direction into then going into the relative "up" or in the relative norm-to-forward-holomorphic direction and so-on, indefinitely, -- this reiterative reversal in a tense of the tensoric-based relative holomorphic direction in which the respective given arbitrary orbifold eigenset is to be going -- will work to form one general antiholomorphic Kahler condition, per each ensuing so-eluded-to said reversal in the holomorphic tendency of the so-stated orbifold eigenset.  Any antiholomorphic Kahler condition, will tend to form the ensuing activity of what may here be termed of as an eigenstate of the Kahler-Metric.  Any antiholomorphic Kahler condition will tend to initiate the Fourier-based activity of what may be termed of here as an eigenstate of the Wick Action.  Any said Wick Action eigenstate will tend to act upon an eigenstate of the Landau-Gisner Action.  The said Landau-Gisner Action will then tend to act, via the Fischler-Suskind Mechanism, in so as to act in so as to place a wave-tug-based leveraging upon an eigenstate of the holonomic substrate of a Klein Bottle eigenstate -- in so as to work at pushing a proximal localized Higgs Boson eigenstate into that activity of the said respective given arbitrary Kahler-Metric eigenstate, that is most Yukawa to what I term of as the activity of a Gaussian Transformation group-metric.  Such a said Gaussian Tranformation, acts, in a Fourier-based manner, in so as to both work at helping superstrings and Fadeev-Popov-Trace eigenstates to re-attain their fractals of that respective discrete energy permittivity and discrete energy impedance that are necessary, in so as to help in the continued existence of discrete energy quanta, as well as to work at freeing-up room in the substringular -- so that the Fourier-based processes of the substringular may be able to both persist and exist.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Next As To Reverberations

Let us here consider a different general case scenario, as to a reverberating orbifold eigenset -- that is to here, circulate in a basically rectangular Lagrangian-based path, at what is to will here be at a relatively internal-based reference frame, over time.  Let us next say that the here respective given arbitrary orbifold eigenset of such a respective case scenario, is to initially move in a relatively "straight" manner -- in such a way, as to where such a relatively "straight" direction is to here be considered as to be going in what may be here called of as the respective holomorphic direction.  Some time later, the so-stated orbifold eigenset is to turn towards the relative right or in the relative Njenhuis-to-reverse-holomorphic direction.  Let us next say, that some time later -- the said orbifold eigenset is to turn to the relative "right" as such, -- at an initial total of four times -- in so as to be reverberating in the earlier stated rectangular Lagrangian-based path.  Let us now say, that, upon the fourth so-eluded-to completion of such a so-stated "right"-based turn of the said orbifold eigenset -- there is to be a mild perturbation or alteration in the Stoke's-based angling of the directoral-based pulsation of the so-stated orbifold eigenset -- to where the said eigenset is to here be starting in the course of a rectangular reveberation, that is cyclical in permutation, over time.  Let us next say that such a just started iterative course of a rectangular-based reverberation, is to here be reiterative, over a successive series of instantons -- at a relatively internal reference frame.  At a relatively more external reference frame --  the so-stated orbifold egienset is to reverberate from going into the relative "down" or reverse-norm-to-holomorphic direction, into subsequently at a future metric -- going into the relative "up" or forward-norm-to-holomorphic direction.  In this given arbitrary respective case scenario -- that group-attractor, that is to help in working to cause the said relatively "down" motion, is to act in a chiral-based manner upon the said orbifold eigenset, whereas that group-attractor, that is to help in working to cause the said relatively "up" motion, is to act in an antichiral-based manner upon the said orbifold eigenset.  This latter mentioned difference from what was said as to happen in earlier posts, is due to the condition, that, at a relatively internal reference frame of this here differing case scenario -- the respective orbifold eigenset is to bear a tendency of a relatively "right" turning mode instead of bearing a tendency of a relatively "left" turning mode.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Alternative Kahler Conditions Part Two

From the immediately prior post, as the left-tending orbifold eigenset is to just proceed from going into the relative "up" direction into then going into the relative "down" direction -- certain superstrings that are to here be Yukawa to those group-attractors that had worked to help in causing this general genus of Fourier-based activity to happen, will then be directly involved with the course of a respective Kahler-Metric eigenstate.  Furthermore -- as the same left-tending orbifold eigenset is to just proceed from going into the relative "down" direction into then going into the relative "up" direction -- certain superstrings that are here to be Yukawa to those group-attractors that had worked to help in causing this general genus of Fourier-based activity to happen, will then be directly involved with the course of another respective Kahler-Metric eigenstate.  Such increments of the Kahler-Metric, will be proximal localized to the general cite at which the tensoric so-stated relative "up-and-down" motion is to here be happening at -- as a gauge-metrical-based Hamiltonian operation, over a sequential series of group-related instantons.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

Alternative Kahler Conditions

Let us initially consider one given arbitrary orbifold eigenset, that is moving in a reverberation -- via a relatively rectangular Lagrangian-based path, that moves at its corners towards the relative left -- as the said respective orbifold eigenset will work here to keep iterating in this case scenario, as a holonomic substrate that acts in a manner that is cyclical as a Hamiltonian operator that behaves in a permutative tense, per each succeeding individually taken cycle of such a so-eluded-to reverberation.  Let us as well, consider that -- at an external reference frame -- the self-same orbifold eigenset  is to reverberate from going into the relative "up" directorial-based direction towards then going into the relative "down" directorial-based direction, as a tensor that is behaving as such a so-eluded-to metrical-gauge-based Hamiltonian operator, over the course of the same group-metric in which such a said eigenset is to be moving via an iterative entity of reverberation, that cycles to the relative left at each succeeding corner of its Fourier-based flow, at what would here be more of an internal-based reference frame.  As eluded-to before in earlier posts, that group-attractor that is most Yukawa to the course of action that is here to be utilized, in so as to work to allow for the just mentioned "up-and-down" tensoric reverberation, acts in a chiral-based manner -- in so as to help in working to allow for the said "upward" motion of the so-stated orbifold eigenset, whereas, that self-same group-attractor that is most Yukawa to the course of action that is here to be utilized, in so as to work to allow for the just mentioned "up-and-down" tensoric reverberation, acts in an antichiral-based manner -- in so as to help in working to allow for the said "downward" motion of the said orbifold eigenset.  Again as eluded-to before, the so-stated relative chiral tendency will tend to work to form torsional eigenindices, that bear  singularities that are of Real Reimmanian roots, while the so-stated relative antichiral tendency will tend to work to form torsional eigenindices, that bear  complex roots.  This alteration of the so-stated orbifold eigenset, from first going into the relative norm-to-forward-holomorphic direction, while then going into the relative norm-to-reverse-holomorphic direction -- will tend to work to form an antiholomorphic Kahler condition, that is proximal localized to certain superstrings that are Yukawa to that Ward-Caucy-based environment -- that is just external to the immediate internal reference frame of the left-tending reverberative flow of the said orbifold eigenset of this given arbitrary respective case.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

The Fourth Part Of Cyclical Reverberations And Reference Frames

Let us initially say that one is dealing with the situation which is as before -- to where there is a respective given arbitrary orbifold eigenset, that is to here be reverberating in a cycle -- in which the said orbifold eigenset is to be moving at the so-eluded-to relatively internal reference frame, via a relatively rectangular Lagrangian-based path that is cyclical permutative -- in such a manner to where it works here in so as to bear a Fourier-based turning at each corner, to the relative left or Njenhuis-to-forward-holomorphic direction, to where, from a relatively external reference frame, the so-stated set of superstrings that are here operating in so as to perform one specific function, is, as well, reverberating back-and-forth in a cycle that goes from moving into the relative "up" or norm-to-forward-holomorphic directoral-based path, into then going into a motion that is then going into the relative "down" or norm-to-reverse-holomorphic direction, and back again, -- to where the so-stated relatively external-based flow, is to here act in a tensoric-based manner, when this is in a direct relationship to the here more relatively internal-based flow. As said before, -- those group-attractors that act upon the said orbifold eigenset -- in so as to help to work to cause the said eigenset to move into the said relative "up"-based direction, act upon the said orbifold eigenset in a relatively chiral-related manner, -- whereas contrariwise, those group-attractors that act upon the said orbifold eigenset in so as to help to work to cause the said eigenset to move into the said relative "down"-based direction, act upon the said orbifold eigenset in a relatively antichiral manner.  The general effect of the just mentioned chiral-based influence, that is of this particular case, will then tend to work in so as to help to form a scalar magnitude of those certain directly corresponding torsional eigenindices, that will then tend to bear the index-based existence of singularities that will have Real Reimmanian roots, whereas, in contrast, the general effect of the here mentioned antichiral-based influence of this particular case, will then tend to work in so as to help to form a scalar magnitude of those certain directly corresponding torsional eigenindices, that will tend to bear the index-based existence of singularities that will have complex roots.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclical Reverberations And Reference Frames, Part Three

Let us initially consider a given arbitrary orbifold eigenset, that is moving, as mentioned before, via a rectangular Lagrangiain-based path -- in such a manner, as to be tending to turn at each correlative corner, towards the relative left.  Let us, as before as well, consider that the said orbifold eigenset is to here work to bear cyclic permutations.  Let us then, as well, consider that the said orbifold eigenest is to, from an external reference frame, be reverberating -- as well -- from going towards the relative "up" (norm-to-forward-holomorphic) to going towards the relative "down" (norm-to-reverse-holomorphic) direction -- in so as to iterate through such a so-eluded-to cyclical path, as a phenomenology that is to reverberate via a binary-based genus of a tensoric-related Lagrangian-based path, over time.  Let us next consider those correlative group-attractors -- that work in so as to help in the influencing of such an orbifold eigenset, to be able to undertake such a back-and-forth reverberation -- that is to here reiterate in such a relative "up-to-down" associated manner.  Those group-attractors that would work here -- in so as to influence such an orbifold eigenset to move into the relative norm-to-forward-holomorphic direction -- would here tend to have a chiral effect upon the holonomic substrate of the said orbifold eigenset, over a sequential series of instantons.  Contrariwise -- those group-attractors that would work here in so as to influence such an orbifold eigenset to move into the relative norm-to-reverse-holomorphic direction -- would here tend to have an antichiral effect upon the holonomic substrate of the said orbifold eigenset of such a case, over a sequential series of instantons.
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.

Cyclical Reverberations And Reference Frames, Part One

Let us initially consider one given arbitrary reference frame -- that is of an orbifold eigenset, that is to be kinematic as a holonomic substrate, that is cyclical in its Fourier-related transformation, while it is in the process of moving along a generic tense of a rectangular Lagrangian-based path -- during which the specific respective so-eluded-to Hamiltonian operand of such a case, is varied per iteration of such a so-stated generic rectangular path, on account of those directly corresponding angular perturbations that are to here happen to the Stoke's-based topological substrate of the Fourier differentiating orbifold eigenset, to here be of a Yukawa-based nature to the core-field-density of the said eigenset, in so as to work to make-up the specific so-eluded-to tense of such a cyclical permutative holonomic substrate, that is of the internal reference frame of the holonomic substrate of the here respective given arbitrary set of superstrings that are here to operate in so as to perform one specific function over time.  Let us then consider, that, at an external reference frame -- the directly corresponding orbifold eigenset is to here work to bear a Fourier-based tensor of field generation -- to where, at the vantage-point of the so-stated external reference frame, the said orbifold eigenset is to, as well, bear a simultaneous motion that is gradually pushed into the relative norm-to-forward-holomorphic direction, as the said orbifold eigenset is in the process of being reverberated through the earlier said rectangular Lagrangian-based path, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Cyclical Reverberations And Singularities, Part Two

Let us initially say, that one is to have a given arbitrary orbifold eigenset -- that is to reverberate in a rectangular-based manner, over time.  Let us then say, that the respective given arbitrary orbifold eigenset -- is to initially go straight for a bit, while then turning to the relative left and then proceding for a bit, while then turning to the relative left and then proceeding for a bit, while then turning to the relative left and then proceeding for a while, while then turning to the relative left, -- to where this will then alter mildly in its Ward-Caucy-based geometric angle, to where this will then work to repeat in its cycle, with the so-eluded-to alteration in its Stoke's-based depth.  Next, let us say that such a cyclical-permutative reverberation, is to then continue to a relatively indefinite degree of manner --over a sequential series of iterations of such so-eluded-to substringular reverberation-based metrical indices.  One could then, in a way, consider that such a relatively mild tense of such a reverberation -- is to here be a relatively loose tense of a Majorana-Weyl-Invariant-Mode -- of which may work here to continue in its metrical-based eigenbase, over a relatively significant duration.
I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Cyclical Reverberations And Chern-Simons Singularities

Let us initially consider an orbifold eigenset, of a respective given arbitrary case -- that is to go from working to bear two consecutive Lagrangian-based Chern-Simons singularities that would work here to form one antiholomorphic Kahler condition, -- while then going in so as to work to bear two consecutive Lagrangian-based Chern-Simons singularities, that are to stem from the relative opposite direction, in so as to work to form an antiholomorphic Kahler condition that is to be of a polarized differential geometric tense from the initially so-eluded-to Lagrangian-based path, that would be formed by the initial condition of the first so-stated antiholomorphic Kahler-based state from the differential geometric condition of the second so-stated antiholomorphic Kahler-based state.  Let us next say that such a so-eluded-to general pattern, is to here repeat indefinitely for a while -- yet with minor angular abberations -- that are to here be affiliated with each of such recurring sets of Fourier-based back-and-forth oscillations.  One may then say, that such a respective given arbitrary group-metric of the said orbifold eigenset, is to here be undergoing a genus of a tense of conformal invariance -- in which case, the consecutive sets of such substringular reverberations -- may be said to here work to bear what may be termed of as a tense of cyclic permutations, when this is taken as the perturbative alterations in the Stoke's-based Lagrangian-related paths, that are to be taken by such a so-eluded-to orbifold eigenset, over time.  I will continue with the suspense later!  To Be Continued! Samuel David Roach.

Consecutive Antiholomorphic Kahler Conditions

Let us initially consider an orbifold eigenset -- that has just worked to bear two consecutive Lagrangian-based Chern-Simons singularities -- in so as to work to bear an antiholomorphic Kahler condition.  Let us next say that the self-same orbifold eigenset, will then act in so as to travel a relatively significant distance, along the eluded-to Lagrangian-based path -- of which the said orbifold eigenset had just began to trespass upon, as it had just worked to start the earlier mentioned motion that had helped at causing the said antiholomorphic Kahler condition.  Let us next say, that, eventually, the respective given arbitrary orbifold eigenset will then work to form another set of two consecutive Lagrangian-based Chern-Simons singularities -- to where the said eigenset will then work to form another antiholomorphic Kahler condition, -- yet from the vantage-point of a relatively Ward-polarized Caucy-based geometric tense of covariance.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.