As To Discrete Energy And Discrete Time

A superstring of discrete energy permittivity is the smallest physical phenomenology that is of a "package' of what may be thought of as a single unit of a fractal of magnetism.  You can not have a fraction of discrete energy.  Yet, there is a basically endless variety of phenomenology that is smaller in the correlative scalar amplitude of its size, that works to help form those superstrings that are the smallest "packages" of energy that are actually what we may term of as energy.  But, due to the nature of those eigenstates of a metrical-gauge-based nature that are smaller in physical sized than superstrings of discrete energy -- we tend to only notice as the smallest substringular phenomenology, as the existence of superstrings.  Likewise, the smallest "package" of time that may be either termed of or thought of as time, is an instanton.  Just as one cannot have a fraction of discrete energy -- when in terms of any respective given Hodge-based-index, of as to any correlative scalar magnitude of discrete energy permittivity -- one cannot have a fraction of time that is smaller than an instanton.  YET, there is basically an endless variety of phenomenological-based durations -- that are smaller in scalar amplitude than that of an instanton.  But, given the nature of those gauge-metrical-based periods that are briefer than the duration of discrete time, -- we only tend to notice the passage of the sequential series of instantons, as the flow of the smallest individual "packages" of time that are actually of "time."  Let me explain it in the following manner, as a metaphorical example that may make this clearer.:  Let us think of a "cartoon" as a relatively decent metaphor, for as to being of the flow of discrete energy over discrete time.  As we are viewing the metaphorical cartoon, we only tend to notice the sequential series of the delineated flow of the discrete individual pages of that cartoon -- as what may here be considered as to be symbolic of the fact that we only notice -- as an extrapolation of energy -- in so as to be the individual superstrings, their correlative counterstrings, their correlative Fadeev-Popov-Trace eigenstates, and their correlative light-cone-gauge eigenstates, -- as the respectively smallest existent "packages" of the respective particle-based discrete energy permittiivty, the correlative wave-functionability of discrete energy permittivity, the correlative particle-based discrete energy impedance, and the correlative wave-functionability of discrete energy impedance.  Again, in the Metphorical cartoon example that I have used here, one only notices as discrete durations -- the individual durations in which the so-stated sequential series of the individual pages that come together in so as to work to comprise the said Metaphorical flow, of what would here work to comprise the so-stated venue of the said Metaphorical cartoon.  Yet, in a cartoon -- there may be phenomenology that is existent in-between the individual discrete pages of the said cartoon, -- as well as there are durations that exist in-between the individual discrete periods of as to when the sequential series of the said pages of the said cartoon are to here be shown.  Yet, due to the nature of the stuff that may be shown in-between the individual pages of the cartoon & yet, as well, due to the nature of the periods that may be present in-between those durations in which the so-stated pages are shown, in so as to work to form the so-stated cartoon -- one will tend to only notice the sequential series of the pages that work to comprise the said cartoon -- as to be during when these pages are to be shown, when the cartoon is done.  Likewise -- due to the nature of those metrical-gauge-based phenomenology that are smaller than the smallest increments of energy, As Well as due to the nature of those gauge-metrical-based phenomenology that are smaller than the smallest increments of time -- such phenomenology that work to come together in so as to work to form discrete energy and time, do not tend to be directly detected upon the activity of what would here tend to be extrapolated.  This helps to explain as to how a quantum leap may be logically thought of as happening.  As the holonomic substrate of a substringular phenomnology appears to immediately be translated from one spot to another without any of the said entity of holonomic substrate being translated here in-between the two so-eluded-to endpoints -- this is due to the condition that there is a generally unnoticed duration of Ultimon Flow that happens in-between each successive group-related instanton that we are able to directly detect.  We only tend to notice the sequential series of instantons, in which discrete energy is to flow through.  During the successive series of the generally unnoticed durations of Ultimon Flow -- the ensuing substringular delineations are encoded for.  During the duration that I have so-termed of as SETS -- the ensuing substringular delineations of discrete energy are then more specifically encoded for.  During what I term of as the ensuing discrete increment of the instanton-quaternionic-field-impulse-mode, which is at the "tail-end" of the generally unnoticed duration of Ultimon Flow -- the ensuing substringular delineations are brought into where these are to be iterated at. Since relatively organized physical existence is only iterated as discrete energy -- that happens at each successive iteration of group-related instanton -- we tend to literally only notice as phenomenology to be of the successive iterations of discrete energy, through the metric of discrete time.  So, when there is one second happening -- there are 10^43 discrete increments of generally noticed Ultimon Flow and 10^43 discrete increments of generally unnoticed Ultimon Flow.  Why this does not work to form 2*10^43 discrete increments instead, is on account of the condition that we are made of a composition of discrete energy that flows during discrete time.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Process Of Substringular Inter-Binding

Let us consider here a given arbitrary two-dimensional superstring of discrete energy permittivity, that is initially moving as one discrete orbifold eigenset -- to where it is brought into the immediate substringular physical bounds of a second given arbitrary genus of an orbifold eigenset, -- to where the resultant physical configuration of the overall net Laplacian-based holonomic substrate, is to then be one overall respective given arbitrary entity -- of what is to then be one whole entire orbifold eigenset, of which is to contain in the immediate physical bounds of its directly corresponding spatial parameters, each of such so-eluded-to superstrings of discrete energy permittivity, that were of the initially so-eluded-to case scenario that I  have here began to imply.  The initial orbifold eigenset of one freely moving bosonic superstring of discrete energy permittivity, is to be moving along an initially hermitian Hamiltonian operand, in so as to be going through a discrete Lagrangian path -- through what is to be here an initially undetermined destination.  One may arbitrarily call the initial path that is of the said initially stated bosonic superstring of a metrical-gauge-based Hamiltonian nature -- as to be in the propagational-related relatively holomorphic direction.  In the meanwhile, there is a relatively larger orbifold eigenset, that is moving gradually into the general region in which the initially so-stated bosonic superstring of discrete quantum energy -- that works to bear basically just enough of a cohesive attractive force, seeing that such a said relatively larger orbifold eigenset in this respective given arbitrary case -- is of such a relatively mild genus of as to being what may here be called a group-attractor that is at the substringualr level.  Let us next say that the combined interdependent Fourier-based activity of the initial kinematic motion of the so-stated solitary bosonic superstring, with the relatively in-coming Fourier-based activity of the kinematic motion of the so-stated relatively larger orbifold eigenset -- works to bear an ever increasing core-field-density of such a genus of Rarita Structure eigenstates, to where this latter-stated Laplacian-based condition of an increase in the Hodge-Index of the holonomic substrate of gravity-based indices, will act in this case as a tense of an ever increasing state of magnetism.  This is since this so-eluded-to genus of an increase in the Hodge-Index of Rarita Structure eigenstates will work to form an ever increasing genus of the presence of interactive Fourier-based Schwinger-Indices, or, in other words, this will work to form an ever increasing genus of the presence of interactive Fourier-based gravity waves.  This genus of a relative build-up of magnetism -- as to the so-eluded-to manner of an increase in the scalar magnitude of characteristics that are directly affiliated with the propagation of both gravity and gravity-based waves -- will tend to form an initial Yukawa Coupling upon this here attracted superstring of which had here acted initially as its own orbifold eigenset, that will "pull" this from the initial state of just being in the Ward-Derichlet bounds of the second so-stated orbifold eigenset, which is of a relatively larger Hodge-related size -- into being in the actual Ward-Neumman and Ward-Caucy-based physical bounds of the so-stated relatively larger orbifold eigenset, that I have discussed in this respective given arbitrary case.  Such a "pull" is actually the "push" that is here to be most directly due to the here increasing influx of that genus of Rarita Structure-based indices that are increased in the amount of their presence in a euclidean-based proportion to the here present increase in magnetism.  Once the here discussed interdependent interaction between these two said orbifold eigensets converges into a relatively more conformally invariant-based nature, then, it may be said that the configuration of the proximal localized eigenmembers of such a case have then become as one overall orbifold eigenset.   I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Relatively Slow Versus Fast Formation Of Chern-Simons Singularities

Let us say that one is to have a superstring of discrete energy permittivity -- that is undergoing four consecutive perturbations, in what would otherwise be the Hamiltonian-based motion of the said superstring, as moving through what would otherwise be a discrete unitary Lagrangian-based path.  Let us then say that the so-stated superstring, of which acts alone as one discrete orbifold eigenset, is to bear such a Yukawa-based torsioning -- to where it has what is formed upon it, as the correlative formation of an initial metrical-based Chern-Simons singularity -- of which will here tend to form both a set of Njenhuis Lagrangian-based singularities ( along with its directly corresponding complex roots), and a Real Reimmanian Lagrangian-based Chern-Simons singularity, to where the said superstring is to then be perturbated into what would then tend to be a new path that is moving at 45 degrees in the counterclockwise direction from its initial path, in so as to work to form a renewed tendency of working to bear a re-established holomorphic flow -- that is to then be considered as the so-stated supertring's newly formed directoral base, of what may then be determined as what its holomorphic-based Lagrangian-based path is then to be.  Let us say that there are to be four of such consecutive changes in the holomorphic-based tendencies, that are then to be applicable to what the mean Lagrangian-based path of the superstring is then to be.  If the rate of such a so-eluded-to Fourier-based kinematic activity of perturbation is to be of a relatively gradual tense of succession, then, there is relatively less of a tendency of the respective given arbitrary superstring of discrete energy permittivity to then work to form the Ward-Caucy conditions, of what may here be termed of as an antiholomorphic Kahler condition.  Yet, if the rate of such a so-eluded-to kinematic activity of perturbation is to be of a relatively quicker tense of succession, then, there is to then be a relatively greater tendency of the respective given arbitrary superstring of discrete energy permittivity that I have been discussing here, to then work to form the Ward-Caucy conditions of what may here be termed of as an antiholomorphic Kahler condition.  
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Perturbative Mean Paths In Conjunction With Singularities

Let us initially consider a superstring that is moving as a metrical-gauge-based Hamiltonian operator, of which is moving through its Hamiltonian operand as an eigenstate of discrete energy permittivity -- of which is going through a mappable tracing that may be extrapolated as having at least some expectation value as to continuing to go through a discrete unitary Lagrangian, over a sequential series of instantons.  Let us next say that this superstring, that is here to be considered as going through a Fourier-based transformation -- acts as one small but entire set of superstrings, that operate in so as to perform one specific substringular function -- to where this respective given arbitrary superstring is here to act as one small but entire tense of being an orbifold eigenset.  Let us next consider, that there is, all of the sudden, the presence of a semi-proximal localized group-attractor -- that is then acting upon the so-stated superstring of such a case -- (this superstring of which is here to act as one whole orbifold eigenset) -- that is situated in the general region of the initially said superstring, at a distance that is localized away from the here consistently redelineated given respective string that was initially to go through a discrete unitary Lagrangian path, this group-attractor that is here to interact with the said superstring of which is in the Laplacian-extended directoral-based path, that is in the direction of the reverse-norm-to-holomorphic parameterization of the correlative substringular region -- in such a manner that is Yukawa to the superstring, yet, as an ansantz, not initially in a Gliosis-based manner of substringular-based coupling.  Let us next say that the interaction of the respective given arbitrary group-attractor upon the initially considered superstring of discrete energy permittivity, will here work to form both a set of metrical-based Chern-Simons singularities, a set of Njenhuis Lagrangian-based Chern-Simons singularities, and a tense of a Real Reimmanian-associated Lagrangian-based singularity, upon the kinematic-based motion of the holonomic substrate of the topological entity of that superstring that would otherwise be going through the so-stated given arbitrary respective discrete unitary Lagrangian, over a relatively transient duration of time.  Let us next say that the tendency that is to exist here -- of that substringular-based torsioning, of which is involved with the correlative "fidgeting" of the so-stated initially considered superstring -- that is due to its interaction with the directly corresponding respective group-attractor, will be of a wave-push upon the holonomic substrate of the reverse-norm-to-holomorphic topological surface of the said superstring that is Gliosis to its core-field-density, of which will tend to make the so-stated superstring that is to work to form the said Chern-Simons singularities, to fidget towards what is here to be the opposite direction on the superstring from where the so-eluded-to Yukawa force was directly working to bear its coupling, to where the resultant wave-tug is to be directed in the relative forward-norm-to-holomorphic direction at the Poincare-based vantage-point of the here extrapolated superstring of discrete energy permittivity, that is to here be acting alone in this case as a single orbifold eigenset.  Let us next consider that the resultant reparamterization of the directoral-based topological sway of the transversel-based Hamiltonian operation of the said superstring -- due to the kinetic-based effect of the directly affiliated Lagrangian-based Chern-Simons singularities that are thus formed, will then Tend to "want to"be at a 45 degree subtended direction in the counterclockwise direction from the supplemental-based path that the so-stated superstring would otherwise be taking.  This is due to the condition that superstrings have a tendency of being perturbated out of their directoral-based holomorphicity along a mean Lagrangian path from the general given arbitrary respective path that such a superstring had been initially taking -- before such a general tendency of an interaction with such a group-attractor is then to have happened.  Such a general genus of such a perturbation will tend to "want to" be going into the relative Njenhuis-to-norm-to-holomorphic directoral-based topological sway from its initial course.  This is only the theoretical tendency.  In the real world, there are a lot of other factors involved.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Duration of Elongated Pulsation

Let us first initially consider one given arbitrary superstring of discrete energy permittivity -- that is interdependently interacting with a group-atractor, in so as to work to allow for the respective pulsation that is of the said superstring, to be temporarily elongated at one set proximal locus -- as the so-stated string that is being discussed here, is to be moving through what would otherwise be a discrete unitary Lagrangian-based path.  Let us say that there are two different general case scenarios, that may be applicable to this given arbitrary respective type of case:  One:  The said elongation of the pulsation of the so-stated superstring, may be happening in this initially stated case scenario, only at one set Laplacian-based locus -- to where this so-eluded-to metrical-based Chern-Simons singularity that would thus form, could form a set of a Njenhuis-based Lagrangian tense of Chern-Simons singularities, to where these said singularities would tend to be propagated along the correlative Rarita Structure eigenstates, over time.  In such a case scenario, the effectual group-attractor will only bear a Yukawa Coupling upon the directly corresponding superstring, whose pulsation is elongated over the course of one respective given arbitrary group-related instanton.  Two:  The said elongation of the pulsation of the so-stated superstring, may be at a less metrically conformal genus of a set locus -- that would then be happening over a sequential series of Laplacian-based settings -- to where this so-eluded-to transient-based maintenance of metrical-based Chern-Simons singularities, would thus tend to form a set of Njenhuis Lagrangian-based singularities, to where these said singularities would then tend to be propagated along the correlative Rarita Structure eigenstates, over time.  This would depend upon if the action of the respective given arbitrary group-attractor -- that acts in so as to work to form that pull that is Yukawa to the Hamiltonian-based angular momentum of the said superstring, is to then  act in a Gliosis-based manner --upon the correlative inter connective so-eluded-to zero-norm-state-projections, that operate in so as to work to form that homotopy that binds the said interdependence that exists in-between the so-stated superstring and the correlative so-stated group-attractor --to where this is happening over the course of just one spurious iteration of group-related instanton, or, if the said action of the respective given arbitrary group-attractor that acts in so as to work to form that pull that is Yukawa to the Hamiltonian-based angular momentum of the said superstring, the said group-attractor will then act in a Gliosis-based manner that, instead, happens over the course of a sequential series of group-related instantons.  In this so-stated second tense of such a general case scenario, the correlative group-attractor will be moving in a planar-based manner, in so as to work to form the so-eluded-to Chern-Simons singularities -- that will here work to involve, in general, the resultant gauge-metrical Hamiltonian operation of what would happen if there was such an elongation of the directly associated pulsation of the said superstring, that is of this given arbitrary case scenario.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Some Stuff As To Attenuated Pulsations

Let us here consider a given arbitrary superstring of discrete energy permittivity, that is initially differentiating in a Fourier-based manner, in so as to be moving in a kinetic-based manner -- through a respective Hamiltonian operand, that may be mapped-out over a discrete unitary Lagrangian, over time.  Let us next consider that the said discrete quantum of energy permittivity that is here being discussed, is initially pulsating at a constant rate -- while such a so-stated superstring is only here to be initially working to form completely hermitian singularities, over the directly corresponding sequential series of instantons, through which the discrete quantum of energy of such a case is moving through its respective medium of space, as the so-stated superstring is moving through the said discrete path that is mappable over the directly corresponding Rham-based cohomology by which it is then working to form its correlative projection of its trajectory.  Let us then say that there is to then be a perturbation in the genus of the metrical-based tense of those singularities, that are then to formed by the resultant motion of the said discrete quantum of energy -- as it is moving along its initially proscribed path.  Let us consider that there is a given arbitrary group-attractor -- that may be situated from a significant locus that is "below" the norm-to-reverse-holomorphic positioning of the said superstring -- that is here being discussed in this respective case.  Let us say that the respective given arbitrary group-attractor that is being mentioned in this said case scenario, is to form a wave-tug/wave-pull -- that works to cause the pulsation of the initially said superstring, to be attenuated from its initial rate of its given arbitrary spin-orbital-based mode.  Such an attenuated pulsation in the rate of the correlative spin-orbital-based mode of the respective given arbitrary superstring, will then tend to work to form a metrical-based Chern-Simons singularity in the mode of the overall Hamiltonian-based fractal of its angular momentum-based indices, just as the so-stated superstring of discrete energy permittivity is being basically pulled in the direction of what was initially the proscribed discrete unitary Lagrangian, as the said superstring is to still be differentiating in a Fourier-based manner, over the continuously spontaneous sequential series of instantons by which the said superstring is to be moving in both a transversel and in a spin-orbital-based manner, over the correlative gauged metric of the so-eluded-to discrete quantum of energy.  Let us next consider, that often -- the establishment of the existence of such a metrical-based Chern-Simons singularity, will work to form a "fidgeting" of the directly corresponding motion of the directly corresponding superstring that is to be considered here.  Often, the formation of such an attenuated genus of a metrical-based Chern-Simons singularity -- will work to mildly pull the said superstring in a "fidgeting"-based manner, in either a Njenhuis and/or in a Real Reimmanian-based manner, in a relatively small degree, into the direction in which that group-attractor is moving to act in, in so as to work to form a set of one or more Lagrangian-based Chern-Simons singularities, just as the activity of that so-stated group-attractor that is here to be acting as the perturbative source that works to form the said respective given arbitrary attenuation of the correlative superstring's pulsation, is moving further into the relative norm-to-reverse-holomorphic direction from the planar-based Hamiltonian operand of the set path of the kinematic-based motion of the said discrete quantum of energy that is being delineated through what would otherwise be a discrete unitary Lagrangian-based path.  If the said perturbative source that had worked to form the so-mentioned Chern-Simons singularites, is both intially situated from a path that is "below" the said superstring from the relative norm-to-reverse-holomorphic direction from the plane in which the directly corresponding superstring is to here be moving, as well as the said perturbative source that is to here be working to form the Chern-Simons singularities that are being discussed in this case, is to be moving further into the relative norm-to-reverse-holomorphic direction from the plane of as to where the said superstring is to be moving in, then, if one were to be theoretically situated at the relative norm-to-forward-holomorphic positioning of the correlative superstring of this given arbitrary respective case, then, the wave-tug/wave-pull that is to here be being applied to the said string -- in so as to work to form a lull in the pulsation of the said superstring, will then tend to work to cause a topological sway or a topological pull upon the so-stated string, to where the so-stated superstring will be mildly pulled into the cross-product direction, or, in the direction that is situated relatively "away from where you are at."  Such a "pull" is actually a "push" that is directed as going in the Opposite direction from the said norm-to-forward-holomorphic positioning that I have here discussed in this respective given arbitrary scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

More As To Ellongated Pulsations That Cause Singularities

If one is to have an ellongated substringular pulsation -- that is to here work to cause a metrical-based Chern-Simons singularity, that is to form one or more Lagrangian-based Chern-Simons singularities -- if the tendency as to the said formation of a set of one or more Lagrangian-based Chern-Simons singularities is to form a motion that is relatively pulling away from the so-eluded-to perturbative force, that would have here worked to form that said metrical-based singularity that is to here work to cause the so-stated Lagrangian-based set of one or more singularities, is considered to be a wave-tug/wave-pull that is in the relative "dot-product" directoral-based holomorphic torsioning, then, one is to here be considering the vantage-point of the interaction of the so-eluded-to "fidgeting" to be from the relative norm-to-forward-holomorphic positioning of the topological-based surface that is Gliosis to the core-field-density of the directly corresponding superstring at the Poincare level.  For instance:  The relative "top" of a superstring is what may be so termed of as the relative norm-to-forward-holomorphic positioning of any respective given arbitrary superstring, that may here be considered of, in such a case of a given arbitrary substringular scenario.  A "dot-product" tense of a consideration is one in which a said respective given arbitrary phenomenology is to move into the vantage-point of as to being going relatively "towards where you are at."  If the source of a given arbitrary perturbative force, that is to form an ellongated wave-tug/wave-pull -- that is enacted upon any respective given arbitrary superstring -- is to be happening from a source that may be considered as coming from relatively "below" the said superstring, or, from starting at relatively coming from the relative norm-to-reverse-holomorphic positioning of the superstring up towards going to the relative norm-to-foward-holomorphic positioning of the superstring -- then, if one is to work to take a bearing at the relative norm-to-forward-holomorphic position of any respective said superstring of such a case, when a directly corresponding perturbative force that is situated From a source that is initially coming from the relative reverse-norm-to-holomorphic side of that self-same superstring is to then work to form an ellongated pulsation that is then enacted upon the said so-eluded-to superstring of discrete energy permittivity, then, the so-expected reaction, of which would be the tendency of a spurious "fidgeting" of one or more Lagrangian-based Chern-Simons singularities -- that would thence often be caused by the Fourier-based activity that would then happen due to the metrical-based Chern-Simons singularity that would then be happening out of certainty, in this case -- this would then cause the directly associated superstring to be pulled into the direction of as to where the Laplacian-based observer were to then be initially at, as the so-eluded-to observer is to make the extrapolation of the equal and opposite reaction that would then be happening in this given case, as a tendency of what would bear a relatively high expectation value, if there is an ellongated pulsation that is to here be due to a wave push that is to be enacted From the relative reverse-norm-to-holomorphic positioning of a so enacted upon superstring To the relative forward-norm-to-holomorphic positioning of a so enacted upon superstring.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

As To Varying Ellongated Pulsations

Let us here consider a given arbitrary superstring of discrete energy permittivity, that is initially pulsating at a constant rate -- as the said string is moving at a constant velocity, through a discrete unitary Lagrangian, over a discrete metric of time.  Let us next consider that the so-stated superstring is to then work to bear an ellongated pulsation, that is at one general locus to where the said discrete quantum of energy is to be differentiating in a Fourier-based manner, over a sequential series of instantons.  The so-mentioned ellongated pulsation of such a case will here tend to work to form a metrical-based Chern-Simons singularity, of which will then tend to be propagated in such a manner to where this so-eluded-to perturbation in the pulsation of the said superstring will then tend to alter the condition of the initially so-eluded-to Rham-based cohomology into a Doubolt-based cohomology -- as the the mappable tracing of the projection of the trajectory of the said superstring of discrete energy permittivity, is to here be in the process of being propagated in the directoral-based holomorphicity that is to here be in conformity to the angular momentum-based flow of the initially stated discrete unitary Lagrangian, that is in the path of the directly corresponding Hamiltonian operand through which the directly corresponding superstring of discrete energy is to be moving through, as a holonomic substrate of a metrical-gauge-based Hamiltonian operator, over the so-proscribed set of instantons that are to here act as the set metric, that is to be gauged in this particular case.  The superstring of such case -- of which, of course, is to here act as a discrete quantum of energy permittivity -- will often tend to either form a Njenhuis-based "fidgeting" of a Chern-Simons-based Lagrangian form of a tense of singularities, that are here  due to the so-eluded-to tense of such a metrical-based singularity, or, if the superstring that is to here work to bear the so-stated ellongated pulsation, of which would here work to bear such a spurious iteration of metrical-based singularity, that is to here be "sensitve" enough to the said conditionality of the tendency of such a "fidgeting" that is to take effect upon the Ward Caucy-based bounds of the said superstring -- then, the so-stated superstring will often then be of such a nature in so as to bear a Real Reimmanian-based Chern-Simons set of one or more singularities, that will then tend to pull the said discrete quantum of energy permittivity away from the perturabtive source,  that had acted in so as to work to form the said metrical-based singularity in the first place, in a relative "dot-product"-based manner, in so as to work to pull the trajectory of the superstring away from the initially mappable Lagrangian-based path -- that the said superstring was to initially be plotted in, in so as to be extrapolated through.  I will continue with what the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Increase In Acceleration Of A Superstring

Let us here initially consider one given arbitrary mass-bearing Noether-based superstring of discrete energy permittivity -- that is accelerating through a discrete Lagrangian-based path, over time.  The Lorentz-Four-Contractions that would then be directly applicable to the said respective superstring, will then, proportionably, be increased -- as the so-stated discrete quantum of energy is moving at a higher and higher velocity -- over a sequential series of instantons.  Let us next consider if the so-stated superstring of such a case is to be increasing in its acceleration, as it is moving through the said discrete Lagrangian-based path -- over the so-eluded-to gauged metric-based duration of time, in which the superstring of such a case is differentiating in the so-eluded-to Fourier-based manner.  Not only will the directly applicable Lorentz-Four-Contractions -- that will be in the process of acting upon the directly associated Ward-Caucy-based conditions of the so-stated superstring, be increasing at a higher rate over time, yet, this tense or genus of as to how the correlative Lorentz-Four-Contractions will then be increasing -- will then tend to potentially form an inverse of a Clifford Expansion upon that mappable tracing that may be drawn-out in a Laplacian-based manner -- along either the topological-based surface of the norm-to-forward-holomorphic-based positioning of the holonomic substrate of the said superstring, or, along the topological-based surface of the norm-to-reverse-holomorphic-based positioning of the holonomic substrate of the said superstring, as such a so-stated mappable tracing may be extrapolated as an etching that may be construed along the so-eluded-to slope that would then be formed by the ever contracting tense of the here increasingly accelerated superstring of discrete energy permittivty, over time.  As such a superstring is to here be accelerating in a tense of a Noether-based flow, over time -- it is going to not only consistently bear metrical-based singularities, yet, since the topological-based surface of the Gliosis-based core-field-density of the holonomic substrate, that is of such a said superstring, when one is considering such a kinematic activity at the Poincare level, will be altering in such a perturbative manner -- such a so-stated superstring will then bear a greater expectation value of then working to bear Lagrangian-based Chern-Simons singularities that are Njenhuis to the Hamiltonian-based operand of the so-eluded-to Lagrangian-based path that the said superstring is to her be moving through, than if it were to otherwise not be accelerating as a mass-bearing superstring -- that is to here be undergoing a tense of a Noether-based flow.  Such a pattern would here be limited to the maximum Ward-Caucy-based restraints as to how much of a Lorentz-Four-Contraction would here be able to be applicable to the said string of discrete energy permittivty.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

An Accelerating Mass-Bearing Superstring

Le us here consider a given arbitrary mass-bearing superstring of discrete energy permittivity, that is accelerating -- as the said superstring is moving through its correlative Hamiltonian operand, through what may be mapped-out as a phenomenon that is going through a relatively discrete unitary Lagrangian, over time.  Let us next consider the condition as to that the so-stated mass-bearing superstring that is being discussed in this case, is accelerating at a smooth rate, that, in a correlative metric-based manner, does not work to include the Fourier-based activity of any jerks in the process of the here existent-based manner of the said acceleration of the so-stated discrete quantum of energy permittivity, that is functioning in so as to perform one specific operation over a sequential series of instantons.  So, in this particular case, the respective given arbitrary superstring that we are here discussing, is to then act as an orbifold eigenset -- in and of itself, in so as to act as one discrete metrical-gauge-based Hamiltonian operator.  This would then work to result in the condition, that the Lorentz-Four-Contractions that may then be applicable to what will then happen to the Ward-Caucy-based bounds as to the mass, the length, and the time of the physical phenomenology of the so-stated superstring of this case that is being accelerated smoothly through an otherwise discrete unitary Lagrangian -- will increase upon the topological holonomic stratum of the phenomenology of the directly corresponding superstring of discrete energy permittivitiy in a homogeneous manner, over the directly so-eluded-to metrical duration that may be gauged here.  This would then mean that the Laplacian-based activity of the gradual delineation of the slope that may be mapped-out here by the Laplacian-based condition of an ever increasing Lorentz-Four-Contraction that is being applied to the said respective superstring -- will be in this case of a euclidean-based nature, -- since the reverse-expansion of the Laplacian-based decrementing slope that is directly correlative here, is not of an exponential-base manner.  So, since the so-stated reverse-expansion that may be mapped-out in a Laplacian-based manner -- at the two ends of the correlative superstring, as it is being contracted smoothly over time, is not of an exponential manner, the said reverse-epansion is not of an inverse Clifford Expansion, -- it is of an inverse euclidean expansion.  (I hope that this post explains things a little bit better.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

The Effect Of Added Dimensions Upon The Force Of Gravity

When one has an isomorphism that is comprised of multiple superstrings that are relatively separated from being in the same general locus, yet, such superstrings are all within an Angstrom of each other, then, one has to consider the condition as to whether or not such extrapolated superstrings, over a time-wise differential association, are under a state of static equilibrium, or, if such a set of superstrings are more along the lines of behaving in both a perturbative and also in a relatively divergent manner. If one has two given arbitrary sets of superstrings that are proximal -- microscopically -- yet, are not of the same general locus, and, if the two said sets of superstrings are under a condition of superconformal invariance, as these said superstrings are non-trivially isomorphic the one set relative to the other, then, these superstrings would need to be acted upon in order to become diverged away from the eluded to condition of static equilibrium. If there happened to be a ghost inhibitor that acted as a buffer in-between the two eluded to general loci of each set of such superstrings that are here of the same universe, then, if some sort of norm-state projection that were to act upon both of the said sets of superstrings via the holonomic substrate of the said ghost inhibitor that were to be in-between the two eluded to orbifolds (physically-based spaces) were able to possibly work to produce an alteration or a perturbation in the said condition of static equilibrium that was here to initially be kinematic in-between the two said sets of superstrings that are in this case initially in a symmetry of non-trivial isomorphism, then, this would then make it possible to end the eluded to condition of static equilibrium. Such an alteration from what was here a given arbitrary case of superconformal invariance would tend to diverge the two sets of superstrings in such a manner in so that the directoral-based wave-tug/wave-pull of each individual set of superstrings would reverse in terms of their holomorphic permittivity. Such a reverse in directoral flow would then here indirectly cause the production of a Wick Action eigenstate, which would consequently cause the activity of a Gaussian Transformation that would act upon the general locus of part of the initial region in which the orbifolds, or, the physical spaces, that are here represented by the two sets of superstrings, so stated, that here work to perform two different functions that are Gliossi upon the holonomic substrate of the same universe. This is a general example as to that activity that may often work to allow for the need for the changes in certain norm-based conditions. Again, norm-conditions need to change often in order for room to be made for the essential operations of space-time-fabric.

Metrical-Based Chern-Simons Singularities

Let us first consider, in this case -- one distinct given arbitrary superstring of discrete energy permittivty, that is moving at a constant transversal speed in a constant transversal direction, over a set metric over time.  Let us next say -- that the said superstring of this respective case were to evenly vary in the rate of its pulsation, even though the so-stated superstring of this given arbitrary case is said to be moving at a constant Real Reimmanian-based velocity -- over a sequential series of directly related instantons.  Since the so-stated given arbitrary superstring, is to here be moving at a constant velocity in this respective case scenario -- the directly applicable Lorentz-Four-Contractions that may be attributed to both some of the consequential and some of the  resultant attributes, that are to then be displayed by the Fourier-based activity of the said discrete quanta of energy of this respective case -- are to tend to be of the same consistent manner of the correlatively-speaking scalar amplitude, per each succeeding iteration of the directly associated instantons in which the so-stated superstring is to here be moving through the directly associated Hamiltonian operand -- which is to here be related to the directly correlative metrical-based substringular duration of the motion of the said given arbitrary superstring.  Yet, since the said superstring of this case is to here be varying in its pulsation, while it is moving at a constant transversal speed in a constant transversal direction -- the so-stated superstring will then tend to bear a set of tensoric Njenhuis-based indices, that will be applicable to the topological sway of the said superstring of discrete energy permittivity, as the so-stated superstring is to be moving through what would otherwise be a discrete Lagrangian-based path that is to be plotted through the given arbitrary respective substringular environment that is of the directly associated Hamiltonian operand of this given case.  This variance in pulsation of the given superstring of this case, will then work to form one set of metrical-based Chern-Simons singularities, that may be considered as what will tend to be a euclidean acceleration and/or a euclidean deceleration of the rate of the perturbative externalized topological sway of the spin-orbital wave-tug/wave-pull of the so-stated superstring at the Gliosis-based topological surface that is Poincare to the core-field-density of that self-same superstring.  Yet, the earlier mentioned tensoric Njenhuis-based indices, that may be formed by that alteration of substringualr pulse, that will act, ironically enough, to not alter the transversal velocity of the said superstrings -- will work to form a set of complex-root-based indices -- that will here be directly affiliated with the existence of a sort of "fidgeting" that will then tend to happen as the said superstring is altering in the rate of its so-eluded-to pulsation, over the said gauged metric of this given arbitrary case.  Such a fidgeting in the transversal Fourier-based delineation that is of the so-stated superstring, will work to form an externalized rippling of the outer-bounds of the directly associated Ward-Caucy condition of the said discrete quantum of energy permitivity -- of which will as well tend to form in that so-stated state or tense of "rippling," the interactive existence of certain directly associated Lagrangian-based Chern-Simons singularities, over the correlative sequential series of instantons by which such a kinematic-based activity is to then be able to take place.  To Be Continued!  Samuel David Roach.

Rotational Cyclical-Moving Superstrings

Let us here consider a given arbitrary superstring of discrete energy permittivity, that is here working to bear an even tense of its directly corresponding Lorentz-Four-Contraction, over time.  Let us next consider that the said discrete quantum of energy permittivity is to here be moving as a Hamiltonian operator -- that is going through a rotational-based Lagrangian, in a cyclical-based manner, over a successive series of instantons.  If the so-stated tense of the directly associated Lorentz-Four-Contraction, that is to here be applicable to the said superstring, is to be maintained as to here be that of the same scalar amplitude -- over the whole metric by which the so-stated superstring is to then be in the process of moving through the whole rotational-based cyclical Lagrangian, over the so-eluded-to duration of time by which the said respective given arbitrary string is to be considered in such a respective given arbitrary case scenario, then, there will then be a higher expectation value as to the condition of the said respective given superstring to here be working to form hermitian Lagrangian-based singularities instead of Chern-Simons Lagrangian-based singularities -- than if the said superstring of discrete energy permittivity were to not be undergoing such an even state of the so-stated cyclical rotational-based Hamiltonian operation, via the so-eluded-to path of the Lagrangian by which the so-eluded-to Hamiltonian operand is to be moved upon -- via the so-stated given arbitrary sequential series of instantons, by which the said superstring is to be moving in a Fourier-based manner through both a coniaxial-based tense of a spin-orbital-based manner and in a coniaxion-based tense of a  transversel-based manner, over time.  Since the scalar amplitude of the applicable Lorentz-Four-Contraction that is to be viable upon the so-state discrete quantum of energy, it to here be of a constant manner -- over the so-implied metric by which the superstring of such a given arbitrary case is to here be of a consistent manner -- the velocity of the said given superstring is to be maintained, when this is taken in a tense of the consideration of a Minkowski-based compactification of the dimensionality of the transversel parameterization of the Lagrangian-based motion of the said string, that is of this case scenario.  This would then mean, that, even though the rotational-based tense of the motion of the said superstring is to bear a conixial-based change in its velocity -- due to the constant change in the directoral wave-based torsioning that is to here be applied to the Hamiltonian-based drive of the so-eluded-to Hamiltonian operation, that is of the Fourier-based motion of the string as it is moving through a cyclical rotational-based path -- since the actual speed of the so-stated superstring of this case is to be maintained over the correlative directly corresponding metric -- by which it is being propagated through a sequential series of instantons, then, the transversel tense of the motion of the said superstring is to only tend to bear Real Reimmanian-based metrical singularities that are of a hermitian-based nature. The only Chern-Simons metrical-based singularities that the said superstring would tend to bear, would be of a Njenhuis-based nature, and, the Lagrangian-based singularities that would be of a resultant-based nature would tend to be of a hermitian-based nature, along the Real Reimmanian-based supplemental Hamiltonian projection of the cohomological mappable tracing that may be extrapolated through the center of the annulus of that ghost-based pattern, that may be mapped along the so-eluded-to propagation of the so-stated superstring of discrete energy permititivty  -- in so long as the rotational-based cyclical nature of the cylindrical-based resultant cohomology of the said mappable tracing -- that is of the physical memory of the Fourier-based differentiation of the said superstring, is of a Rham-based nature, over the overall considered Real Reimmanian-based Lagrangian that is to be considered here in this respective given arbitrary case scenario.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To The Flow Of Lorentz-Four-Contractions

Let us initially consider a distinct given arbitrary superstring, that is perturbating over a set metrical-based sequential series of instantons -- when this is taken in terms of the scalar amplitude of its directly corresponding Lorentz-Four-Contractions, that are acting in a Gliosis-based manner --  at the Poincare level to the topological surface of the holonomic substrate that is of the so-stated superstring of discrete energy permittivity of such a case, over time.  Let us next consider that the said superstring of discrete energy permittivity of this case, is to here be differentiating in a Fourier-based manner -- through a given Hamiltonian operand -- that is to here span the space by which the so-stated given Hamiltonian operand-based operation in this scenario is to be pulled in a kinematic manner, through the path that is correlative to its directly corresponding discrete Lagrangian, that the so-stated eigenstate of discrete energy per charge is to being moved into -- over the said sequential series of iterations of instanton.  Let us next say that the tense of the directly appertaining perturbation of the correlative Lorentz-Four-Contractions, that are being directly applied to the Polyakov-based mechanism of the kinematic manner, whereby the so-stated discrete quantum of energy permittivity of this case is to be of a harmonic-based cyclical manner -- that would here work to form an even tense of a gradual increase in the directly applicable scalar amplitude of the quantum effect as to how an increase in how the linear-based increase in velocity, that is moving in a unitary transversel-based motion, in a direction -- is to effect the gradual increase in the degree of the amount of a Lorentz-Four-Contraction that is to take hold upon the gradual decrease in the scalar amplitude of the directly associated degree of its correlative Polyakov-based action, -- to where this is to then work to form, over a discrete number of a successive series of instantons -- a condition to where the self-same superstring of discrete energy permittivity, is to then subsequently work to bear an even tense of a gradual decrease in the directly applicable scalar amplitude of the quantum effect as to how the linear-based decrease in velocity in a unitary transversel-based motion in a direction, is to here effect a gradual decrease in the degree of the amount of a Lorentz-Four-Contraction that is to be able to take-hold upon the condition as to the gradual increase in the scalar amplitude of the directly associated degree of the correlative Polyakov-based action that is to happen, over a sequential series of a discrete number of instantons.  Such a gradual and even fluctuation in both the acceleration and the decceleration of a linearly-transversel pull of a superstring -- through a discrete unitary Lagrangian, will tend to form a higher probability as to potentially working to form hermitian Lagrangian-based singularities -- even though the cyclical manner as to the acceleration of a superstring, that is still to be of a cyclical-based nature in its eventual process of decceleration -- will here form changes in the metrical pulsation of the directly associated superstrings in question -- to where this said general process will tend to consistently work to form metrical-based Chern-Simons singularities, over time.

LFCs and Cohomologies

Let us first consider here a superstring of discrete energy permittivity, that is differentiating in a Fourier-based manner -- over a sequential series of instantons.  Let us next consider the condition of such a so-stated superstring, as in the state of affairs -- to which it is moving at a constant velocity, in a terrestrial-based environment, over time.  Such a said condition -- as to any given arbitrary superstring of discrete energy permittivity, that is of a respective light-cone-gauge topology that is to here be of a Kaluza-Klein-based nature -- that is of a mass-bearing nature, of which is to here be moving in a terrestrial-based nature over time, at a constant velocity, is to here be in a condition by which it will then tend to work to bear a constant tense of having a consistent scalar amplitude  of its correlative Lorentz-Four-Contraction.  Let us next consider the condition -- that the initially mentioned given arbitrary superstring of discrete energy permittivity, of which is here to be moving in a kinematic-based manner, in so as to work to maintain a constant state of its correlative Lorentz-Four-Contraction -- is to form such a projection of its trajectory, to where the correlative cohomological-based pattern, of which it is to then form, as a physical memory as to the where, how, and when the so-stated superstring of discrete energy permittivity had differentiated in a Fourier-based manner, over time -- is to then form a mappable tracing of its ghost-based indices, that is to then tend to work to bear a relatively higher expectation value as to its probability of forming a Rham-based cohomological-based pattern, than if it were to, instead, exist in a state of a perturbative tense as to what its directly correlative Lorentz-Four-Contraction, that it would otherwise tend to bear, would happen to be, if it were to vary in its velocity in its said environment of being in a terrestrial-based medium by which the said quantum of discrete energy permittivity is to be propagated or delineated through, over time.  This would then mean, that any given arbitrary superstring of discrete energy permittivity -- that is moving in a terrestrial-based environment at a constant velocity, as well as moving through the same general medium as to the basis of the holonomic substrate of its correlative Hamiltonian operand -- will not only tend to work to bear a consistent state of the scalar amplitude of its directly corresponding Lorentz-Four-Contraction, yet, such a so-stated Fourier-based tense of a respective given arbitrary superstring of discrete energy permittivity will as well tend to bear a higher probability of bearing both hermitian Lagrangian-based singularities and hermitian metrical-based singularities, as such a said discrete quantum of energy permittivity is to be moving over such a so-eluded-to consistent Hamiltonian-operand-based medium, over a tense of a homogeneous terrestrial-based general locus, that is to here be bearing a directoral-based angular momentum, through a discrete Lagrangian, over a discrete quantum of time.  This will then tend to mean, that such a respective superstring -- that is to be in the process of working to maintain an even tense of its directly corresponding Lorentz-Four-Contraction, will tend to bear, both less of a tendency of exhibiting Lagrangian-based Chern-Simons singularities and metrical-based Chern-Simons singularites -- as such a so-stated respective given arbitrary superstring of discrete energy permittivity is to here be in the process of differentiating in a Fourier-based manner, over the directly correlative metric in which such a superstring is being delineated through the duration of a directly corresponding sequential series of instantons.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Countering States Of Gravitational Waves

Let us take into consideration a certain condition, at which there are two different distinct given arbitrary third-order Schwinger-Indices -- these two said respective Schwinger-Indices, when individually taken in a covariant retrospect to one another, are moving towards each other with a supplemental-based helicity -- via a tense of both a codeterminable and a codifferentiable Fourier Transformation that is made of a Yukawa-based nature -- via a prevailing condition of Ward-Polarization, when this is taken at the Poincare level to the interfacing of the gauge-metrical-based Hamiltonian operation, that is involved with the interaction that is to happen -- as the two so-stated Schwinger-Indices are to act upon each other in a Gliosis-based manner, via the traversel of these so-eluded-to Hamiltonian operators that is upon the Lagrangian-based paths of their respective given arbitrary Hamiltonian-based operands.  Let us next consider in this given arbitrary scenario, that these two mentioned covariant vibrational oscillations -- that are here to be moving along the general region of the respective given arbitrary proximal locus of the directly associated Rarita Structure, are to collide upon the general group-metric, that is gauged upon both the binary-related spin-orbital and the binary-related transversel topological sways, that are related to both the overall radial and the overall angular momentum-based scalar amplitude and scalar magnitude of the holonomic substrate of those vibrational indices -- that are of a gauge-metrical-based binary tense of a converging Hamiltonian operator of a kinematic Fourier-based gauge-action. This said Fourier-based gauge-action is to happen over a sequential series of group-related instantons.  Let us next consider that, although the two said Schwinger-Indices, of this respective case -- that are to here work to bear a completely supplemental-based tense as to the helicity that is here related to the given correlative tense of Ward-polarization, is that of a completely covariant-based even chirality -- when this is taken in a direct relationship to the Hamiltonian-based eigenindices of their Yukawa-related approach, over time, but still, the so-eluded-to tense of the said Schwinger-Indices, will here, in this respective case, work to bear a completely opposite tense of both a spin-orbital-based and of a transversel-based condition of parity -- over the whole dimensional-based tense of the correlative Ward-Caucy-based parameterizations that are Yukawa to the said Schwinger-Indices, over the correlative gauging of the here correlative group-related metric.  This will then work to cause the resultant interaction of the holonomic substrate, that is of the converging binary phenomenology of disturbance in this case, that had been acting as a dual Hamiltonian operator that functioned as a dual group-attractor of vibration, to approach a proximal localization of a set conipoint in space -- at a set locus, that may be mapped along the here respective given arbitrary Rarita Structure eigenstate of this case, in so as to work to undue the vibrational oscillations that had been of the converging so-eluded-to gravity waves that had just previously been rippling along the said Rarita Structure eigenstate, -- to where, the two said kinematic-based vibrational propagations of the said Hamiltonian operators of this case, will then act in so as to cancel each other, in so as to work to elliminate the here converging dual state of a disturbance of the directly correlative mini-stringular segmentation, that will have had just worked to act as the substrate of the Hamiltonian operand that had been at the proximal locus of that topological stratum of mini-stringular holonomic substrate, that had earlier been pulled into the respective correlative kinematic interface that had here interacted at the Poincare level to  the correlative Gliosis-based topological interface, to where this will thereby work to indirectly cause an external locus of the Rarita Structure, to then subsequently work to bear an ensuing disturbance along the so-mentioned respective given arbitrary external-based topological stratum of mini-stringular segmentation -- at some ulterior general locus in space -- in so as to tend to result in a general tense of the Fourier-based conservation of the quantum scalar magnitude of the overall gravity-wave-based topological-based phenomenology, that tends to move in the direction of existing as such over space and time.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

Universal Setting As To Schwinger-Indices

If two different individually taken Schwinger-Indices work to form a helicity, that is to directly involve a supplemental eigenbase of Ward-polorization -- when this is taken in retrospect to the propagation of the so-stated Schwinger-Indices or gravity waves, in a covariant interdependence to one another over a sequential series of group-related instantons -- then, this will work to indicate that the discrete energy quanta that had worked to form the two different distinct respective given arbitrary Schwinger-Indices, are to here tend to be of the same universal setting.  Yet, if two different individually taken Schwinger-Indices work to form a helicity that is to directly involve a complementary eigenbase of Ward-polarization -- when this is taken in retrospect to the propagation of the so-stated Schwinger-Indices, or gravity waves, in a covariant interdependence to one another, over a sequential series of group-related instantons -- then, this will work to indicate that the discrete energy quanta that had worked to form the two different distinct respective  given arbitrary Schwinger-Indices are of two different universes.  Yet, if the two different individually taken Schwinger-Indices that are of such a related case scenario -- are to work to form a helicity that is to directly involve a Yukawa-based torsioning, that is of the holonomic substrate of the so-eluded-to gravity waves -- that is not Ward-polarizable at one set convergent locus as to where  the Gaussian normalization of the vibrational indices that are at the Poincare level to the interfacing of those covariant Hamiltonian-based indices -- that are Gliosis to the interaction of the eigenstates of the topological stratum that is of the said holonomic substrate, that is of the so-stated Schwinger-Indices, then, if the ordering of the chirality that is taken along the topological interfacing of the so-eluded-to Gliosis-based contact of the one tense of the Fourier-based interactive helicity of what may here be arbitrarily called the initial Schwinger-Index in this respective given arbitrary case scenario, is of an even chirality with respects to the delineation-related angle-based positioning of what may here be arbitrarily taken as the second stated Schwinger-Index of such a respective given arbitrary case, then, the directly associated discrete quanta of energy that had worked to form both of the said Schwinger-Indices, are going to tend to be of the same universal setting.  Yet, if the two different individually taken Schwinger-Indices of such a related case scenario are to work to form a helicity that is to directly involve a Yukawa-based torsioning, that is of the holonomic substrate of the so-eluded-to gravity waves -- that is not Ward-polarizatlbe at the Poincare level to the interfacing of those covariant Hamiltonian-based indices that are Gliosis to the interaction of the eigenstates of the topological stratum that is of the said holonomic substrate of the so-stated Schwinger-Indices, then, if the ordering of chirality that is taken along the topological interfacing of the so-eluded-to Gliosis-based contact of the one tense of the Fourier-based interactive helicity of what may be arbitrary called the initial Schwinger-Index in this respective given arbitrary case scenario, is of an odd chirality with respects to the delineation-related angle-based positioning of what may here be arbitrary taken as the second stated Schwinger-Index of such a respective given arbitrary case, then, the directly associated discrete quanta of energy that had worked to form both of the said Schwinger-Indices are going to tend to be of two different universal settings.  I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

Back-To-Back Changes In General Genus Of Expansion

Let us say that there was an initial substringular activity, that were to then work to cause a relatively chaotic substringular-based Rayleigh-scattering-associated implosion, that would here happen to an initially relatively organized grouping of what would here be a set of orbifold eigensets -- that were then initially harmonic in their relative delineations, as individually taken eigenindices that worked to form an initially Reimman configuration of a Majorana-Weyl-Invariant-based mode in time and space.  The ensuing so-stated Rayleigh-based implosion, that would then happen as an annharmonic scattering of an initially ordered Reimman set of orbifold eigensets -- of which, although the said annharmonic scattering were to work to pull the eigenindices of the said set of orbifold eigensets closer together, as an overall proximal localized set of Hamiltonian operators that had been put into a relative scalar magnitude of entropy, such an annharmonic scattering would tend to cause the adjacent of such so-eluded-to eigenindices to bear an odd chirality -- after the so-stated chaotic activity were to here occur.  Let us then say that there was to next off be a binary tense of a mode, as to the ensuing expansion of the Poincare-based locus of the correlative eigenmembers that had just been pulled inward in a chaotic manner -- to where this cross-product-based resulting outward thrust would be a sequence of what would first be a Clifford Expansion as to the mode of the proximal delineations of the original eigenmembers of the orbifold eigensets, of which would then move into a euclidean expansion of the so-stated original eigenmembers of the self-same orbifold eigensets, to where this works to become a back-and-forth successive series as to the mode of the expansion of what were initially the Yukawa-based existence of the eigenmembers of the said set of orbifold eigensets, by which the earlier mentioned tense of activity that had happened in so as to be caused by the chaotic implosion of the initially harmonic ordering of the eigenmembers that were of the so-stated set of orbifold eigensets, would subsequently -- via the gauge-metrical Hamiltonian operation of the said general genus -- of what would here be, in this given arbitrary case, the sequential expansion mode -- in so as to work to form what is to here become an asymptotic approach of a Reimman scattering, -- to where, although the whole initial tendency as to the gambit of each of the initially directly corresponding eigenindices of the said set of orbifold eigensets, will here not be able to, by such a said respective given arbitrary means, work to bear all of such said eigenindices to spontaneously, by this method, be able to all bear adjacent eigenmembers that would be of an even chirality -- theoretically, then, the directly correlative Njenhuis spin-orbital tensors that would here act as Li-associated oscillation-based Hamltonian operators, would here approach a closer and closer scalar amplitude as to bearing the desired perfectly even eigencondition of chirality, for all of the correlative respective eigenindices of such a case.  Yet, the covariant activity of external forces would tend to cause an impending Yukawa interaction -- that would then tend to spontaneously cause what I had just said would continue to move in the direction as to be of the given arbitrary respective case, in theory, to instead, change in its mode -- over an ensuing series of group-related instantons, -- particularly if there is a relatively transient duration into which the said set of orbifold eigensets is to be forced into a Gliosis-based contact with the Yukawa-based torsioning of external substringular forces.  I will continue with the suspense later!  To Be Continued!  Sincerely,
Samuel David Roach.

Supplemental Ward-Polarization

Let us first consider here, two different second-order light-cone-gauge eigenstates -- at which each of such said second-order light-cone-gauge eigenstates are, when individually taken, struck by a gauge-boson eigenstate, in so as to work to form a third-order Schwinger-Index -- over a discrete covariant iteration of BRST.  This would then mean, that there are here, in this specific Laplacian-based localized case of both codetermination and codifferentiation, two different distinct third-order Schwinger-Indices that are being taken into consideration here, in total, in this relative respective given arbitrary case -- that are formed by by the plucking, like a harp, of two different distinct second-order light-cone-gauge eigenstates.  This happens here, in so as to form two different individually taken distinct vibrational oscillations, that will here ripple along the Rarita Structure, in general, in so as to work at helping to form the gauge-metrical-based link between the activity of discrete quanta of energy permittivity, and, their directly associated gravitational particles, in so as to work at helping to form the interaction between discrete energy and its relationship with the fabric of space-time-bearing phenomenology.  Let us next consider that in this case, the helicity of the here given arbitrary gauge-action -- that is to be formed between the holonomic substrate of the two said Schwinger-Indices that have been mentioned in this case, were to then work to form an  ensuing Fourier-based activity -- that is of both the covariant, the codeterminable, and the codifferentiable delineation and distribution of the flow of the so-stated Schwinger-Indices -- to where this is happening, as such said vibrational-based indices are propagated along their correlative Rarita Structure eigenstates. This so-stated interaction of such a case, is to be bear a relatively proximal interface -- that is Yukawa in this case, in a supplemental-based tense of Ward polarization, over time, over the course of the directly pertinent so-eluded-to ensuing sequential series of group-related instantons.   On account of this genus of Ward-polarization,  the resultant Gliosis-based interface that is to end-up happening amongst the two here said Schwinger-Indices -- will be of a viable manner -- to where the said resulting wave-related interface, will be of a Gaussian-based nature, that will be of a covariant-based genus, that will then relate the two metrical gauge-actions, as two different Hamiltonian operators that will bear a Real Reimmanian-based spatial relationship between each other, to where this so-eluded-to Gliosis-based interaction will be of such a nature by which these will then act as being of the same universal setting.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Harmonic Versus Annharmonic Perturbations

Let us first consider a harmonic perturbation.  Such a said perturbation is here a scattering, of what would here be an initial set of relatively unorganized orbifold eigensets -- that are brought from a condition of relative disorder into a condition of relative order.  The orbifold eigensets of such a given arbitrary case, are to here be brought into a Reimman scattering, of which causes these eigensets to be brought into a condition as to having adjacent eigenindices to then bear an even chirality.  This is an example of a harmonic perturbation.  Yet, if such a Reimman scattering is perturbated out of such a harmonic condition, into an anharmonic condition -- by an ensuing Rayleigh scattering, then, the adjacent eigenindices of such an anharmonic resultant perturbation would then bear an odd chirality.
To Be Continued!  Sincerely, Samuel David Roach.

Complementary Tenses Of Light-Cone-Gauge-Based Helicity

Let us first consider here two different cites -- as to where there are two different second-order light-cone-gauge eigenstates that are each being plucked like a harp, by two different gauge-boson eigenstates -- over a covariant iteration of BRST.  Let us say that the helicity of the first respective given arbitrary Schwinger-Index -- that is formed by the plucking of its respective second-order light-cone-gauge eigenstate, is propagated at a complementary Ward-normalizable angle in retrospect to the helicity of the second respective given arbitrary Schwinger-Index -- that is formed by the plucking of its distinctly different respective second-order light-cone-gauge eigenstate -- in this given arbitrary case scenario.  Since the so-stated covariant-based Ward-normalizable angle, by which the two respective given tenses of helicity of the correlative individually taken vibrational oscillation of their respective second-order light-cone-gauge eigenstates, is of a complementary nature -- the pulsation of the vibrational effect of the one so-eluded-to tensor of Rarita Structure eigenstate will not tend to be of a Real Reimmanian nature to the other pulsation of the vibrational effect of the second so-eluded-to tensor of Rarita Structure eigenstate, of such a respective given arbitrary case.  This would then tend to make the viable gravitational effect of the first of such given arbitrary Rarita Structure eigenstates to be of a Li Algebra tensor, or, of a Njenhuis tense -- to the other of such given arbitrary Rarita Structure eigenstates.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Clifford Expansions -- The General Gist Of It

Let us here consider two different distinct given arbitrary orbifold eigensets, that begin to exist at a relatively adjacent proximal localization -- to where both of these said orbifold eigensets are initially existing in a tense of Majorana-Weyl-Invariance -- over an initial relatively transient duration of a sequential series of group-related instantons.  Let us next say that the two respective given arbitrary different distinct orbifold eigensets of such a case, are perturbated out of their initial covariant-based condition of Majorana-Weyl-Invariance -- to where the two initially so-stated orbifold eigensets are to here go from being of a proximal localized nature, in so as to being of Laplacian-based adjacent manner, into going into a divergence that happens in so as to increase the scalar amplitude as to the relative substringular distance that is to now exist between and among the two said orbifold eigensets, over a set duration of time.  Let us say, that, in the process of the so-eluded-to Cevita interaction that is to operate as a gauge-metrical Hamiltonian operator or operation -- in so as to work at causing the two so-eluded-to metrical-gauge-based Hamiltonian operators, that exist as the holonomic substrate of two distinct given arbitrary orbifold eigensets, to diverge in a space-wise manner over time -- this will happen to where the Lagrangian-based path that may be mapped-out here, in so as to work to show the manner as to how the two said metrical-gauge-based Hamiltonian operators are to move through their respective individually taken distinctly different Hamiltonian operands, to where this is to happen in both cases when taken individually as a hyperbolic path of an euler-based divergence in space, over a euclidean-based time-frame.  This general manner of divergence, is one genus as to what a Clifford Expansion of covariant localization may be -- when this is taken in consideration as to the relative divergence of two different distinct metrical-gauge-based Hamiltonian operators -- that are brought into a tense of separation, that may be mapped-out in a Laplacian-based manner, after the two said Hamiltonian operators (in this case, the two said orbifold eigensets) have differentiated in a Fourier-based manner, in so as to have gone through a relatively viable tense of both a transversal and a viable tense of a spin-orbital particle and wave-based sequential series of motions through time and space.

Cyclic Lagrangian Paths As To Stoke's Theorem

Let us say that one were to have two sets of orbifold eigensets, that keep going relatively back-and-forth from one Ward-supplemental-based flow to a relatively reversed-holomorphic Ward-supplemental-based flow -- on account of each of such orbifold eigensets undergoing a binary Lagrangian-based tense of Chern-Simons singularities, to a Njenhuis tense as to each of such orbifold eigensets as then to be undergoing a second metrical-based Ward-supplemental-based flow of a second of such binary Lagrangian-based Chern-Simons singularities, over a relatively persistent duration of group-related metric -- as a tense of a cyclic permutation that acts here as a static equilibrium of subatomic reverberation, over time.  Let us say that each directly ensuing path that is thence formed by such a respective reverberation, has a different mappable tracing of relatively Njenhuis layering -- due to the potential set of conditions that may be conceived of as by Stoke's Theorem.  Let us say -- arbitrarily -- that after 50 of the so-eluded-to back-and-forth reverberation modes, the pattern as to the mappable tracing of the layering of the so-stated Ward-supplemental-based flow is then repeated.  This will then work to cause the directly corresponding Majorana-Weyl-Invariant-Mode, that would then be directly associated with the continual repeat of the activity of a directly corresponding  antiholomorphic Kahler condition, that would then happen each time that there is the so-stated and so-eluded-to activity of what would then form as a Kahler-Metric -- to be of a tense of a set of covariant cyclic permutations that are of the directly corresponding Lagrangian-based mappable tracings, via the medium by which the so-eluded-to Hamiltonian operator as to which would here be the said orbifold eigensets, to have the Fourier-based tendency of being re-delineated through their respective Hamiltonian operands, -- in a pattern that would here work to bear a wide variety of Li-based Gaussian tensors.  As such a pattern is repeated -- the directly respective Gaussian indices as to the mappable tracing, will here tend to be more and more prone to bear a Yukawa-based contact with those ghost-based inhibitors that may work to cause a Rayleigh scattering of the correlative cyclic permutations of the directly correlative patterning of cohomological-based holonomic substrate, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely,Sam Roach.

About Certain Ward-Supplemental Lagrangians

Let us here consider two different orbifold eigensets, that have moved into such a group-related metric -- by which they will then have both worked to each bear a binary Lagrangian-based Chern-Simons singularity -- to where both of the so-eluded-to respective given arbitrary orbifold eigensets will have then acted in a Fourier-based manner -- in so as to be perturbated from their initial Hamiltonian operand, along their respective Lagrangian-based paths -- in so as to then each bear a tense of a Ward-Supplemental mappable tracing, over a group-related metric by which these two so-eluded-to orbifold eigensets will have then acted in so as to each bear an antiholomorphic Kahler condition.  Let us then say that there is then an ensuing second occurring binary Lagrangian-based Chern-Simons singularity, at a later occurring moment, that will then happen to both of the said orbifold eigensets once again.  This will then tend to cause a second tense of a Ward-Supplemental motion -- which may cause such an antiholomorphic Kahler condition -- that may or may not tend to then work to retrace the initial said Lagrangian-based path.  This depends upon what the manner of the Njenhuis tensors that act upon the two so-stated orbifold eigensets happens to be,  in each of the directly appertaining circumstances that are to be applicable here.  I will continue with the suspense later!  To Be Continued!
Sincerely, Sam Roach.

About Perturbation of Divergent Motions

Let us initially consider two different relatively adjacent orbifold eigensets that are initially divergent -- on account of the condition that these have both just undergone a covariant Hamiltonian operation, that had worked to cause the formation of a binary Lagrangian Chern-Simons singularity upon the immediate surroundings of the field-density of each of the said individually taken orbifold eigensets, over a relatively transient duration of time. In this given arbitrary respective case, this will then cause there to be the formation of at least one metrical Chern-Simons singularity to be formed at the cite of both of such orbifold eigenstates.  Let us consider that it was the interaction of one given arbitrary ghost-based inhibitor, that had acted upon the general covariant field that had worked to inter-bind the two so-stated given arbitrary orbifold eigensets of such a case -- that had here worked to cause the said initial tense of divergence that had happened upon the Yukawa field that had worked to involve the interdependent interaction of the two said respective orbifold eigensets, during that group-metric by which the two so-stated orbifold eigensets had existed in a covariant, codifferentiable, and in a codeterminable manner, over the correlative sequential series of group-related instantons -- by which the comparison may have been able to be extrapolated.  Let us next consider -- that, after an ensuing sequence of Fourier-based differentiability had worked to interplay amongst the two said orbifold eigensets, to where this is after a brief span as to after the two so-eluded-to divergent Hamiltonian operators have become mildly more separated -- in terms of the index of the scalar amplitude of their proximal localizations in correlation with one another, there is a group-attractor that were to have here acted upon the holonomic substrate of both of the so-eluded-to Hamiltonian operators, to where one is to have a set of norm-state-projections that act in a Yukawa-based manner upon the Gliosisi-based topological stratum of the two so-stated orbifold eigensets at the Poincare level -- over a sequential series of group-related instantons, by which such a so-eluded-to Fourier-based interaction will have here worked to cause the two said orbifold eigensets that had been initially of a divergent nature, to then be pulled into a genus of what is to here form a set of reversed binary Lagrangian-based Chern-Simons singularities -- to where the two initially stated orbifold eigensets are then pulled into what is instead, of a convergent sequential series of gauge-metrical Hamiltonian operation,  this of which will then tend to work at causing the two initially said orbifold eigensets to be brought back into a closer proximal localization.  This would then work to form, as well in this given arbitrary case, a reversed set of metrical-based Chern-Simons singularities.  As the two so-stated orbifold eigensets move, in so as to converge towards one another -- there will then be a tendency of there being an increased Hodge-Index of interdependent covariant field indices, that will then work to inter-bind the general cite of there convergence, If there is a relative lack of a Yukawa-based state of a perturbative quantum entanglement that is over the course of the directly corresponding sequential series of the correlative iterations of BRST, --  in which the activity of such a metrical-based convergence is to happen in a time-wise manner.  I will continue with the suspense later!  To Be Continued!
Samuel David Roach.

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 Info As To Adjacent Electrons

Electrons exist in d-fields -- of which exist in a Fourier-based manner, in at least 6 spatial dimensions plus time.  Photons exist in p-fields -- of which exist in a Fourier-based manner, in at least 10 spatial dimensions plus time.  Any hermitian-based flow of the spinning motion of a particle that would here exist in a Fourier-based manner in 6 spatial dimensions plus time, will tend to often bear a change in the sixth derivative as to the Ward-Derichlet conditions of the perturbative tense of the overall directoral-based discrete momentum, that is of that said given arbitrary respective particle.  This means that any given arbitrary electron, that is differentiating as a Hamiltonian operator in a Fourier-based manner, in such a way in so as to be of a Yau-Exact manner -- which would then be as a hermitian particle -- this will then tend to bear an overall directoral-based discrete momentum, that will then often tend to change in the sixth derivative as to the Ward-Derichlet conditions of the perturbative tense that is of that so-stated electron, over time.  When an electron undergoes the Fujikawa Coupling, which happens via the Green Function -- which is as is according to Chan-Patton rules -- it will then form a photon, and, a photon exists in a p-field -- this of which exists in a Fourier-based manner of which exists here in at least 10 spatial dimensions plus time.  Let's say that an electron is differentiating in a Fourier-based manner -- by such a means that would here work to involve, in this case, a condition of only two genre of dimensional-based tensors -- in such a manner to where a discrete increment of the kinetic energy of that so-stated given arbitrary electron, would then exist in eight spatial dimensions plus time -- immediately before it is to go through the respective said eigenmetric of the said Fujikawa Coupling, -- then, as the so-stated discrete increment of kinetic energy that is being released from the said electron, is going through the so-stated process of the respective eigenmetric of the Fujikawa Coupling, which is at that inferred general locus in the substringular in which the so-eluded-to discrete increment of quantum energy is here being converted into a photon -- there will then tend to be a binary Lagrangian-based Chern-Simons singularity, that would then be formed in the process of the said eigenmetric of the here proximal localized activity in which the Fujikawa is to here be happening at.  This process works to cause any given arbitrary respective photon -- that is formed by the process of any given arbitrary respective electron that has here just dropped an energy level -- to tend to be pulled-out of the Ward-Neumman bounds of the respective atom in which such a discrete increment of the kinetic energy of an electron is converted into a discrete quantum of electromagnetic energy.  This is indirectly why there is the Chan-Patton-based condition, that electrons that are adjacent must always bear an assymetric spin -- in order for such electrons to not totally impede upon each others space.  This latter point is the Pauli-Exclusion Principle.  I will continue with the suspense later!
Sincerely, Samuel David Roach.

Diverging Orbifolds Of Two Different Covariant Doubolt Cohomologies

Let us here consider two different covariant cohomologies, that are initially kinematic in so as to be differentiating in a Fourier-based manner -- as two different Ward-Caucy-based Hamiltonian operators, that are being delineated per each successive iteration of group-related instanton, as quanta that act as parallel moving phenomenology of holonomic substrate that are relatively adjacent, that are initially working to form two distinct Rham cohomologies that are of the same universal tense of Gaussian-based spaces, over a relatively transient duration of time.  Let us next consider the condition -- that, there is a set of two different respective ghost-inhibitor eigenstates, that work in so as to pull both of the so-stated Rham cohomologies of this given respective arbitrary case, into each of such ghost-based patterns, to where these are then working to bear a change in their respective Ward-Derichlet-based derivatives in two more of such derivatives than the number of spatial dimensions that each of such Gaussian-based orbifold eigensets were moving in, when this is taken immediately prior to the so-eluded-to Cevita interaction that would have here worked in so as to help at forming the so-eluded-to Lagrangian-based Chern-Simons singularities -- that would here work to form at least one metrical-based Chern-Simons singularity, for each of such orbifold eigensets, as well in this respective given case.  In so long as the gauge-metrical Hamiltonian operation that would have here worked in so as to form the Cevita-based Chern-Simons singularities, does not cause the two so-stated orbifold eigensets to approach each other, over time, in a spontaneous manner (if by such conditions as I have stated alone), then, the so-eluded-to set of Chern-Simons singularites that would have then be formed by the Fourier-based activity of the two said orbifold eigensets, would then tend to work to cause the holonomic substrate of the phenomenology of the two said orbifold eigensets to bear a euler-based curvature -- that would then work to cause the spatial entities that are here of the two individually taken orbifold eigensets, to at least temporarily result in forming a divergent set of two different sets of superstrings that operate in so as to perform two different respective corresponding functions in the substringular.
I will continue with the suspense later!  To Be Continued! Sincerely, Sam Roach.

Euclidean Expansion Versus Clifford Expansion

Let us initially take into consideration, a set of five orbifold eigensets -- that are initially localized in a proximal-based general region that is in the substringular.  Let us next consider the Ward-Caucy-based condition of all five of such orbifold eigensets -- as initially existing in a tense of Majorana-Weyl-Invariance, at a relatively set general locus -- over a duration that would here involve a relatively transient sequential series of group-related instantons.  Let us next consider the given arbitrary condition of such a case -- to where the said set of eigensets will have here worked to bear the Laplacian-based condition of having one central orbifold eigenset, that was to here be surrounded by the other four of such so-eluded-to orbifold eigensets, as may be extrapolated here in the said relatively transient sequential series of group-related instantons.  Let us say that a group-attractor were to act upon the so-stated set of external-based orbifold eigensets of this respective given arbitrary case -- in so as to cause the four said orbifold eigensets that were said to initially surround the so-stated central orbifold eigenset, to be then perturbated from being adjacent to the said central orbifold eigenset of such eigensets, -- in such a manner in so as to cause the so-stated surrounding orbifold eigensets to diverge in a covariant-based manner, away from the central said orbifold eigenset, over a relatively transient duration of time.  Let us next consider, that the Hamiltonian-affiliated Lagrangian-based path of the four so-stated diverging orbifold eigensets, were to each, when this is individually taken, be translated along the so-eluded-to Hamiltonian operand -- in which these said eigensets are to here be moving through, to where this will be of a mappable tracing -- that is here to be translated as a unitary gauge-metrical Hamiltonian-based operation, that is to here be differentiating in a Fourier-based manner, over time.  One could then say that the expansion of the scalar magnitude of the region that would then exist, that is of the then diminishing scalar amplitude of the field that may here be extrapolated by the respective given arbitrary ever weakening coniaxial, that had initially worked to join the five said orbifold eigensets, that could be traced among the interdependent field that would here work to interconnect the interactions that would then exist among the eigenindices that would act in so as to work to form the five so-stated orbifold eigensets, would be an expansion that could be considered as increasing in its scalar magnitude in a euclidean-based manner over time.  Soon -- a similar example, yet, instead, as a description of a Clifford Expansion.  I will continue with the suspense later!
To Be Continued!  Sincerely, Sam Roach.

Tendency Of Genus Of Lagrangian-Based Flow

When any given arbitrary orbifold eigenset is moving -- in whatever the general tendency of holomorphicity as to the directoral-based flow of its integrative eigenindices happens to be moving through, as a Fourier-based Hamiltonian operator that is being delineated in a kinematic manner, over time, the tendency of its motion will be in so as to move through its respective given arbitrary Hamiltonian operand -- in a best-fit mean Lagrangian path.  So, if an orbifold eigenset is initially moving in the relative forward-holomorphic direction, in a best-fit Lagrangian path -- as it is moving through its respective correlative Hamiltonian operand, over the so-eluded-to directly corresponding group-related metric, while then its Lagrangian-based delineation is to all of the sudden spontaneously alter -- in so as to work to form a Ward-supplemental shift in its homotopic covariance, in so as to cause the said orbifold eigenset to then reverse its general tendency of holomorphic-based flow, as a Hamiltonian operator that is to then bear an antiholomorphic Kahler condition -- then, as the so-stated orbifold eigenset is reversed in so as to the relative direction that is to here be considered as the relative holomorphic direction, the general directoral-based flow of the mappable tracing, as to what is now to be the extrapolatable best-fit mean Lagrangian-based path -- will then, in general, be of the reversal of the initial mapping of the holomorphic-based flow of which the so-stated orbifold eigenset had initially worked to bear, before the so-eluded-to Chern-Simons singularities that may be attributed to the reversal of the Fourier-based motion of the said orbifold eigenset, were made Yukawa to the Gliosis-based topological stratum of the so-stated orbifold eigenset -- that would here be at the Poincare level to the core-field-density of the said orbifold eigenset.  I will continue with the suspense later!  Samuel Roach.  To Be Continued!