As To The Poisson Integral

When one is to have two adjacent waves, that are being physically delineated in a common manner of holomorphicity -- then, one is to then be able to integrate the phase exchanges that are to here exist among the two said waves -- in so as to form a Laplacian-based potential overlapping of the topological holonomic substrate of the phenomenology of the two said wave-based patterns, when in terms of the mappable tracing of the entity that may be utilized here, in so as to be an extrapolation of as to how the two said waves are to here then be made in equivalence to each other.  Such a so-stated integral, that I have just here described, in so as to make the two said adjacent waves of a common holomorphicity, equal -- is a manner as to here working to describe what may be called in general, a respective given arbitrary example of what acts here as the Poisson Integral. Next, consider with me an example as to there being the arbitrary existence of two different Njenhuis waves, that are adjacent, yet, are moving in a common manner of holomorphicity, in one manner or another.  Let us say that one were to then utilize an Imaginary-number-based integration of the phase exchange that is to here exist among the two waves, that I have just mentioned in this second so-stated example, in the substringular.  Let us here consider in this given arbitrary case, that the Imaginary-number-based integration of the said phase exchange that I have just mentioned here, is to make the two so-stated waves of this second said example, to then be of the same Laplacian-based topological-based stratum of holonomic substrate of wave-based phenomenology.  One may then call this second so-stated integration of phase exchange, to be a usage of what may be called a Njenhuis-based Poisson Integration.  Such a Njenhuis-based Poisson Integral may be extrapolatable, when in terms of working to determine a mean field oscillation -- that would exist as a common ground between two waves of two respective different universal settings.  The field density of such a common wave-based stratum -- that would here work to strattle between two different universal settings -- would then tend to work to bear a Li-Algebra-based Rarita-Index, that would work to bear a set of complex Gaussian roots -- in so as to form an interdependence of the predominant universal setting of such a given respective case scenario, with the less predominant universal setting of this self-same case scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Part One of Session 12 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

A Yang-Mills light-cone-gauge topology is, by definition, a non-abelian light-cone-gauge topology.  A Yang-Mills or a non-abelian light-cone-gauge topology, works to bear -- along the topological surface of each of the individually taken second-ordered light-cone-gauge eigenstates, that work to comprise any one given arbitrary respective first-ordered light-cone-gauge eigenstate -- chord-like segmentation, that exists in a Laplacian-based manner, that has the characteristic of having 60 sinusoidal affiliated loops (60 peaks and 60 troughs) that are then formed, along the so-stated topological surface of the said second-ordered light-cone-gauge eigenstates -- during the multiplicit gauge-metric that is to occur, that happens over the directly pertinent sub-Fourier-based activity of BRST.  During the so-eluded-to iteration of BRST, when such so-stated sinusoidal loops are to exist in a Laplacian-based manner, during the respective majority of one iteration of instanton -- the directly affiliated gauge-bosons will then work to "pluck" the directly associated second-ordered light-cone-gauge eigenstates, at the correlative peaks of harmonic disturbance, of each of the so-stated sinusoidal-based topological holonomic substrate, in so as to work to form the directly associated third-ordered Schwinger-Indices.  (Such a disturbance, will be consistently at either the relative "peaks" or at the relative "troughs" of the said sinusoindal waves -- at one respective given arbitrary cite of a correlative second-ordered light-cone-gauge eigenstate -- depending upon where the peak of the harmonic disturbance is at, along the topological surface of the directly pertinent said light-cone-gauge eigenstates.)  Often, as a phenomenology that works to bear a Yang-Mills light-cone-gauge topology, is to exist in a tense of relative conformal invariance, such a correlative tense of a light-cone-gauge eigenstate will then tend to work to bear a tense of a set of Gaussian-based Ward-Caucy conditions -- that are supplemental to the Gaussian set of Ward-Caucy-based conditions that would exist for a phenomenology that would otherwise be of a Kaluza-Klein light-cone-gauge topology.  This is because a Kaluza-Klein topology is of an abelian light-cone-gauge topology, while a Yang-Mills topology is of a non-abelian light-cone-gauge topology.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Field Density

The field density of the metrical-gauge-based Hamiltonian operators -- that are of the discrete energy quanta of the holonomic substrate, that is of the key substringular phenomenology-based entities, that come together in a Yukawa-based manner and /or quantize into an interdependent manner -- in so as to work o form both the covariant, the codeterminable, and the codifferentiable intertwining of discrete integrable energy, more often than not, -- work to bear a relatively inter bound inter-relation of the genus and/or the tense of the nature, as to what the manner that is of what comprises the field density of discrete substringular phenomenology.  Substringular fields are comprised of the phenomenology, that is basically made-up of zero-norm-state-based projections.  Zero-Norm-State-Projections are basically the holonomic substrate-based compositions, of what may act here as both the Laplacian-based and the Fourier-based phenomenology of bear mini-stringular segmentation.  Mini-Stringular segmentation, in general, is the 10^(-129) of one meter cross-sectional thick chord-like appendages, that come into play in the interconnections that exist in the interrelations among first-ordered point particles and/or second-ordered point particles with other first-ordered point particles and/or second-ordered point particles, over any directly corresponding Laplacian and/or Fourier-based transformation.  The multiplicit interbinding that is caused by both the Laplacian and the Fourier-based differentiation, that is of the so-stated bear mini-stringular segmentation that I have here stated, that works to form substringular fields -- is the main metrical-gauge-based general genus of Hamiltonian operator, that works to both imbue and/or retie the fabric-based interconnections that exist in the space-time-fabric that exists in the substringular.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To The Details Of The Regge Action

Let us here consider a superstring, that is in the process of undergoing the Kahler-Metric -- over a relatively transient sequential series of iterations of group-related instantons, at a relatively set Majorana-Weyl-Invariant mode -- that is to happen here as a Fourier-based translation of metrical-gauge-based Hamiltonian operators, that act here over time.  Let us particularly here, consider the "heart" of the Yukawa-based interaction, that is of the Fourier-based involvement of the directly corresponding  Kahler-Metric with the so-stated superstring of discrete energy permittivitiy -- that is effective in this given arbitrary instant under consideration.  This would then be the general particular case, of as to when the so-eluded-to discrete energy quantum of energy of such a said case, is in a Gliosis-based tangency with the directly corresponding holonomic substrate of the Klein Bottle eigenstate.  Such a so-eluded-to eigenstate of the holonomic substrate of the said Klein Bottle,  that will here tend to work to move in a kinematic manner, over such a definitive portion of such a so-eluded-to portion of the Kahler-Metric -- will then tend to happen in such a manner, in which the said Yukawa-based interaction, that has been so-inferred in this case, is to be of a sequential series of those so-eluded to direct contacts of the said superstring of discrete energy permittivity, with the respective given arbitrary Klein Bottle eigenstate.  Over the course of one single iteration of group-related instanton -- in which the so-stated superstring of such a case has just directly interacted with the said holonomic substrate of the so-stated Klein Bottle eigenstate, of which will occur for (2pi-6)/2 of one Planck instant of Real Reimmanian time, right after the directly corresponding iteration of the correlative associated iteration of BRST -- the remaining (2pi-6)/2 of one Planck instant of Real Reimmanian time, that is to directly ensue from that gauge-metrical activity that is of one Gliosis-based interaction of the said superstring with the said Klein Bottle eigenstate, is to be of the involvement of the so-stated superstring with the sub-Fourier-based activity of the directly corresponding iteration of one Regge Action eigenstate.  When the Kahler-Metric is to be directly involved with the kinematic activity of a suiperstring of discrete energy permittivity -- right after the Gliosis-based contact of the said superstring with the said Klein Bottle eigenstate -- the said superstring will then tend to move at 45 Ward-Caucy-based degrees, in such a manner to where the superstring will here go from a condition of complete compactification to a condition of complete decompactification, in so as to go into such a Laplacian-based condition in so as to be redyed for the generally unnoticed or Njenhuis duration of Ultimon Flow.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

About The Entry Of Discrete Energy Quanta Into Klein Bottle Eigenstates

Let us initially consider a superstring of discrete energy permittivity, that is inextricably bound to its directly corresponding counterstring that is at its relative forward-holomorphic side, -- and with its directly corresponding first-ordered light-cone-gauge eigenstate and its correlative Fadeev-Popov-Trace eigenstate, that are here being positioned just to its relative reverse-holomorphic side -- during the course of one specific given arbitrary iteration of BRST, of which is happening over a substantiable portion that is of the most part of a respective given arbitrary iteration of instanton, that is at a set locus in the substringular.  As the so-stated superstring of such a case is decompactified to the inverse of the scalar magnitude of its directly corresponding Lorentz-Four-Contraction -- the directly affiliated counterstring, that is of what mainly acts as the wave-based characteristic of the said discrete energy permittivity-based quantum -- is decompactified over the course of the respective eigenmetric of the Polyakov Action, as its directly associated superstring that mainly acts as the pointal-based characteristics of the said discrete energy permittivity, is working to bear its Laplacian-based condition over the respective given arbitrary iteration of BRST that I am here working to describe in this case scenario.  If any given arbitrary discrete quantum of energy is to then be undergoing what is known of as the Kahler-Metric -- over the course in which the said respective given arbitrary discrete energy is in the need of re-attaining those fractals of discrete energy that the said discrete energy quanta need -- in order for the said discrete energy quantum to both exist and persist as discrete energy, -- the discrete energy of such a given arbitrary case, will, right after a correlative iteration of BRST, fall into a proximal localized eigenstate of the holonomic substrate of a Klein Bottle eigenstate.  As the said discrete quantum of energy is to here be pulled into a proximal localized Klein Bottle eigenstate -- the directly associated superstring and its counterstring will then have its correlative Polyakov Action-based scalar magnitude of its correlative tense of decompactification, to be undone -- in the process of going into its entry upon the Gliosis-based bounds of the so-stated holonomic substrate of the said Klein Bottle eigenstate, that I have here inferred.  The discrete energy -- during the directly associated eigenmetric of the Kahler-Metric, will spend (2pi-6)/2) of a Planck-Bar affiliated duration of metric -- in the Ward-Neumman bounds of the said Klein Bottle eigenstate -- right after the initial 6 Planck-Bar duration of the generally noticable span of the directly corresponding period, in which the respective given arbitrary discrete energy were to be iterating in both the simultaneous Polyakov Action and the Beti (Bette) Action, that had happened during the so-stated iteration of BRST that is thus differentiable upon -- over the course of all but (2pi-6/2pi) of the whole duration of the so-eluded-to iteration of such a respective given arbitrary sub-Fourier-based translation of instanton.  (This is via the vantage-point of a central conipoint.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Altered Cohomologies

When one is to have a given arbitrary orbifold eigenset, that is only curved to both the scalar amplitude and the manner in which the proximal localized space-time fabric is to curve in the Lagrangian-based path of its correlative Hamiltonian operation, over time, to where such a said orbifold eigenset is to then be pulled into the respective condition of going from bearing exclusively both Lagrangian and metrical-based hermitian singularities -- into bearing the condition of then working to bear either Lagrangian and/or metrical-based Chern-Simons singularities, -- this will then work to cause the mappable tracing that is of the correlative directly corresponding cohomology, that may be then extrapolated from the so-eluded-to physical memory as to the when, where, and how that the superstring had just previously differentiated at as a kinematic metrical-gauge-based Hamiltonian operator, -- to where this will then go from an initial set of integrated ghost-bases indices that are potentially set in what may here be thought of as a Rham cohomololgy, into such a change by which it is then to be of a mappable tracing that is to be of what may be thought of here as a given arbitrary Doubolt cohomology.  To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

The Higgs-Landau Action

The Higgs-Landau Action is that multiplicit eigenmetric -- in which the correlative and respective Landau-Gisner Action, acts in a Fourier-based manner, in so as to operate  upon that directly corresponding eigenstate of the Fischler-Suskind Mechanism, by which the directly corresponding Higgs Boson eigenstate is guiding the directly corresponding holonomic substrate of the Klien Bottle eigenstate, in so as to work to pull the so-stated holonomic substrate of the said respective Klein Bottle eigenstate into the Kahler-Metric -- so that those discrete quanta of energy that are in the need of being able to re-attiain their fractals of discrete energy quanta, are thus able to go about this said process -- so that the needed Gaussian translations that need to be achieved, are then put into the process of then being achieved.  This works to not only allow for the re-attainment of the needed fractals of energy quanta to be re-attained, so that discrete energy may both persist and exist -- yet, this process also works to help in the Fourier-based activity that is needed, so that the multifarious differential geometries that are proximal localized to the multiplicit cite of the Kahler-Metric, may be able to better orientate into a condition of a more stable morphological-based setting.

Ellongated Versus Attenuated Pulsation

Let us say that one was to be considering -- in a specific given arbitrary case scenario -- an orbifold eigenset that was to here be moving in a Fourier-based manner, in what is to here be taken as the relative forward-holomorphic direction.  Let us next say that there is, all of the sudden -- an external force that is to here exhibit a relatively mild scalar amplitude of an antiholomorphic-based wave-tug/wave-pull, that is to then happen to work to cause an elongation of the pulsation of the initially so-stated orifold eigenset.  This  would, in this particular respective given arbitrary case, tend to cause an acceleration of the pulsation of the said given respective orbifold eigenset in question.  As a second case -- let us say that one is to here be considering an orbifold eigenset that is, as well, moving in the relatively forward-holomorphic direction -- except that there is, instead, an external force that is to here exhibit a relatively mild scalar amplitude of a holomorphic-based wave-tug/wave-pull, that is to then happen to work to cause an elongation of the pulsation of the second so-stated case scenario of an orbifold eigenset.  This would, in this particular respective given arbitrary case, tend to cause a deceleration of the pulsation of the said given respective orbifold eigenset in question.  Let us next say that one was to here be considering two other case scenarios, that are of two different individually taken orbifold eigensets -- that are to here, as well, be moving in what may be considered in this case, as the relatively forward-holomrphic direction, -- the first of these last two cases is to here involve an external force that is to here be working to form a relatively mild scalar amplitude of an antiholomorphic-based wave-tug/wave-pull, that is to work to cause an attenuation of the pulsation of the general case of this general genus of such an orbifold eigenset, and the second of these last two cases is to here involve an external force that is to here be working to form a relatively mild scalar amplitude of a holomorphic-based wave-tug/wave-pull, that is to work to cause an attenuation of the pulsation of the general case of this general genus of an orbifold eigenset.  The relatively mildly antiholomorphic pulled orbifold eigenset that is to be attenuated here, will then tend to be decelerated in the process of the so-eluded-to directly corresponding Fourier Transformation -- while, the relatively mildly holomorphic pulled orbifold eigenset that is to be attenuated here, will tend to be accelerated in the process of the so-eluded-to directly corresponding Fourier Transformation.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

A Little About A Rebounding Orbifold Eigenset

Let us consider here an orbifold eigenset, that is to rebound from off of a relatively superconformally invariant set of orbifold eigensets -- to where this latter mentioned set of orbifold eigensets is to be in a proximal localized state of static equilibrim, that is at the Poincare level to the cite where the said initial orbifold eigenset is to collide with the so-stated Majorana-Weyl-Invariant associated set of orbifold eigensets.  Such a so-eluded-to collision will tend to cause the rebounding orbifold eigenset of such a given arbitrary case, to accelerate into a relatively reversal of its initially so-eluded-to holomorphic direction that it was initially traveling through -- via the relative reversal of its Lagrangian-based path, through a relative reversal of its projection upon its directly corresponding Hamiltonian operand, over the immediately ensuing sequential series of group-related instantons.  Such a so-stated acceleration in the Fourier-based motion of the initially said orbifold eigenset, will tend to accelerate the pulsation of the said respective eigenset -- to where there will consequently be the formation of a set of either Real Reimmanian and/or Njenhuis-based metrical-based Chern-Simons singularities.  This case scenario will tend to be of the Fourier-based activity, that is of the rebounding of one mass-bearing orbifold eigenset that is to interact here upon a more stationary and larger set of mass-bearing orbifold eigensets.  Such a so-eluded-to collision of two different masses, will tend to form a friction that will work to produce heat energy -- that will be transferred, at least in part, upon both of the so-eluded-to sources of mass-bearing holonomic substrate of metrical-gauge-based  Hamiltonian operation.  This will then tend to result in a source that, as well, will then work to form a Calabi-Yau interaction upon both of the so-stated sources of mass-bearing Hamiltonian operators of a metrical-gauge-based physical phenomenology.  Such a spurious formation of metrical pulsation, will then tend to form a spontaneous and eventual ebbing -- that will go into a gradual attenuation of the initial acceleration of pulsation -- due to the condition that physical phenomenology tends to go into the direction of optimum rest.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

A Little Bit As To Substringular Harmonics

The harmonics mode of the vibrational oscillation of a superstring -- during the generally noticed duration of instanton -- is related to the format of its spin. For example, if a superstring bears a harmonic mode during BRST, then, the said superstring will be said to have a whole spin. Yet, if a superstring bears an anharmonic mode during BRST, then, the said superstring will be said to have a fractional spin. Bosonic superstrings are closed strings. Closed superstrings that are not heterotic, are two-dimensional superstrings. Fermionic superstrings are open strings. Open strings are one-dimensional superstrings. Fermionic superstrinigs bear an anharmonic mode of vibrational oscillation, when in terms of the pulse of their spin-orbital indices during BRST. Fermionic strings are said to have a fractional spin. Bosonic superstrings bear a harmonic mode of vibrational oscillation, when in terms of the pulse of their spin-orbital indices during BRST. Bosonic strings are said to have a whole spin. During the generally unnoticed duration of Ultimon Flow, fermionic superstrings bear a harmonic mode of vibrational oscillation, when in terms of the pulse of their spin-orbital indices over the period of the said general format of duration mentioned here in this sentence. Also, during the generally unnoticed duration of Ultimon Flow, bosonic strings bear an anharmonic mode of vibrational oscillation, when in terms of the pulse of their spin-orbital indices. Superstrings, though, have more to do with the angular momentum of discrete energy, while, their directly corresponding Fadeev-Popov-Trace eigenstates have more to do with the spin-orbital momentum of discrete energy. Superstrings are discrete quanta of energy permittivity, while Fadeev-Popov-Trace eigenstates are discrete quanta of energy impedance.  Yet, to some extent, every physical phenomenon bears at least some sort of angular momentum, and every physical phenomenon bears at least some sort of spin-orbital momentum. Both superstrings and Fadeev-Popov-Trace eigenstates have more to do with the pointal-based nature of discrete energy than of the wave-based nature of discrete energy.  However -- the directly corresponding counterstrings of discrete energy have more to do with the wave-functionability of energy permittivity, while the directly corresponding first-ordered light-cone-gauge eigenstates, when taken individually, have more to do with the wave-functionability of discrete energy impedance.  The drive of a phenomenon through a directoral-based Lagrangian, is the general operation of a tense of angular momentum. The shaking-like wave-tug/wave-pull of a phenomenon through a directoral-based Lagrangian -- is the general operation of a tense of spin-orbital momentum. The angular momentum of superstrings, and, the spin-orbital momentum of Fadeev-Popov-Traces -- works to relate the basis as to how the various spaces and sub-spaces of the substringular inter-relate, while, the spin-orbital momentum of superstrings and the angular momentum of Fadeev-Popov-Traces -- works to relate the basis as to the covariant-based parity that exists among the various spaces and subspaces in the substringular. Again, superstrings are discrete units of energy permittivity, while, Fadeev-Popov-Traces are discrete units of energy impedance. Hold onto your hats, and, I will continue with the suspense later! Sam Roach.

Part Two Of Convergence Upon Hermicity

Let us initially consider a superstring of discrete energy permittivity, that is consistently working to bear a basically similar scalar amplitude -- as to both the degree and the manner of its directly corresponding Lorentz-Four-Contractions.  Over the course of each succeeding iteration of BRST, the directly corresponding eigenstate, as to the correlative successive series of the iterations of the given arbitrary tense of the correlative Polyakov Action -- works to consequently work to form an euler or exponential tense of an iterative genus of a Clifford Expansion -- that bears one general tense of an operational function, in so as to work to help to bring those correlative Lagrangian-based Chern-Simons singularities that are to here tend to be form in any of such a case, as to when there is a set of perturbations in the delineation of the Hamiltonian-based angular momentum indices of the successive pattern of the reiterative tense of the superstring in question, over both the manner and the magnitude of the cohomological mappable tracing that is of the so-stated genus of the successive physical memories of the projection of the trajectory of what is here to be considered as the "overall" Fourier-based re-distribution-based index of the correlative core-field-density that is of the so-eluded-to kinematic eigenbase of the said superstring.  This is to where, when this is as taken from an exponentially taken externalized Polyakov-based field -- as taken from being at a general covariant-based field that is propagated from a localized field that is considered here as being of a Ward-Neumman field, that is physically placed in a Laplacian-based manner from being away from the Gliosis-based topological region of the so-eluded-to core-field-density of the said respective initially considered Polakov field -- to where this will then tend to here work, in so as to help to form a tendency of working to bring the so-eluded-to homotopic residue that is thus formed -- towards a localized region that is to move in the resultant direction of both a condition of optimum rest and a condition of an increased tense of homotopy.  This Fourier-based process of the interdependent covariant-based forces, that appertain towards a condition of increased  homotopy -- works in so as to act in such a manner that tends to propagate into a tense of working to "unitize" the so-eluded-to Lagrangian-based Chern-Simons singularities, that were to here have initially formed by the condition of one or more changes in the derivatives to have here happened, than the number of spatial dimensions that are here being traversed, in such a motion that happens via the holonomic substrate of the correlative Hamiltonian operand -- to go into a converging pattern, that acts in so as to cause the so-eluded-to externalized field, that is proximal localized from the exterior framework of the Ward-Neumman bounds of the so-stated Polyakov field -- in such a manner that acts in so as to move in the direction of this, in so as to tend to work towards a convergence of the activity of the so-eluded-to said respective homotopic residue, to go into a more hermitian-based nature, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Convergence Upon Hermicity

Let us initially consider a superstring of discrete energy permittivity, as it is undergoing the Polyakov Action during an individual iteration of BRST.  Let us next say that the said respective given arbitrary string, is in a condition of a terrestrial-based rest -- to where it is fully decompactified, or, in other words, the so-stated respective superstring works to bear no affective scalar magnitude of a correlative Lorentz-Four-Contraction to be interactive upon the topological stratum of its holonomic substrate, during the said iteration of BRST, during an individual iteration of instanton.  Due to the so-stated condition of complete decompactificaction -- the relative scalar amplitude of that general genus of a Clifford Expansion that is to be directly associated with what is here to be a "maxed-out" tense of an eigenstate of the Polyakov Action, will bear a heightened tense of an euler expansion of the so-eluded-to influx of mini-stringular segmentation, that is to here be fed into the directly corresponding light-cone-gauge eigenstate, that is of the wave-based characteristic of the discrete quantum of energy impedance that is here most directly correlative to the so-stated superstring of discrete energy permittivity, that is being discussed in this particular case.  The Fourier-based activity that is most directly associated with the perturbation of the Lorentz-Four-Contractions that are effectual upon the topological stratum of the holonomic substrate of a discrete quantum of energy, will tend to propagate into a condition of a Lagrangian-based Chern-Simons set of singularities -- over the course of a correlative sequential series of instantons, when the interdependent interactions of discrete quanta of energy -- that are to here be considered as acting upon each other, is to take its natural course, over time.  The euler of the natural log of any respective given arbitrary specific variable will be the variable itself.  So, let us think of what may here act as Lagrangian-based Chern-Simons singularities -- that may be formed by a "spike" in the cohomological mappable tracing of a superstring, that has just acted in so as to alter in one more derivatives than the number of spatial dimensions than its is to be moving through -- at a respective Laplacian-based instant under consideration.  Such a singularity may be of either a relatively infinitesimal value, Or, such a singularity may be of a relatively infinite value -- given the specifics of the given arbitrary substringular situation.  The negative of the limit of the natural log of a value that is here to be approaching zero from a positive attribute to a negative attribute, is the negative of negative infinity, or, in other words, this would be infinity.  The euler of zero is one.  So, the substringular tendency of the hyperbolic Clifford Expansion, that is of the general field of the multiplicit light-cone-gauge eigenstate -- that is of a scalar amplitude that is correlative to both the degree and the manner of the given arbitrary decompactification that is here to happen over the course of any individually taken eigenstate of the correlative Polyakov Action -- works to act upon whatever the predominant proximally local homotopic residue happens to be acting as, in the general substringular region, in so as to work to help in causing the correlative Lagrangian-based Chern-Simons singularities -- that are to here act upon the general topological locus, to be kept within the Ward-Caucy-based limits of the condition of what may here be termed of as Cassimer Invariance.
Again, Cassimer Invariance is the perpetual tendency of substringular phenomena to interchange eigenstates in so as to maintain homotopy, per instanton.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

The Holonomic Substrate Of The Light-Cone-Gauge

Let us consider in this case, the light-cone-gauge topology that is directly associated with a fully uncontracted mass-bearing superstring of discrete  energy permittivity.  The topology of such a given arbitrary superstring, if of a Noether-based flow, will be one in which the light-cone-gauge is of a Kaluza-Kleiln-based nature.  A fully uncontracted mass-bearing superstring, will be fully decompacitified -- to the inverse of the scalar amplitude as to to how such a string is here to be fully uncontracted, over the course of a directly correlative iteration of BRST -- when such a superstring is to behave as I have here so-eluded-to.  Since the light-cone-gauge topology of such a superstring is of a Kaluza-Klein-based nature -- the inter bound twining of the mini-stringular segmentation -- that is utilized here in so as to work to form the so-eluded-to second-ordered light-cone-gauge eigenstates -- will bear a relatively supplemental Laplacian-based delineation, during the course of the respective directly associated duration of BRST, in which such a mass-bearing superstring is to be undergoing such an iteration of a Noether-based flow, during one given arbitrary individual setting of a group-related instanton.  As the respective superstring of discrete energy permittivity is undergoing a given arbitrary metrical eigenstate of the Polyakov Action -- its directly correlative second-ordered light-cone-gauge eigenstates, that are here to be directly associated with the quantum of the respective superstring's discrete energy -- will have a certain scalar amplitude of an incoming mini-stringular segmentation, that is to here be fed into the Ward-Caucy bounds of the proximal localization where the correlative superstring is to be iterating at --  in such a manner that is needed, on account of the condition that the correlative superstring is to here be undergoing the process of bearing a "maxed-out" decompactification, that is of the so-eluded-to superstring's length and mass, that will work to then bear a core-field-density of the fields of the directly associated second-ordered light-cone-gauge eigenstates, of which  is here to then be undergoing a Clifford Expansion upon the holonomic substrate of its directly affiliated so-stated second-ordered light-cone-gauge eigenstates' topological stratum.  The process in which the Polaykov Action works to decompactify the length and the mass of a mass-bearing superstring of discrete energy permittivity, is to the inverse of what we normally think of what is considered here as to being the tense of a superstring's Lorentz-Four-Contraction.  I will continue with the suspense later!  To Be Continued!  Samuel David Roach.

Specific Genus Of A Special Case Scenario

Let us consider a given arbitrary initial case of an orbifold eigenset -- that is moving through what is to here work to form an initial Rham cohomological mappable tracing -- in such a manner, to where the actual path of the said orbifold eigenset in question is to here be moving through its directly corresponding Hamiltonian operand -- via the so-eluded-to initial tense of what is to here be the mappable tracing of a discrete unitary Lagrangian path, in which the so-eluded-to set of superstrings that are to here operate in so as to perform one specific function, is to be moving through -- as the so-stated orbifold is to here be differentiating in a Fourier-based manner, as it is being kinematically propagated as a metrical-gauge-based Hamiltonian operator, that is being delineated across what is to here be a relatively limited field transmitance, a group metric that is here to be over a relatively transient sequential series of iterations of group-related instantons.  As the said orbifold eigenset is to then collide with a relatively steady-state tense of a codifferentiable set of orbifold eigensets -- this set of codeterminable orbifold eigensets, of which are to here exist in a relatively higher scalar amplitude of a Majorarna-Weyl-Invariant-Mode, -- when this is taken in terms of the field-density of superstrings that are to be collided into by the initially stated orbifold eigenset -- to be of a relatively more stable tense or genus of a conformally invariant mode -- to where the initial Fourier-based activity of the Gliosis-based contact of the initially said orbifold eigenset with the second so-stated set of orbifold eigensets, will tend to work to form a relatively mild amount of heat energy, due to the frictional force that is exhibited by the manner of the so-eluded-to Yukawa-based interdependent contact that is to here occur amongst the two so-eluded-to metrical-gauge-based Hamiltonian operators that have been infringed each other, at the externally-based Poincare level of the dual interaction of the so-eluded-to core-field-density of their relatively outer Ward-Neumman-based field indices.  This mild scalar magnitude of infrared energy, that is to formed by the said collision of the two so-stated Hamiltonian operators -- will then tend to scatter upon the proximal localized field indices -- in such a manner in so as to form a tense or a genus of a Calabi-Yau interaction, -- since the so-stated interaction is to here be a scattering of a form of electromagnetic energy with the holonomic substrate of certain given arbitrary set of mass-bearing superstrings of discrete energy permittivity.  Any given arbitrary Gaussian Transformation, that is to be involved with any respective given arbitrary genus of a Calabi-based interaction -- will be of a tense of what may be termed of here as a gauge-transformation.  In a gauge-transformation -- this general tense of the directly corresponding Kahler-Metric, will be one in which the directly corresponding Klein Bottle eigenstates that are here to be involved, will work to bear a tensoric-affliliated state of a Njenhuis topological sway -- that will be more touched upon in course 20 (as to Calabi-Yau, Calabi-Wilson-Gordan, and Calabi-Calabi Interactions).  Just as this respective given arbitrary collision of this given case scenario, will here cause the initially so-stated orbifold eigenset to bounce into the relatively opposite tense of holomorphicity -- this will then tend to form an antiholomorphic Kahler condition, that will then indirectly work to form an ensuing Kahler-Metric.  This tense of a scattering, is of an annharmonic-based genus.  This will then be a general genus of what may be here described of as tense of a Rayleigh-based scattering of those so-stated infrared-based photons, that are to here be made entropic -- in the course of striking the directly associated mass-bearing superstrings that are to here be associated with the so-stated Gliosis-based contact that is of this respective given arbitrary case scenario.  Since the so-eluded-to tense of this said case in point is of an annharmonic-based perturbation -- this general case scenario is a given arbitrary genus of what may be termed of as a Cevita Interaction.  I will continue with the suspense later!
To Be Continued!  Sincerely, Sam Roach.

An Example Of A Calabi-Yau Genus Of Interaction

Let us consider an initial orbifold eigenset that is comprised of superstrings of discrete energy permittivity, that is moving through a discrete unitary Lagrangian -- in what is here to be considered as to be moving in the relative holomorphic direction. Let us next say that the said orbifold eigenset is to then collide with a relatively motionless set of orbifold eigensets -- in such a manner in so that the initially so-stated orbifold eigenset is to then bounce into what may here be considered as the relative reverse-holomorphic direction.  Let us consider here that both the initially mentioned orbifold eigenset and the so-eluded-to conformally invariant set of orbifold eigensets that it is to collide with, are all comprised of mass-bearing superstrings of discrete energy permittivity.  Let us, as well, consider here that the initially mentioned orbifold eigenset and the said conformally invariant set of orbifold eigensets that it is to collide with -- will, upon the course of the so-eluded-to Gliosis-based contact, act in so as to work to form a relatively mild yet existent amount of heat energy, in the process of their interdependent contact -- due to the relatively slight amount of friction that is to happen in the process of their so-mentioned impact.  The scattering of the so-stated heat energy that is formed -- in part by the contact of the two so-eluded-to tenses of holonmic substrate, will then work to form a Calabi-Yau interaction that will here work to involve a gauge-transformation.
To Be Continued!  Samuel David Roach.

The Kahler-Metric and Conformal Invariance

Let us say that one is to have a set of superstrings, that are to here be differentiating in a Fourier-based manner, as an orbifold eigenset that is of a Noether-based flow -- over a relatively transient sequential series of iterations of group-related instanton.  Let us next consider that the so-stated Noether Flow of the superstrings that are here appertaining to one discrete orbifold eigenset, are here to be undergoing the Kahler-Metric -- at a proximal localization that is of a relatively conformally invariant Majorana-Weyl-Invariant-Mode.  During the sequential series of instantons in which the directly corresponding set of superstrings that work to form an orbifold eigenset, is of a nature to where the so-eluded-to given arbitrary individually taken superstrings that work to comprise the said orbifold eigenset, during each individually taken iteration of BRST -- work to bear an orientable tense of their holonomic substrate -- by operating in so that the directly corresponding field that is to here exist in-between each of such said superstrings and their counterstrings, is to then be of a homeomorphic topological genus, over the course of each individually taken Bette (Beti) Action eigenstate in which the so-eluded-to superstrings of discrete energy permittivity are to then be in a condition of Noether Flow, as the so-stated set of superstrings that operate in so as to perform one specific function are to here be undergoing a tense of conformal invariance in their directly associated Majorana-Weyl-Invariant-Mode.  Let us next say, that right after the so-stated directly corresponding Kahler-Metric is completed -- for the directly associated respective given arbitrary superstrings that have here just completed the task of re-attaining those fractals of discrete energy permittivity that these needed to re-attain, in order for the correlative discrete energy quanta -- that have here worked to comprise the Ward-Caucy-based condition of being those respective superstrings of discrete energy permittivity that have here come together in so as to form the correlative orbifold eigenset -- happens, to where the so-stated superstrings that have here worked to comprise the so-stated orbifold eigenset, are to here begin to lack a homeomorphic field in-between each of such directly corresponding superstrings and their directly corresponding counterstrings.  This will then work to cause the said respective superstrings of such a case, to then not be orientable during the directly corresponding individually taken increments of BRST, in which each of such individually taken superstrings that had then been iterating from within this, had been differentiating in a Fourier-based tense.  Let us next say that these directly corresponding superstrings that are of the said respective given arbitrary orbifold eigenstate of this case, are then to not be orientable in the individually taken ensuing iterations of the Regge Action, as well.  This will then cause these said superstrings -- that have here worked to comprise the said orbifold eigenset of this case -- to not be of an orientable nature.  Superstrings that are neither orientable during both the correlative Bette (Beti) Action, and the correlative ensuing Regge Action, as well -- will then become of a tachyonic-based flow.  This will then mean -- in this case -- that the superstrings that had here worked to form the said orbifold eigenset will then become of such a Fourier-based manner -- in so as to then become of such a manner that is not to here be of a Noether-based flow.  This is due to the condition, that such a lack of orientation in the tense of a superstring -- will temporarily convert the light-cone-gauge topology of the directly corresponding superstrings to go from being of a Kaluza-Klein-based nature into being of  a Yang-Mills-based nature.  I will continue with the suspense later!  To Be Continued!  Sincerely,Samuel David Roach.

Re-Adjustment Of Fischler-Suskind-Mechanism

Whenever there is an antiholomorphic Kahler condition happening in the substringular, there is consequently an ensuing Wick Action eigenstate -- of which indirectly works to form what may be termed of here as the Kahler-Metric -- from within the general region in which such a so-stated antiholomorphic Kahler condition had just recently happened.  The said antiholomorphic Kahler condition, works to initiate a directly corresponding Wick Action eigenstate -- in so as to work to apply a physical torsioning of what may be termed of here as the directly corresponding Landau-Gisner Action, in so as to work to cause the consequent leveraging upon the directly corresponding Fischler-Suskind-Mechanism, that is here to be most proximal localized to the initial said Fourier-based activity of the said Wick Action eigenstate, that is to here be of such a respective given arbitrary case scenario.  Upon the 96th consecutive iteration of the applied torque that is to exist, that is of the directly corresponding Fischler-Suskind-Mechanism of such a case -- that is to happen upon the directly corresponding holonomic substrate of the local proximal Klein Bottle eigenstate -- the Gliosis-based interactions of the correlative and local discrete quanta of energy with the said respective Klein Bottle eigenstate, is to then be initiated -- and is to continue for a total of 191 consecutive iterations of group-related instanton, for the correlative respective given arbitrary case scenario.  In the process of the correlative Fourier-based activity that is of the so-eluded-to Gliosis-based interactions of discrete energy quanta, with the so-mentioned respective and correlative Klein Bottle eigenstate -- the discrete quanta of energy that have then interacted in such a manner with the said Klein Bottle eigenstate, will have then re-attained those fractals of discrete energy that these need, to have then built-back into the Ward-Neumman bounds of their physical composition -- to have then be brought in such a condition, to where these are to now be properly refurbished.  After the said 191 consecutive Gliosis-based interactions of the said discrete quanta of energy with the said Klein Bottle eigenstate -- the so-stated Klein Bottle eigenstate is to then exit from the general Ward-Caucy bounds of the directly associated discrete energy quanta, while then re-adjusting over the course of three additional iterations of group-related instanton, to then be primed in so as to work to help in the course of the Gaussian-based transformation of a relatively adjacent substringular cite, to where the respective adjacent discrete quanta of energy that are to have a need of re-attaining their fractals of discrete energy, will have then been put into such a position in so as to need to be "operated upon" by an ensuing Fourier-based activity of the Kahler-Metric.  The multiplicit Klein Bottle does not repeat at one specific spot, over the span in which it is iterated over the course of one specific Kahler-Metric-based activity.  This overall so-eluded-to process, that is directly applicable to the correlative motion of any given arbitrary respective Klein Bottle eigenstate -- when including the re-adjustment -- lasts for 384 consecutive iterations of group-related instantons.   I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Tenses Of Relative Stability

Let us first consider an initially relatively stable atom, that is functioning as a metrical-gauge-based Hamiltonian operator -- at one set locus, in which such a respective stable atom is in a tense of conformal invariance, from within its general Ward-Caucy-based physical framework -- in which the said atom is to be operating at -- over a relatively transient duration of an initial set metric.  Let us next consider that this said atom had just previously been slowed into the earlier mentioned tense of conformal invariance -- to where the so-stated atom was kinematically converging into that so-eluded-to tense of Majorana-Weyl-Invariance, that was eluded to at the beginning of this post.  In the process of the so-mentioned atom being brought here into the said condition of conformal invariance -- the here so-eluded-to harmonic-based perturbation, that had then worked to cause the said atom to go into a state of relative Majorana-Weyl-Invariance, happens in such a manner to where the so-stated atom was then brought into a relatively stable kinematic condition of being at a steady-state, that is to here exist from within the general proximal localized region of its Poincare-based framework, to where such an atom may be said to have undergone a tense of a Wess-Zumino genus of an interaction -- over the directly corresponding sequential series of instantons, by which such a convergence that leads into a tense of conformal invariance had to have then happened, directly prior to the conditions that I had stated at the beginning of this given arbitrary respective post.  Let us then say that there is an interaction of that form of electromagnetic energy, that is of the genus of an infrared or heat-based energy -- that is to then be applied to the topological surface of the holonomic substrate of the atom that I have been discussing here in this given arbitrary post.  Let us then say that the interaction of heat energy with the said atom, will then tend to work to cause one or more electrons -- that are from within the Ward-Neumman bounds of the said atom, to be excited -- to where the so-stated one or more electrons that have then become excited, will then drop an energy level, while then "leaping" back to its initial energy level that I have here so-implied.  This will then tend to work to cause the emission of one photon per electron that had dropped an energy level.   The so-eluded-to electrons, that had just been excited by the Gliosis-based interaction of heat with the topology of their holonomic substrate -- happens, to where this said heat will have had been applied to the Ward-Neumman bounds of the so-stated atom that I have been writing about, in this respective given case scenario.  This so-eluded-to enharmonic tense of a perturbation, may be viewed of as an example of a Cevita interaction.  Thurthermore, whenever electromagnetic energy is scattered upon any general genus of phenomenology -- this general genus of a Fourier-based activity will tend to form a gauge-transformation, during which there is then what may be termed of as a Calabi-based interaction.  Calabi-interactions always tend to work to form a certain scalar magnitude of entropy, which is needed in order for the changes of physical states to happen. (For instance, such entropy is needed in order for ice to melt into plane water.)  Whenever any electromagnetic energy is scattered upon any orbifold eigenset of mass-bearing superstrings, that are of discrete energy permittivity -- this general genus of interaction is known of as a Calabi-Yau interaction.  This is why the orbifold eigensets, that are directly associated with mass-bearing superstrings -- are known of as Calabi-Yau manifolds.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Physical Re-Delineation Of Masses

Let us consider a set of discrete masses.  Let us say that the masses that are to be considered here, are in a relationship that is to then involve the initial Laplacian-based condition of three basic hydrogen atoms.  In this given arbitrary case scenario, one is to here be considering the fundamental sub-atomic particles that are to then work to comprise the three so-stated basic respective hydrogen atoms -- that I have eluded-to in this given arbitrary case.  What I am more specifically referring to as the physical substrate of each of such individually taken discrete masses -- of which are to be considered here as the eigenmembers of this respective given arbitrary case scenario, are the two fundamental basic cases of what always exist in any stable atom, by which I am simply referring to as the initial Laplacian-based condition of the existence of one relatively stable proton, that is being surrounded by the kinematic-based orbiting of one relatively stable electron, -- that are of the nature of as to being of either the holonomic substrate of a proton, or of the nature of being of the holonomic substrate of an electron.  Let us say that all three of such mentioned fundamental hydrogen atoms (each of which are a stable atom that is comprised of one proton that is being orbited by one electron), are to then each become positively charged all of the sudden -- by losing their respective multiplicit electron -- due to a proximal localized group-attractor.  The then resulting three loose protons would then tend to move towards whatever loose negatively charged adjacent source, is most aptly to be able to bring this so-eluded-to loose set of three positive charges into a state of optimum rest.  In the course of such a basic situation -- one is to then have a re-adjustment of the local delineation of the distribution of the proximal gluonic force of this specific case scenario -- since the three directly corresponding protons of such a basic case that I have described here, are made unstable, in order to move into a changed delineation, in so as to move into the respective individually taken spots where these are then to be at more of a state of optimum rest.  Individual protons each consist of two quarks that bind to one lepton.  Any given quark has a gluon that is situated within the Ward-Neumman bounds of its topological-based holonomic substrate.  Gluons -- of which are an example of what works to act as being a metrical-gauge-based Hamiltonian operator of the strong force -- are an example of a general condition as to the cite as to where there is a centralized knotting of the Rarita Structure.  (Where there is a gluon, there is an eigenstate of the centralized knotting of the Rarita Structure.)  So, whenever a proton is re-distributed in so as to form a re-delineation of its component gluons that are directly associated with the here so-eluded-to  Ward-Caucy bounds of the so-stated respective proton -- there is then to be a re-delineation of an eigenstate of the strong force.  So, whenever there is a re-delineation of the strong force -- there is thereby a directly corresponding re-delineation of an eigenstate of the centralized knotting of the respective multiplicit Rarita Structure eigenstate.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

As To The Integration Of Superstrings Into Orbifolds

Let us here consider a given arbitrary superstring of discrete energy permittivity, that is differentiating in a Fourier-based manner through a discrete mean Lagrangian path -- in a medium that is of a "pure" vacuum-based Hamiltonian operand.  Let us next consider in this particular case, that what is here to be the general substringular region of this scenario -- is here to be composed of a relatively large Hodge-Index of other superstrings of discrete energy permittivity, these individually-based superstrings of which, as well, are also differentiating in a Fourier-based manner through a discrete mean Lagrangian path -- in which each of such multiplicit-based superstrings of this case, is, as well, in this scenario, to be going through a medium that is of a "pure" vacuum-based Hamiltonian operand.  Let us next say that there is some tense of a group-attractor, that is proximal localized in what is here to be the general substringular region in which the many superstringular metrical-gauge based Hamiltonian operators -- are here to be moving towards each others field-density, in a greater scalar amplitude of potential collision, over a relatively transient duration of time.  Let us then say, that in this respective given arbitrary case -- once the relatively large quantum of superstrings that are here to each be initially acting as their own orbifold eigenset, are here to then be infringing upon a relatively close to Gliosis-based multiplicit proximal locus to the each others core-field-density -- the velocity that each of such superstrings had been bearing, as a scalar amplitude of their relative and respective genre of Noether-based translation, will be significantly lowered in scalar magnitude, as such superstrings are then to be pulled (actually pushed, in part, by gravitational waves from the other side) into a codifferentiable, codeterminable, and in a covariant manner, in such a manner, to where all of the here so-implied superstrings of such a case -- that were initially of the respective different independent orbifold eigensets, are now to be of the same larger overall so-eluded-to orbifold eigenset.  At this point, the overall quantum as to the composition of what is now to be one larger set of superstrings, that are to then perform one group-related function -- is to then to tend to work to bear a relatively more steady-state tense of a Majorana-Weyl-Invariant-Mode, than the initially so-stated individual superstrings of discrete energy permittivity that I had started out mentioning, were to have had at the respective start of this given arbitrary case scenario.
 I wil continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.