Part Three of the Interim In-Between Session 7 and 8 of Course 18

In so as to the divergent nature of an orbifold -- that is interially perturbated by the directly corresponding changes in the respective genus of the Hamiltonian-based nature -- of those superstrings that work to comprise the orbifold -- this format of kinematic inter-play works to produce a repulsion-based redistribution of the component eigenmembers of the directly inherent homotopic index, which tends to work to pull in the physical presence of group attractors.  This general type of activity tends to work to cause the here respective given arbitrary homotopic index -- of the topological condition of the so-stated orbifold, to bear a hightened tense of a fractal of magnetic-based qualities. This is since this genus of activity will work to increase the scalar magnitude of the Hodge-based index of the spin-orbital-based activities of the here directly corresponding superstrings -- that are here going through such an eluded-to change.  Whenever such a newly formed tense of superconformal invariance is altered relatively more rapidly, the potential for a hightened tense of change in the directly corresponding spin-orbital indices is bound to occur, at the here generally considered orbifold-based locus.  Yet, the less that various covariant superstrings act as being of a local tense, when this condition is to be of a bearing of one set of such superstrings relative to another set of such superstrings, the lower that the fractal of magnetism is -- that would then exist the one toward the other.  This latter tense of covariance, that acts as at more of a distance, will involve a weaker degree of homotopic interchange than if the tense of covariance were to instead  act at more of a local manner.  So, as an ansantz, magnetic flux density tends to be strongest when the eigenmembers that covariantly work to form such an inter-relation are local -- the one toward the other.  To be continued!  Sam Roach.

Part Two of the Interim In-Between Sessions 7 and 8 of Course 18

If the proximal encodement of the superstrings of the scenario that we have been dealing with here is maintained over the sequential series of group instantons of the so-stated group-related metric, then, the general condition of the first-ordered point particles that have worked here -- in so as to help to cause the directly corresponding superstrings to be of such a conformally invariant nature, in so as to be near each other, in such a tense of a Majorana-Weyl invariant nature, will work to allow for the so-stated point particles to bear  of a relatively proximal nature to a certain extent as well.  This is when this is taken in consideration of their correlative neighborhoods in the globally distinguishable.  Yet, if the directly corresponding reverse-fractaled tense of the electrostatic nature that is propagated from the directly corroberative superstrings will then here bear a divergent tense of residual homotopic Hodge-based indices, over the so-eluded-to sequential series of group instantons that work to correspond to the time in which the correlative superstrings are here being associated -- in the course of the so-eluded-to tense of superconformal invariance of this corroberative scenario, then, there will here be at least some sort of alteration in the localization of some of the superstrings that were directly associated with the so-stated group metric of this general scenario.  Yet, if the correlative superstrings are to remain relatively unchanged locally after each iteration of group instanton -- when in terms of their respective codeterminable codifferentiation, over each corresponding discrete increment of time that is to be metrically mapped-out in so as to work to help determine the genus of the specific tense of superconformal invariance that is involved here, then, the index of the prior tense of the respective perturbation of electrostatic differentiation is to be nullified in consideration.  The higher the Dirac factor is in terms of the non-local substringular phenomena -- that is to bear an exterial spin-orbital and/or a transversel effect upon the more directly involved interial-based phenomena, of such a format of a scenario, in spite of the degree and/or the level of the scalar magnitude of the physical separation that may exist here, the more assymetrical that the correlative superstirngs will tend to covariantly be propagated through in a kinematic manner -- relative to one another, over the so-eluded-to group metric -- when such a tendency is considered time-wise through a coniaxion that is centered at the convergent-based loci of the directly corresponding Fadeev-Popov-Trace eigenstates.
I will conclude with this interim later! To Be Continued!  Sam Roach.

Part One of an Interim In-Between Sessions 7 and 8 of Course 18

I am about to explain a certain genus of parity interactions of eigenstates, that are in reference to superstrings that are formed in an alternating sequential manner, in order for the correlative superstrings to be able to release wave homotopy that would here work to encode for a specific unique superstringular trait.  Let us initially say that one was to here consider ten superstrings of discrete energy permittivity that will have, over a correlative group metric, been reiterating, per directly corresponding respective group instanton, in their correlative substringular neighborhoods.  Let us now here consider that, after about one quadrilion successive group-related instantons, the sequential eigenmetric of the ten here mentioned superstrings of this particular case -- although maintaining their relative proximal encodement -- starts to differentiate kinematically in a different Majorana-Weyl covariant-based mode, when one is to compare the Hamiltonian-based codetterinable interactions of each of the ten so-stated superstrings, in relation to one another, as both a substringular index of their individual substringular behavior when taken individually and also when taken as a substringular index of their group substringualr behavior when taken as a group that acts as an orbifold. This alteration in both the individual activity of the ten component superstrings of the just eluded-to orbifold, and in the activity of the said orbifold as a whole, will work to form a tense of a divergent singularity in the encodement of its resultant integrative Hodge-based Hamiltonian operation, that will work to cause the homotopic residue that is then here formed by the so-eluded-to alteration in the genus of the activity of the so-eluded-to orbifold to change at least one globally distinguishable overall trait -- that will then be able to be detectable by the domino effect of this orbifold -- when the result of such a perturbative reaction is inversely traced into a corresponding extrapolation that may be observable in a here correlative reverse-fractaled chain of events.
I will continue with the second part of this interim later! To Be Continued!  Sam Roach.

Part Three of the Seventh Session of Course 18

Any given arbitrary either conformally isolated superstring of discrete energy permittivity, or, any given arbitrary conformally isolated set of superstrings of discrete energy permittivity, that act in such a manner in so that these behave as kinematically acting in a codifferentiable way that is geometrically parallel in their relatively outer Ward-Neumman-based topological settings, with another of such a superstring or set of superstrings  -- can not, solely on their own account, propagate that fractal of their magnetism that is directly associated with the relatively intetial-based Hamiltonian operational-based spin-orbital indices, that these produce by their radial-based motions, over time.  Yet, if such a respective so-stated superstring or set of superstrings that are geometrically parallel with another of such a superstring or set of superstrings, at the Poincaire level of their exterial topological-based Ward-Neumman settings, works to bear one or more Njenhuis tensors -- that act in such a manner in so as to help the said dual condition of a superstring or set of superstrings to act in a covariant manner that is codeterminable, then, the directly corresponding Real Reimmanian directoral-based coniaxials will be facillitated to move more freely -- in so as to help to cause the norm-conditions of the correlative Majorana-Weyl-based substringular structures, that have been eluded-to here, to act as bearing a cubic Gaussian-based relationship, that will here kinematically inter-play as a multiplicit-based eigenstate in three or more spatial dimensions, over time.  So, when superstrings go from not spontaneously propagating their fractal of discrete magnetism -- to any viable extent -- to spontaneously propagating their fractal of discrete magnetism, to a viable extent -- in terms of the delineation of their Majorana-Weyl-related Hodge-based indices -- this is a tense of a cyclical-based Majorana-Weyl covaraince.  Since an orbifold works to involve a tense of a fractal of discrete magnetism, any given arbitrary orbifold, over time, alters in the manner of the production of its spin-orbital indices -- when in relationship to those spin-orbital indices that are produced by the surrounding orbifolds.  This is more of a general tense as to what a Majorana-Weyl covariant mode would happen to be.  When a conformally isolated string enters a manifold of other superstrings, this will work to involve a tense of a Majorana-Weyl covariance as well.   To Be Continued!  Sam Roach.

Part Two of the Seventh Session of Course 18

A fractal of the magnetic force happens at the substringular level -- in such a manner in so that this fractal of the just stated genus of force exists in manifold, or, in other words, this so-stated genus of force exists as being in the form of kinematically interplaying Hamiltonian operators that work together in groups, that may be described of as orbifolds.   As I have stated before, superstrings that work in so as to function in order to perform one specific operation, exist in manifolds or membranes that may be termed of as orbifolds.  Likewise, orbifolds that work in so as to function in order to perform one specific operation, exist in manifolds or membranes that may be termed of as orbifold eigensets.  The transversal display of the Hamiltonian operational index of an orbifold or an orbifold eigenset, exists as the angular momentum of such so-eluded-to orbifolds or orbifold eigensets -- in so as to act as a fractal of a tense of an electrical-based field.  Likewise, the radial display of the Hamiltonian operational index of an orbifold or an orbifold eigenset, exists as the spin-orbital momentum of such so-eluded-to orbifolds or orbifold eigensets -- in so as to act as a fractal of a tense of a magnetic-based field.  When the fractal of such a so-stated tense of a magnetic field exists in that general genus of a manifold, that I have here described of as being of either the nature of an orbifold or of the nature of an orbifold eigenset, it is propagated in such a manner in so that the spin-orbital context of the Hamiltonian-based index of such an eluded-to kinematic display of such a substringular membrane -- works to cause and behave in the proscribed general format of radial freedom that would here work to involve the potential for optimum rest -- when this is here taken in consideration of the overall Ward-Caucy genus of the physical bounds,  as this is appertaining to the said general condition of the so-stated respective given arbitrary orbifold or orbifold eigenset.  Just as well, when the fractal of such a so-stated tense of an electric field exists in that general genus of an orbifold or an orbifold eigenset, it is propagated in such a manner in so that the angular momentum-based context of the Hamiltonian-based index of such an eluded-to kinematic display of such a substringular membrane -- works to cause and behave in the proscribed general format of transversal freedom, that would here work to involve the potential for optimum rest -- when this is here taken in consideration of the overall Ward-Caucy genus of the physical bounds of that said general condition of the so-stated respective given arbitrary orbifold or orbifold eigenset.  I will continue with the suspense later!  Samuel David Roach.

Part One of the Seventh Session of Course 18

Superstrings exist in fields.  Any given arbitrary one-dimensional superstring of discrete energy permittivity and/or any two-dimensional superstring of discrete energy permittivity will always bear a tense of a fractal of magnetism -- in terms of their spin-orbital momentum, when this is taken in relation to their Hamiltonian-based operation, over time.  The said fractal of the given arbitrary discrete magnetism -- that may be extrapolated, for any given arbitrary relatively conformally isolated superstring -- can not propagate through a discrete Lagrangian, over a codeterminable group metric that is Majorana-Weyl invariant, without at least bearing one eigenbasis that is directly related to one or more Njenhuis tensors -- on account of the condition that the total spatial dimensionality of the most basic Majoran-Weyl fractal of magnetism, in terms of the functionability of whatever the directly associated Hamiltonian-based operation of the so-eluded-to superstring, that one may here consider in this case, happens to be, is based upon the kinematic covariant codifferentiability of a core-field-density that will always work to involve two or more spatial dimensions at once -- over any given arbitrary sequential series of group instantons in which the so-stated superstring of discrete energy permittivity will be involved with, over time.  It takes at least three or more spatial dimensions, in any kinematic inter-play of superstrings, to propagate a fractal of magnetism, in a directly correlative Hamiltonian-based operation, so that a cubic genus of a Gaussian Transformation may work to fulfill anywhere from a freedom of 4pi degrees of radial Ward-Neumman potential delineation to a freedom of 32pi I degrees of radial Ward-Neumman potential delineation, in order for the directly corresponding norm-conditions to exist in such a manner in so that at least all of the correlative directorals of the here relative Real Reimmanian space may be viably functional by the so-eluded-to given arbitrary tense of the here given case of the fractal of discrete magnetism, over any kinematic eigenbase of Hamiltonian-based operation.  Think about it.
I will continue with the suspense later!  Sam.

As to The Genus of the Symmetry of Cohomologies

When any given arbitrary cohomological mappable tracing works to bear a trajectory that is projected in an euler-based manner, then, the expansion of such a projected trajectory of the so-eluded-to general cohomological mappable tracing will be of what may be termed of as a Clifford Expansion -- when in terms of the manner of the Laplacian-based divergence of the integration of the disturbance of the so-eluded-to ghost-based indices, as such an integration of a cohomolgical eigenbase may be traced from one endpoint of a Lagrangian-based origin to the ensuing respective given arbitrary endpoint of the just eluded-to Lagrangian, that one would here be extrapolating in this case.  Yet, if any given arbitrary cohomological mappable tracing works to bear a trajectory that is projected in a euclidean-based manner, then, the expansion of such a projected trajectory of the so-eluded-to general cohomological mappable tracing will tend to be of what may be termed of as a hermitian-based expansion -- when in terms of the condition of the directly corresponding Lagrangian of this second here mentioned case not tending to change in any more Ward-Caucy-based derivatives than the number of spatial derivatives that the so-eluded-to cohomological-based mappable tracing would here be extrapolatable in, over the course of the manner  in which the Laplacian-based divergence of the integration of the distribance of the eluded-to ghost-based indices will have traversed, over the time in which the second here mentioned projected cohomological trajectory had been delineated, in so as to form the so-stated second scenario of such a mappable tracing.  Anyway, any given arbitrary respective set of directly related and proximal Clifford Expansion eigenbases -- in terms of a correlative set of the here corresponding euler-based disturbances of an eigenset of cohomological-based mappable tracings -- will tend to form a differential geometry that will here tend to  more appertain to an antichiral or a Kusomo-Suzuki-based Gepner model, when in terms of such an eluded-to cohomological symmetry being of an assymetric-based manner.  And, any given arbitrary respective set of directly related and proximal hermitian-based expansion eigenbases -- in terms of a correlative set of the here corresponding euclidean-based disturbances of an eigenset of cohomological-based mappable tracings -- will tend to form a differential geometry that will here tend to more appertain to a chiral or a Calabi-Yau-based Gepner model, when in terms of such an eluded-to cohomological symmetry being of a symmetric-based manner.

Some Ideas as to Slater Equations

Let us here consider the motion of an orbifold -- an orbifold that moves as a substringular projection through a discrete Lagrangian, over time.  Let us now consider the here present condition, that the so-stated substringular projection works to map-out a cohomological-based projection -- as the physical memory of the orbifold that I have here mentioned is pulled in the relatively holomorphic direction, through the said Lagrangian that the superstring had projected itself through, in so as to form a ghost-based extrapolation as to the what, when, and how the said set of superstrings that are here functioning in so as to perform a specific substringular operation -- in the Ward-Caucy-based confines of the codifferentiablity of the proximally local Poincare-based indices, to the so-eluded-to scenario.  Let us now consider the condition, that, the fractal of the angular momentum -- the Hamiltonian-based permittivity that the so-stated orbifold exhibits, by its here eluded-to substringular behavior -- that the said orbifold works to show, over a discrete period of time, is pulled by an exterial wave-tug.  This genus of a wave-tug-based activity works to exhibit a median-based euclidean expansion of the said orbifold's Hamiltonian-based operand, over the time in which it is moving across the so-stated discrete Lagrangian that I have here mentioned.  This general format of an expanding field of an orbifold, that works to bear a relatively optimum abelian geometry -- in the process of the said orbifold's traverse across that Lagrangian in which it has been moving in, over the here mentioned group-related metric -- will bear an orbifold that is pulled at a subtended angle, through the vantage-point of the here eluded-to coniaxion, that is of a 45 degree-based nature.  If one were to multiply the permittivity of the directly corresponding Hamiltonian, that appertains to the scalar magnitude of such a median eigenbase of a relatively hermitian-based relatively abelian flow of corroberative superstrings, over time,  by the reciprocal of the square-root of two, -- when one here considers the Hodge-Indices that work to depict the initial so-eluded-to Hamiltonian of the so-stated orbifold that we are here dealing with -- this will help to establish what the multiplets of the so-eluded-to Hamiltonian of this case are.  This format of working to determine what such a euclidean-based median substringular expansion may be extrapolated as -- in terms of what the correlative Hamiltonian eigenbase of such a case is.  This is, in general, the idea behind determining what a Slater equation is. To Be Continued!!! I will continue with the suspense later!  Sam Roach.

Some More As To Lorentz-Four-Contractions

When a phenomenon travels closer to the speed of light -- from the underside of the said speed of light -- the so-stated phenomenon undergoes what are termed of as a certain degree of Lorentz-Four-Contraction.  When any given arbitrary phenomenon is not moving in a tachyonic-based nature, it is undergoing what may be termed of as a Noether-based flow.  So, what works to distinguish the various degrees of relative velocities, for any given arbitrary phenomenon that is moving?  I will here give a little bit of an explanation as to this.  When a phenomenon is at a relative stand-still, the substringular aspects of this so-stated given arbitrary phenomenology is in a state of superconformal invariance.  This just-eluded-to condition of superconformal invariance is a manner here in which the superstrings  -- that work to comprise the phenomenon that we are discussing here, move in a kinematic manner that is completely in static equilibrium.  This is to where the directly corresponding superstrings move around, over the here implied sequential series of instantons, yet, these superstrings amount to no alteration in the general eigenbase of their integrative Hodge-based locus, over the so-eluded-to time period -- in which the directly associated phenomenon is moving at a standstill in the globally distinguishable.  When such a manner of superconformal invariance is applied to a said respective given arbitrary phenomenon, there are no overt Lorentz-Four-Contractions here acting upon the said phenomenon, and thus, the degree of Polyakov Action in this case is of a fully reverse-compactified manner when taken to the inverse of the absence of the so-stated Lorentz-Four-Contractions.  The less of a degree of such a so-eluded-to manner of conformal invariance, that there is upon the said phenomenon that we are discussing here -- the more that the said globally distinguishable phenomenon will then here be moving at what may be termed of as being of a higher velocity -- to where the so-mentioned phenomenon will then bear more of a Lorentz-Four-Contraction, over time.  The greater the Lorentz-Four-Contraction is upon a given arbitrary physical phenomenon, the lower the relative degree is upon the directly corresponding Polyakov Action for that so-stated phenomenon, during the directly appertaining individual group-related instantons.  Let us now say that a one-dimensional superstring is  Lorentz-Four-Contracted by a factor of 10.  Its conformal dimension will then technically be 2^((3*10^7)/(10^43)).  Anything to the zero power is one -- so, this would here be pretty close to exactly one.  Let us now say that the said one-dimensional superstring is now LFC by a factor of 3*(10^7).  Its conformal dimension will then here be 2^((10/(10^43)).  This would then mean that the superstrings under the two different respective conditions will bear 3*10^7 of what I have termed of as  partitions in the first case, and, 10 as what I have termed of as partitions in the second case.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

As To A Special Tritiary Abelian Wave-Tug/Wave-Pull

Let us here consider a certain general genus of a tritiary abelian wave-tug/wave-pull, that is physically embodied by an organized working-together of the holonomic substrate of three individual interdependent cohomological-based substringular projections -- that work to bear a group-based bonding at a conipoint, that would here function at the apex of the so-stated kinematic-based physical substringular conipoint -- at the front of what may be termed of here as the holomorphic end of the so-stated respective given arbitrary cohomological-based projection.  There are, in this scenario, three orbifolds, that function in so as to bear a Hamiltonian-based operation, as an orbifold eigenset, that works to form a Gliossi wave-tug/wave-pull at a general apex-like conipoint -- at the relative forward-holomoprhic end of the said substringular projection, as a general format of such a Laplacian-based superstringular scenario.  The so-eluded-to apex-based Laplacian Ward-Neumman condition that I have just implied, will bear a discrete genus of an abelian differential geometry -- this so-eluded-to kinematic format of a movement of the said projection, of which, works to bear a unitary orbifold-based wave permittivity -- that moves in the eluded-to relative forward-holomorphic directoral-based flow, over a sequential series of group instantons.  In so long as the vibrational oscillation of the directly corresponding Hamiltonian-based operation does not either ellongate nor attenuate in its kinematic-based pulsation, over time, such an eluded-to Fourier Transformation of the here mentioned tritiary cohomological-based projection -- that here is transferred through the eluded-to unitary Lagrangian, over time, will tend to bear no spontaneous Chern-Simmons singularites, at the Fourier-based kinematic substringular locus of the time-wise differential conipoint -- where the conipoint of the correlative apex of the three said cohomological-based projections, is spatially differentiated -- over the correlative integration of the directly corresponding sequential series of group-based instantons.  Such an extrapolation of a kinematically depicted Sterling approximation will then here tend to bear a local relative respective given arbitrary tense of being Yau-Exact, when this is not here considering any extraneous alterior conditions, that would otherwise work to effect the overall scenario here.  Yet, when one considers the kinematic-based activity that acts toward the relatively reverse-holomorphic direction -- when taken as away from the so-eluded-to apex-based conipoint that I have mentioned here -- there will, instead, tend to be Lagrangian-based Chern-Simmmons singularities -- due to the so-implied warping of space-time-fabric, that would tend to eminently happen, in so long as the curvature of the here mentioned tritiary projection bears any spurious changes in derivative over time.   The more spurious the tendency of the reverse-holomorphic-taken cohomological indices -- that exist in the opposite direction from the directoral wave-tug/wave-pull of the apex of the said tritiary abelian motion, through the said unitary Lagrangian, are, the more likely that there will be the existence of at least some sort of Chern-Simmons singularities at the vantage-point of such a kinematically differenatiable general locus -- as taken away from the locus of the said Gliossi-based binding, of the so-eluded-to apex that will have here inter-binded, prior to the motion of the said cohomological projection.  To Be Continued!  Sam.

A Little Bit of an Aside as to Cohomological-Based Symmetries

When a set of relatively forward-holomorphic-norm-states are initially scattered harmonically upon set of superstrings that directly appertain to the presence of a mass -- that are moving in the membranal context of an orbifold eigenset -- the resultant ghost-based cohomological-based setting, that is formed by the just eluded-to Reimman-based scattering, may be termed of as a chiral-based cohomology that is of a Calabi-Yau-based cohomological setting.  Yet, if the situation is still of the same general nature, yet, the substringular phenomenology that is scattered by the here relatively forward-holomomorphic-norm-states is directly appertaining to the presence of a quantum of plain kinetic energy -- the reslultant ghost-based cohomological-based setting that is here formed by the just eluded-to Reimman-based scattering is a chiral-based cohomology that is of a Calabi-Wilson-Gordan-based cohomological setting.  Furthermore, if the situation if still yet of the same general nature, yet, the substringular phenomenology that is scattered by the here relatively forward-holomorphic-norm-states is directly appertaining to the presence of a quantum of electromagnetic energy -- the resultant ghost-based cohomological-based setting that is here formed by the just eluded-to Reimman-based scattering is a chiral-based cohomology that is of a Calabi-Calabi-based cohomological setting.  The respective ensuing initial annharmonic scattering of the just mentioned ghost-based cohomologies, is a Rayleigh scattering -- that is of an antichiral or a Kusomo-Suzuki-based nature.  This is on account of the condition that a chiral-based cohomology is of a Calabi-based nature, while, an antichirial-based cohomologyi is, again, of what may be termed of as a Kusomo-Suzuki-based nature.  Calabi-based cohomologies are of either a trivially isomorphic or of a non-trivially isomorphic symmetry.  Kusomo-Suzuki-based cohomologies are of an assymmetric nature.  These here just mentioned descriptions of certain general formats of cohomological symmetry, are directly appertaining to the nature of the scattering of the ghost-based indices -- that are here correlative to the cohomological eigenbase of a set of extrapolatable mappable tracings of distinct physical memories that may be detectable in the substringular.
I will continue with the suspense later!

Part Four of the Sixth Session of Course 18

Phenomena that is contingent to that of a mass that enters a worm-hole is of a bosonic nature, so that the phenomena that is propagated through the said worm-hole works to obey a tense of the correlative Lortentz-Four-Contractions that work to effect it, over the group metric in which the so-stated phenomena that enters the said worm-hole -- in a manner in so that the initially eluded-to mass is transferred in here as having a Yang-Mills light-cone-gauge topology, in a tachyonic manner, through the multiplicit and multidirectoral curl-based curvature of space-time-fabric. That scattering of the so-eluded-to mass that is made tachyonic, by the altering of its light-cone-gauge topology -- is a perturbation of the directly related given arbitrary Calabi-Yau action.  The kinematic activity of such a perturbation in the Calabi-Yau action is a perturbation of the correlative given arbitrary Calabi-Yau metric.  And, the so-eluded-to phenomenology that is perturbated out of the tendency of that mass from having the initial Kaluza-Klein topology -- to having, instead, a Yang-Mills topology (in order to here be of a tachyonic nature), is a perturbation of a given arbitrary tense of a Calabi-Yau manifold. The projection of such a perturbated manifold of an orbifold eigenset of a mass is a respective given arbitrary example of a perturbative Calabi-Yau projection.  The cohomological-based nature of such a Rayleigh-based scattering, is a genus of a perturbative Gliossi-Sherk-Olive projection, since this respective given arbitrary tense of an annharmonic scattering is an alteration in the mode of an initial tense of one unique respective given arbitrary unit of a discrete mass, in this case.  Yet, since the propagated cohomology of a mass in and of itself -- in terms of the hermitian nature of its Poincaire-based indices --  that is transferred through a worm-hole, tends to be  harmonically delineated, in the course of its propagation through the said worm-hole, it works to bear a harmonic and thus a chiral cohomological symmetry that is either of a trivially isometric or of a non trivially isometric geometric correlation.  Yet, if the delineation of a phenomenon that is propagated through a Lagrangian works to bear an assymetric cohomological genus, that is thus an antichiral cohomology, over time, then, its said cohomology may be termed of as a Kosoma-Suzuki cohomological index.  The scattering of light -- in and of itself, forms a cohomological-based patterning, that is an example of a Kosoma-Suzuki cohomology (since it is of an assymetrical-based nature, that is thus, an antichiral cohomology).  Both symmetric and assymetric cohomological-based projections are examples of Gepner models.  The potential energy of a superstring may be termed of as a superpotential.  Such a potential may be considered here in terms of what is known of as a Landau-Gisner potential .
To Be Continued!  Sam.

As to the Mode of Various Hamiltonian Operators

Let us say that there is one Hamiltonian operator -- that may be here be depicted as the holonomic substrate of the pulse of one respective given arbitrary orbifold, that would bear an eigenbase of an acceleration through a Lagrangian -- in such a manner in so that the so-stated pulsation of the said orbifold will bear Chern-Simmons singularities that are of a metrical-based format, even though this so-stated orbifold will not necessarily here bear Lagrangian-based Chern-Simmons singularities -- unless there is a Gliossi-based interaction that is not colinear, as I will explain in a little bit.  After a discrete quantum of time later (over the kinematic activity that would involve here a sequential series of group instantons), the said orbifold will alter or perturbate in the mode of its Hamiltonian-based pulse, or, in other words, the acceleration of the so-stated orbifold will change in its scalar magnitude of Hamiltonian-based momentum -- in the process of the so-eluded-to set of superstrings that bear the eluded-to given arbitrary function of operation will be either ellongated in its given arbitrary respective pulse or attenuated in its given arbitarry respective pulse, over the so-stated general consideration of time, in this respective given arbitrary scenario.  This will here mean that the initial eigenbase of the overall Hamiltonian-based momentum of the said orbifold will have here, over the course of the so-eluded-to perturbation of its pulse, been interactive, in a Yakawa-based manner, with an exterial-based substringular phenomenon or phenomena -- that will have here initiated a Gliossi-based wave-tug/wave-pull, that will have brought a spontaneous response upon the initial orbifold, to where such a response will have changed the genus of the Hamiltonian eigenbase. Such an alteration in the so-eluded-to Hamiltonian-based eigenbase of "momentum" will have directly corresponded to the Hodge-based extrapolation of the scalar magnitude of the rate of change of the so-stated initial orbifold here mentioned, in the respective directoral-based Lagrangian of that said orbifold, that may here then work to also cause a set of one or more Lagrangian-based Chern-Simmons singularities to happen to the said initial orbifold, over time.  The directoral-based addition of the Hodge-based Hamiltonian expression of the exterial-based orbifold upon the initially mentioned  directoral-based Hodge-based Hamiltonian -- that works to help define the resultant pulsation of the initial orbifold, after the so-eluded-to perturbation that I have here implied -- will work to cause both the directoral-based pull of the initially stated orbifold, and, its resultant manner of changed pulsation -- to where the additional eigenbase of Chern-Simmons singularities, in terms of both the Lagrangian-based singularities and the metrical-based singularities, will work to help indicate the resultant behavior of the initially mentioned orbifold, over time.  This will often inevitably be the case, since any corroberation of Gliossi-based interactive orbifolds -- that bear any given arbitrary Yakawa-based interaction over any definitive projection -- will be of such a remote difference from being of a Wilson-based colinearity -- to where the resultant implied Gliossi-based wave-tug/wave-pull of the interacting orbifolds will actually tend to bear at least some manner of Lagrangian-based singularity, upon impact.  I will continue with the suspense later!  Sam.

Part Three of the Sixth Session of Course 18

Chiral cohomologies tend to depict harmonic topological-based flows of the mappable-tracing of the physical memories as to the where, how, and when, of any given arbitrary respective substringular kinematic activity.  This is while, antichiral cohomologieis tend to depict annharmonic topological-based flows of the mappable tracing of the physical memories as to the where, how, and when, of any given arbitrary respective substringular kinematic activity.  The kinematic activity of space-time-based fabric -- when in terms of both the existence and the activity of worm-holes -- tends to be a chiral-based spatial transposition, that is kinematically differentiable in both a harmonic and in an annharmonic manner, as one works to map-out the directly corresponding bending of space-time-fabric that is eminent to the multiplicit and multidirectoral-based Lagrangian-based nature of any one unique respective given arbitrary worm-hole, over time.  The harmonic differentiability of any one given arbitrary so-eluded-to worm-hole, is the even transfer of phenomena -- that enters in at one end of the so-stated worm-hole, while, such a respective so-eluded-to general format of physical phenomena leaves the other end of the so-stated worm-hole, relatively shortly after it does the so-stated initially mentioned entering of the worm-hole.  This is since the vast majority of the kinematic inter-play of the "speed" of any given arbitrary worm-hole is due to the contoursioning of space-time-fabric.  Yet, tachyonic transfer of phenomena happens a lot more often than many people may think.  If a phenomena of mass works to temporarily convert its light-cone-gauge topology from an abelian or Kaluza-Klein topology to a non-abelian or Yang-Mills topology, then, it is possible for the so-stated respective given arbitrary mass to temporarily become tachyonic.  A mass is typified as bearing of both a Kaluza-Klein light-cone-gauge topology, and also as bearing Yau-Exact singularities in-between its constituent superstrings.  So, a mass may be temporarily transferred as tachyonic at times -- simply by temporarily altering its light-cone-gauge topology.  The annharmonic nature of any respective given arbitrary worm-hole is contingent to the condition, that, the phenomena that leaves the said worm-hole at the exiting side of the so-stated worm-hole, tends to not be brought back to its potentially tachyonic origin.
This is enough for now!!! To Be Continued!  Sam.

Part Two of the Sixth Session of Course 18

Both orbifolds and orbifold eigensets may exist as either a bosonic-based configuration or as a fermionic-based configuration.   Cohomologies may exist in terms of world-sheets that work to inter-bind other substringular phenomena, as well, as a fractal of magnetic topological-based settings that work to correspond to those multiplicit respective orbifolds -- that operate in so as to form a mappable tracing that forms the so-stated given arbitrary cohomologies.  Unique relatively codifferentiable, codeterminable, and covariant cohomological-based physical patterns may be symmetrically orientable in either a relatively chiral isometric geometrical-based manner, or, other unique relatively codifferentiable, code terminable, and covariant cohomological-based physical patterns may be symmetrically orientable in a relatively antichiral isometric geometrical-based manner, over time -- as the physical memory as to the where, how, and when the directly corresponding orbifolds -- that had worked to form the so-eluded-to cohomoogical-based patterns that I had inferred -- have been mappably traced.  A chiral-based symmetry may be either trivially isometric, or, such a general genus of a chiral-based symmetry may be non-trivially isometric.  An antichiral symmetry bears a reversal in the handed-based nature of a general isomorphism, that may be reverse-symmetric in either a trivially isomorphic manner or in a non--trivially isomorphic manner.

Part One of Session Six of Course 18

Superstrings that are unfrayed always exist in a topological-based setting.  Superstrings of discrete energy permittivity work to emit field-density that exists as a fractal of discrete units of magnetic-based force.  Such superstrings act in groups of such discrete units of energy -- that come together to form a specific given arbitrary operational-based kinematic activity, to where such superstrings of discrete energy permittivity always tend to act as individual Hamiltonian operators that integrate, in so as to form the holonomic substrate that I term of as an orbifold.  One or more orbifolds that function in so as to perform an overall specific operation come together in order to form what I term of as an orbifold eigenset.  All orbifolds work to form one or more fractal-based tenses of magnetic-based force -- the superstrings that work to form any given arbitrary orbifold emit spin-orbital-based indices, that come together in so as to form one overall fractal of discrete magnetic force, in so as to form a here respective given arbitrary wave-pull/wave-tug that is necessary in order for substringular phenomena to be both pulled toward any other physical phenomena, and/or to allow for substringular phenomena to be pullled away from any other physical phenomena, over time.  So, any given arbitrary orbifold eigenset works in so as to form a potentially larger eigenstate of a fractal of magnentism -- since an orbifold eigenset consists of one or more orbifolds.  Such a condition of the here being fractals of magnetic-based force are both effected by the activity of electromagnetic energy, as well as being effected by the activity of gravitational-based force.  Gravity is caused by much of the kinematic activity of the Rarita Structure eigenstates, that are both prominent and viable to any given arbitrary scenario.   This is to where the Ricci Scalar acts in so as to cause any relatively local Rarita Structure eigenstates to behave as these do, over time.  Any reversal in the genus of a magnetic condition will tend to reverse the tendency of the Ante-De-Sitter/De-Sitter-based mode of the directly associated gravitational-based pull -- at any multiplicit-based system of Poincaire-based phenomena -- that are local to the scene of the so-eluded-to reversal in magnetic-based genus.  For instance, if one were to immediately change a tense of magnetism to a tense of reverse-magnetism, this will bear more of a potential of forming antigravity. Such a format of activity will always tend to cause the existence of the directly corresponding Wick Action eigenstates -- in so as to initiate a Gaussian Transformation -- since such a reversal in the fractals of a relatively local magnetic-based drive will work to form an antiholomorphic Kaeler condition.  Enough for now!!!Sam.

Part Two as to Displacement Magnitudes

Once that the relative so-eluded-to Dirac is completed by the convergence of the series of wave-iteration -- that is shared at a relative distance, that, because of the same relative covariant differentiation of roll, spin, and first-ordered-point-particle-based-reformation -- act here in a proximal-based manner -- the directly associated strings will here work to exist in state of static equilibrium, when such superstrings of discrete energy permittivity are here considered as here being relative to one another, to where a fractal of an internal magnetic shift will then here work to maintain its magnitude -- by not "hyper-extending" in terms of its correlative core-field-density.  (The directly associated mini-stringular-based segments will bear at least some degree of a genus of a non-abelian-based differential geometric spatial association, for the directly associated eigenbase of holonomic substrate, to where, this is to tend to happen over the directly corresponding sequential series of instantons, in this given arbitrary case.)  Since the homotopic Ward-Caucy conditions that I have just worked to describe here, for the 10 million initially considered supertrings, will interact as proximal in the substringular-based scenario, this Hamiltonian-based orbifold eigenset that I have here eluded-to will act as if these states of discrete energy are relatively adjacent, at the vantage-point of an observer that may extrapolate a detection of such eigenstate-based indices.  Such homotopies that exist, per superstring, tend to exist outside of the stringular band level -- to where those holonomic substrate-based indices that are here most affected by the exterial-based photons that I had mentioned as part of the scenario that I had implied in my last post, will be less affected by the so-eluded-to fractal of magnetic field. (The spin-orbital momenta of superstrings that have just been scattered by photons -- will tend to bear a higher genus of interaction with a conformal invariance that is associated with their angular momentum, than with the conformal invariance that is associated with its roll, over a relatively transient duration right after the so-eluded-to scattering.)  This is, while those superstrings that are more codifferentiable with the band level of the here overall resultant field homotopy, by not bearing as much of a Gliossi-based interaction with the so-eluded-to photons -- will tend to bear more of a fractal of magnetic conformal invariance, since the here correlative spin-orbital permittivity of this set of superstrings will be able to bear a relatively more invariant mode, when in terms of the static equilibrium of its relative roll. So, a homotopy that has an analogous spin, roll, and pointal reformation, per general iteration of group instanton -- will tend to behave to where the just implied orbifold eigenset will bear a higher potential as appearing as a whole group, that will act as adjacent, to where  that general condition may be detectable as acting as one proximal set of substringular indices -- which will work to form a more potential fractal of magnetic-based attraction.  Session 6 next.  Sam Roach.

Part One As to Displacement Magnitudes

How about if I explain to you a little bit about more as to  how superstrings of discrete energy permittivity kinematically differentiate at a displacement magnitude, which is relatively large in scalar amount in the substringular -- yet works to bear a Yakawa-based spatial condition that is so close in proximal covariant-based locus in the globally distinguishable, that the said codeterminable and codifferentiable superstrings act as if these so-stated superstrings are adjacent -- to the extrapolation of any given person that were to work to detect the general locus of the said group of superstrings, over a sequential series of group-based instantons?!  Let us say, in this just-eluded-to scenario, that we are dealing with a Hodge-Index of 10 million superstrings of discrete energy permittivity.  Let us now say that all of these corroberative superstrings are all initially within the same general distribution of tori-sector-based-range -- all 10 million of such so-stated superstrings are of the same layer of reality, that is likewise of the same set of parallel universes.  As all of these given arbitrary superstrings of this so-eluded-to group of strings are struck by alterior-based photons over the directly associated group metric, in which the here discussed scenario is kinematically differentiable, the counterstrings of the so-struck superstrings -- which act as the wave-based holonomic substrate of the corroberative so-eluded-to set of discrete energy increments -- such a wave-based pattern of covariant interactive mobility will then here begin to form a fractal of a covalent sharing of their Hamiltonian-based operational indices -- with the immediately surrounding superstrings.  This will work to form a repulsion factor that will here operate in-between the interial Ward-Neumman bounds of the initially so-stated 10 million covariant superstrings -- that I had mentioned at the beginning of the scenario of this post -- which will work to make it appear, from the vantage-point of the globally distinguishable, that the operational function of all of the so-stated intially mentioned superstrings will be of a different general nature.   Yet, when one is to consider the overall resultant kinematic activity of the so-eluded-to 10 million superstrings, over a relatively less transient sequential series of group-interactive instantons, the Hamiltonian operation of this so-stated given arbitrary scenario of multiple small Hamiltonian-based operators will here integrate, in so as to form a group operational function that works to form a more similar general nature -- when one will here consider the here implied conformally invariant pattern activity, that one may describe as a given arbitrary case of covariant determinism.  I will continue with the suspense later!  Sam Roach.

Part Two of the Fifth Session of Course 18

The process of the first-ordered point particles -- that have worked to comprise a superstring of discrete energy permittivity -- to partially dissociate into a format of holonomic substrate, that is relatively loosened from its initial genus of composition, that had existed at the beginning of any given arbitrary substringular state that exists at the start of one locus of one given arbitrary iteration of BRST, is called the Polyakov Action.  After many sequential iterations of group instanton -- more particularly, after many sequential iteration of group-related BRST -- the directly associated superstrings of discrete energy permittivity either gradually and/or more immediately alter in their  tense of directoralization and position, over the so-eluded-to general conditions of time that will have here been allotted.  As superstrings of discrete energy alter in the Hamiltonian-based indices that are correlative to a fractal of what may be termed of as the indices of their eigenbase of angular momenta over time -- the diretoral-based wave-tug/wave-pull of the directly corroberative superstrings will tend to alter in their individually considered Lagrangian-based path as to what will then be the newly-extrapolatable holomoprhic direction of any respective given arbitrary  superstring that will have then altered in the base as to the path integral genus as to the physical-based inclination as to the Hamiltonian-based operand that is most optimum for maximum physical-based rest. And, as the optimum fractals of both the angular momentum and the spin-orbital momentum of any given arbitrary respective individually taken superstring works to bear a directoral-based eigenbase of Hamiltonian operation that has altered in its most liable Lagrangian-based path integral over time,  the correlative Polyakov Action eigenmetric of the so-eluded-to superstring will be at least partially affected by the prior-based kinematic-based activity -- which will, at least to some degree or another, alter the manner in which the directly associated first-ordered point particles that work to comprise the correlative superstring of discrete energy permittivity act, in the details by which such constituent so-stated particles behave -- in the process of the so-stated mild dissociation, so that these may undergo such a change,  in so as to allow for the said process of the said eigenstate of the Polyakov Action. This just implied transformation in the manner of Polyakov-based nature is related to the degree and the manner of the correlative Lorentz-Four-Contractions that are applied to the so-eluded-to superstring, of any respective given arbitrary specific substringular case that may be individually considered.  Often, such a perturbation in the said Polyakov Action will ebb back-and-forth from one genus of condition to another of such a condition.  Such topological-based sways -- that are related to the activity of a Polyakov Action eigenmetric -- will always bear a state of multiplicit directoral-based indices that are pulled in some sort of oscillitory-based pulsation, over each of such individually-based gauge-metrics.  When the activity of a local respective Polyakov Action eigenstate -- that is individually considered in a specific scenario -- does the so-stated genus of ebbing that I have recently mentioned, then, this conformally invariant genus of local field delineation may be termed of as a relative conformal Polyakov field transformation.  Yet, such a so-stated transformation is often altered by an exterial interactive state that acts upon a respective superstring that had initially began in the initially stated manner.  When such a superstring is altered in this latter-based format of activity by an exterior Hamiltonian operator, the resultant kinematic activity may be viewed of as a divergent Polyakov field transformation.

Part One of the Fifth Session of Course 18

Let us here consider an initially basic common situation, in general.  From that point in discussion, I will elaborate the initial situation into a more of a specific type of scenario.  A superstring and its directly corresponding counterstring iterates at a given arbitrary spot, over one given arbitrary duration of group insanton. The vast portion of any given arbitrary duration of instanton is the metrical situation of BRST.  The directly correlative first-ordered light-cone-gauge eigenstate that appertains to any one particular given arbitrary superstring of discrete energy permittivity, is -- at the beginning of BRST -- activated, in part, by the coiling genus of activity of substringular topological sway, this coiling of which is caused by the kinematic activity of  the so-stated superstring and its counterstring, bearing a wave-tug/wave-pull, that is directoral-based in the relative antiholomorphic so-eluded-to topological-based sway -- over the course of BRST.  After the duration of one given arbitrary metrical-based increment of BRST, a given arbitrary discrete unit of physical phenomena goes either into the Regge Action and/or into one gauge-metric of the Kaeler Metric, while then going into the Regge Action. After the Regge Action happens to a discrete unit of physical energy, the directly corresponding superstring is pulled into one group metrical increment of the generally unnoticed duration of what I term of as Ultimon Flow.  As one increment of  the generally unnoticed duration of Ultimon Flow begins, the first-ordered point particles that work to comprise the so-eluded-to superstring and its directly corroberative counterstring are more definitively dissociated -- to where such so-stated directly involved first-ordered point particles are "snapped" into a condition of being loosened from the directly previous state of bearing a genus of being of an integration of positive-ground-state holonomic-based substrate (superstrings) that were inter-bound in a manner with an integration of negative-ground-state holonomic-based substrate (counterstrings) -- in the manner that the so-eluded-to superstrings had existed as entities -- that existed as the pointal-basis of discrete energy permittivity (superstrings), that were primed, in a difinitively unique manner with the wave-functional-basis of discrete energy permittivity (counterstrings).  Yet, as this is happening, the overall phenomenology that I have just described is homotopically inter-bound by core-field-density -- in the form of what I term of as mini-string segments. I will continue with the suspense later!  Sam.

More As To Around The Metric Of BRST

While superstrings of one layer of reality converge upon their immediately respective ensuing spatial loci -- that are to be each individually inhabited, over the course of the ensuing iteration of group-based BRST -- each tensoric-related Hamiltonian-based increment of permittivity, when in terms of the correlative redistributed group-attractor-based eigenstates, works to re-associate the respective holonomy of the homotopic stringular function, when this is taken as an integration of the multiplicit morphological-based substringular phenomena, that work to comprise the sum of discrete energy-based quanta that operate in so as to form the substringular scene of one iteration of group-based instanton.  This is particularly the case in the substringular scene of one iteration of group-based BRST.  The so-eluded-to convergence of the re-distribution of directoral-based substringular phenomena, at this point, as a harmonic/annharmonic-based function -- operate, as a multiplicit venue of Hamiltonian-based indices, because of the ebbing of group attraction/group repulsion-based substringular phenomena.  This format of activity -- through the successive series of group instantons -- works to form the field-based multiplicit holonomy of the substringular neighborhoods of the directly pertinent superstrings, that work to form the said layer of reality.  The correlative field covariance and the correlative field codifferentation of the members of such a layer of reality, through the process of the sum of that re-assortment of substringular phenomena that happens over time, for the so-eluded-to tori-sector-range, works to help define the progressional-based alterations or perturbations that happen, in so as to relate the individual members of that layer of reality towards one another.

Right Around the Metrical Duration of BRST

Just after the vast majority of the quaternionic-instanton-field-impulse-mode has occurred, those first-ordered point particles of one layer of reality, that are directly associated with what is to become the holonomic substrate of the topological structure of superstrings of discrete energy permittivity, during the immediately ensuing iteration of the metric of BRST, work to conform to the re-distribution function of the set of point particles -- whose homotopic encodement bears an indical basis with the group trajectoral index of what had become -- over the immediately prior generally unnoticed portion of Ultimon Flow, the partially dissociated so-stated superstrings of discrete energy permittivity.  This is, to where, what is to become the ensuing superstrings -- that will work to act as the unique discrete quanta of energy, will then bear, per individual superstring, one translational transformation matrix of converging proximity.  This is to where each of the said superstrings will reiterate at a spot that is not precisely identicle, at the relative Poincaire level, to where each of these had been at -- during the directly prior iteration of group-based BRST.  The so-eluded-to superstrings of one layer of reality will then re-localize within their proscribed tori-sector-range, since such a re-localization is based upon the translation of the directly interacting group encodement.  Yet, the resultant partially differentiating group repulsion wave-tug-based matrix will, at this point, be applied to the field of the total wave-tug permittivity of the directly associated so-stated tori-sector-based range. Such a group-based permittivity of one layer of reality, that, as an ansantz, bears a resultant topological pull that is basically of a non-abelian-based differential geometric nature, will work to re-delineate the spatial locus of each of the directly pertinant superstrings, in such a manner that is relative to the resultant partially integrated group attractor matrix, to where this activity will tend to converge the relatively associated phenomena of the so-eluded-to layer of reality to the multiplicit loci that each of the directly associated superstrings are to spatialy iterate at -- over the course of the immediately ensuing iteration of group instanton.

Part Four of the Fourth Session of Course 18

After succeeding iterations of group instanton, the spatial relationships between any given arbitrary superstring of discrete energy permittivity and its directly corresponding counterstring tends to alter -- in one manner or another.  If any given arbitrary superstring of discrete energy permittivity and its counterpart are not orientable during one or more of the just mentioned successive iterations of group instanton, and also, if the same so-stated superstring and its counterpart are -- at this metrical point in time -- not orientable during the correlative iterations of one or more Regge Action eigenmetrics, then, such a superstring that I have been discussing here will not be orientable -- which will work to indicate the characteristic as to that the said superstring will be tachyonic during the immediately following iteration of group instanton, once again, when the so-eluded-to superstring is not orientable during both the Bette Action eigenmetric and its correlative Regge Action eigenmetric, that would here appertain to the same singular iteration of group instanton.  Generally, though, any given superstring and its correlative counterstring will tend to be renormalizable -- as may be denoted by the condition that superstrings tend to move as is according to Noether Flow.  Yet, if a superstring and its correlative counterstring were always normalizable -- with not chance for tachyonic flow at all -- the eigenbase of all substringular activity would spontaneously become of a static-based nature, which would work to eventually end the activity of energy, over time.   This works to indicate the need for at least a certain degree of tachyonic flow, in order for energy to be perminently existent.  Yet, because of what may be termed of as the Bette Field Transformation, observable activity is conditioned to be of a perminantly existent nature, over time.  Bette Field Transformations may often, though, in one specific general locus or another, be of a superconformal nature, when the energy at a relatively limited set locus is conditioned to be in a tense of static equilibrium.  Also, often, Bette Field Transformations may be of a conformally invariant nature that is not superconformal -- when one is here dealing with a harmonic-based system that operates in a manner that works to form  Hamiltonian-based field-indices that may be denoted as bearing an extrapolatable manner of viabely detectable re-delineation, over time.  Yet, also, a Bette Field Transformation may be of a divergent nature -- when the correlative substringular activity is perturbative -- to where the activity that is here denoted is perminently scattered from a relatively speaking general locus.  To Be Continued!  Sam.
 I will continue with the suspense later!!!

Some Stuff As To The Motion of Gauge-Bosons

As the Polyakov Action is happening to one given arbitrary superstring -- as the so-stated superstring is expanding, during a given arbitrary duration of BRST --  toward the inverse extent that it is Lorentz-Four-Contracting to -- the directly corresponding gauge-bosons, that pluck to directly associated second-ordered light-cone-gauge eigenstates, in so as to form Schwinger Indices, are being redistributed in a such a manner, in so that these may remain along with the correlative respective mini-string segments that these so-eluded-to heterotic strings are being directly associated with -- as the said gauge-bosons work to form vibrational-based oscillations, via their motion upon the topological surface of the so-eluded-to holonomic substrate of the directly corresponding light-cone-gauge eigenstates.  Since any given arbitrary superstring that is Lorentz-Four-Contracted will tend to reverse-expand, over the course of BRST, to the inverse extent that such a superstring appears, in the globally distinguishable, to be contracted,  such a superstring will do such an expansion of their core-field-density in such a manner in so that it is internally homeomorphic during the directly related general genus of such a Clifford Expansion.  Such a homeomorphic expansion will tend to be trivially isomorphic from the vantage-point of a central conipoint.  This will mean that the gauge-bosons that are timelessly positioned at the start of BRST in a relatively norm-to-holomorphic vantage-point -- when this is taken in comparison to other of such gauge-bosons -- will often work to tend to cause the concavity of the so-eluded-to covariant-based second-ordered light-cone-gauge eigenstates to be comparitively of a reverse-isomorphic manner.  This will then mean that the so-eluded-to second-ordered Schwinger-Indices that are thus formed by the two just mentioned different geni of topological holonomic substrate will bear a covariant-based inverse-relation to the wave-tug/wave-pull of the parity that these will bear, when these are delineated upon the correlative Rarita Structure eigenbase -- which works to form a fractaled tense of two different wave-based indices that bear a Njenhuis relationship to one another.  Such a relationhship helps to inter-relate the Real Reimmanian eigenbase of the wave-functionability of any given arbitrary superstring of discrete energy permittivity with the Real Reimmanian eigenbase of the wave-funcionabilty of any other given arbitrary superstring of discrete energy permittivity, when one considers the correlative kinematic-based Ward-Caucy bounds of such generally considered superstrings, over time.  I will continue with the suspense later!  Sam.

Part Three of the Fourth Session of Course 18

The actual holonomic substrate that is composed of kinematically re-twining mini-stringular segments, that work to interconnect one given arbitrary superstring with its directly corresponding superstringular counterpart -- is known of as a Bette Manifold.  As the Polyakov Action that directly corresponds to one given arbitrary superstring, is happening during one iteration of BRST, there is mini-stringular fabric that is fed into the core-field-density, that works to comprise one general eigenstate of a Bette Manifold -- as the correlative so-eluded-to example of a Clifford Expansion happens to the directly associated stringular-based field.  As this happens, the field that works to inter-bind the correlative superstring with its directly associated Fadeev-Popov-Trace eigenstate will here alter, by means of a different genus of a Clifford Expansion -- as the directly corresponding gauge-metric of a Polyakov Action eigenmetric is undergoing its proscribed activity.  As the so-eluded-to duration of BRST happens -- as the Polyakov Action and the Bette Action happen to the so-stated given arbitrary superstring of discrete permittivity at the same tense of gauge-metric -- the general topological stratum of core-field-density that works to form each second-ordered light-cone-gauge eigenstate, that works to form the correlative first-ordered light-cone-gauge eigenstate, increases in its correlative Hodge-Index, in such a manner in so that the activity of the correlative gauge-bosons upon the said second-ordered light-cone-gauge eigenstates forms a recoiling activity -- as the directly associated second-ordered Schwinger Indices are then formed.  These just mentioned Schwinger Indices are vibrational-based oscillations that ripple upon the correlative eigenstates of the holonomic substrate of the Rarita Structure -- that is directly affiliated to the given arbitrary superstring of this given arbitrary case.  The result of such a ripple is the affect that the Ricci Scalar has upon the Calabi Manifold that is associated with the said superstring -- that is discussed in this case.  Depending upon the genus of such a vibrational-based oscillation, the directly affiliated gravity will work upon the holonomic substrate of the said given arbitrary superstring in a certain manner.  If the activity of the so-eluded-to Schwinger Indices does not work to interact upon an eigenbase of an antiholomorphic Kaeler condition, then, there will be no tendency of a Wick Action to be thus formed.  Yet, if such an activity of the so-eluded-to Schwinger Indices, instead, works to interact upon an eigenbase of an antiholomorphic Kaeler condition, then, there will actually be a tendency of a Wick Action to be thus formed.  There is an antiholomorphic Kaeler condition formed when the general directoral pull of a substringular locus is reversed in its supplemental wave-tug, over a relatively transient duration of group metric.  Such a reversal in holomorphic delineation works to form the potential need of either an alteration of Lagrangian-based spatial freedom, and/or the need for a re-attainment of those fractals of discrete energy that are needed in order for energy to remain as energy.  The Wick Action works to initiate a Gaussian Transformation eigenmetric.
I will continue with the suspense later!  To Be Continued!  Sam Roach.

Part Two of the Fourth Session of Course 18

The coiling activity of the light-cone-gauge is due, in part, to the activity of the plucking (like a harp) of the second-ordered light-cone-gauge eigenstates by gauge-bosons, while the directly associated Clifford Expansion happens to the topological stratum of the mini-string fabric, that works to form the so-eluded-to light-cone-gauge eigenstates -- while the directly affiliated superstrings undergo the Polyakov Action.  This so-stated coiling action, here, results in a modulae-based response, that is a recoiling action of the correlative light-cone-gauge eigenstates. During BRST, the directly associated superstrings and their counterstrings, as always, are connected by segments of what I term of as mini-stringular topological phenomena.  These mini-stringular fabric-based eigenstates attach correlative Poincaires -- that are Poincaire at the stringular level -- with the relative Poincaires of the directly associated counterstrings, each taken individually.  As this is happening during the simultaneous (at the vantage point of a central conipoint) activity of the Polyakov Action and the Bette Action, the correlation of the Poincaires of any given arbitrary superstring, and, the Poincaires of its directly associated counterstring, may be viewed of as a Grassman Manifold.  This is due to the condition that, the condition of the core-field-density that exists in-between a superstring and its counterstring, during BRST is to be homeomorphic, in order for the correlative discrete unit of energy to be orientable.  Such a homeomorphic core-field-density works to bear a scalar magnitude -- that may be viewed of as the Grassman Constant.  An orientable superstring is not tachyonic in its ensuing interation of instanton.  A tachyonic superstring is not orientable during both the Bette Action and its ensuing Regge Action. A tachyonic superstring is less controlled by gravity than a non-tachyonic superstring.  This works to mean that a tachyonioc superstring is less pulled by the correlative Ricci Scalar eigenstates -- via the activity of the directly associated Rarita Structure eigenstates.  This also means that such a superstring is less likely to be undergoing, over the process of such a given arbitrary group-related metric, a sequential series of Kaeler-Metric eigenmetrics.  This works to associate the oreintability of the discrete energy impedance, that is involved with the so-eluded-to discrete energy permittivity, the latter of which is embodied by the holonomic substrate of the so-stated superstrings.  To Be Continued!  Sam Roach.

Part One of the Fourth Session of Course 18

A superstring and its directly corresponding countersting iterate -- at one given arbitrary correlative group instanton.  At this so-stated pulse of duration, the metric of BRST happens -- as the predominant metric that happens, in so as to complete the majority of the so-stated instanton.  BRST is when the correlative supestrings are iterated at basically a standstill -- in so as to demarcate one Hamiltonian-based pulse of each correlative superstring, in the course of one correlative index of what works to become of a sequential series of such instantons -- that then work to form the flow of those group instantons that happen in so as to form the kinematic activity of energy through time.The light-cone-gauge is coiled by the activity that happens during the integration of the sequential series of instantons, that is primarily due to the integration of a sequential series of discrete durations of BRST.  This coiling is due, in part, to the interaction of gauge-bosons upon the topological fabric that works to form the correlative light-cone-gauge eigenstates.  I will explain this better later!  This is a start to this topic.  I will continue with the suspense later!!! Sam.

Part Four of the Third Session of Course 18

As I have eluded-to before, the dimensionality of the Gliossi-Sherk-Olive field of the three-dimensional field of a two-dimensional superstring of discrete energy permittivity, that kinematically differentiates over time, tends to work to form a world-sheet that bears a mappable tracing that can be extrapolated as a majorized plane -- that pulls in the relative holomorphic direction of the path of its Lagrangian -- with an annulus in its center.  The orbifolds that are higher in dimensionality than that of a three-dimensional world-sheet, as well as all of the other membrane-based topological entities that are also higher in dimensionality than a three-dimensional world-sheet, bear cohomologies that work to involve either relatively holomorphic or relatively antiholomorphic Gliossi-based Poincaires -- at the topological surface of the so-eluded-to cohomological stratum that I have implied here.  Cohomologies of what may be termed of as being of either a holomorphic or an antiholomorphic Gliossi-based Poincaire will tend to form cyclic permutations at the topological surface of their mappable tracing, over time.  Cyclic permutations often form, at least to a certain extent, Chern-Simmons cohomologies that are perturbative and non-hermitian.  Such Lagrangian-based perturbative Chern-Simmons singularities may be formed, due to the cohomological-based conditions of the directly related ghost-based indices going from being of a Real Reimmanian based setting to being of a Njenhuis based setting -- over a sequential series of group instantons.  Such metrical-based perturbative Chern-Simmons singularities may be formed, due to the cohomological-based conditions of the directly related ghost-based indices -- being propagated in such a manner, in so that these so-stated indices, at the Poincaire level, will here tend to fluctuate annharmonically over time.  In other way of looking at the Lagrangian-based tendency of here not being of a Yau-Exact manner, is that the directly corresponding cohomology of such an eluded-to topological-based setting is not smooth in all of its derivatives that equal the number of spatial dimensions that such a Ward-Caucy-based substringular phenomenon is being translated through, over time.  Also, any substringular phenomenon that accelerates and/or decelerates in its pulse, over a sequential series of instantons, works to bear a non-metrically smooth substringular oscillation -- that will make it, to one degree or another, Chern-Simmons, when taken in a metrical-based manner.  As I have said before, any cohomolocial-based setting that is not hermitian in both a Lagrangian-based manner and in a metrical-based manner, is not Yau-Exact.  I will continue with the suspense later! Sam.

More As To Before About Group Attractors

As the earlier mentioned superstrings of discrete energy permittivity modify the redistribution of their morphologies -- taken as a whole -- the directoral-based generation is localized at each resultant topological sway, as an instituted re-parameterization of the indical bases of each of the so-mentioned superstrings.  This activity works to differentiate-out a kernel of that sub-space of each Hamiltonian-based path operand flux-line, that is divergent from the convergent series of reiterated substringular transition kernel homotopy.  Such a kernel acts as a repulsion factor, that pulls-in the residue from the directly associated substringular holonomic substrate, in order to allow for that activity of the correlative group attractor matrices -- of which is to devolve upon the spatial integration of the given superstrings, that are at the given proximally covariant locus.  As the so-eluded-to general locant kinematically differentiates, the correlative superstrings act as a series-invariant-mode -- that changes subtly over time.  While the given homotopic eigenbase that has thus been discussed here differentiates conformally, the correlative trait encodement holonomously, after each successive reiteration of group instanton, happens in such a manner in so as to be operated as a harmonic oscillation -- within a smoothly integrated motion of the here implied directly associated indical-based convergence.  I will continue with the suspense later! To Be Continued!  Sam.

As To Group Attractors

I am about to start to explain the idea behind what a group attractor eigenmatrix of directly associated strings is, as such an eigenmatrix acts as one group trait encodement.:  Let us initially say that three superstrings of discrete energy permittivity function as one homotopic-based trait -- as an orbifold -- of which devolves the basis of one particular unique holonomic substrate.  Two of the so-eluded-to strings that are eigen to the directly associated homotopy are one-dimensional, and work to form a cohomology that acts as a dually bound  conical-shaped mappable tracing, that forms a core-field-density that bears a closing of the otherwise open looping, while one of the so-eluded-to strings that are eigen to the directly associated homotopy are two-dimensional -- and works to form a core-field-density that acts as an integration of a large Hodge-Index of  toroidal-based eigenstates of morphology, that, when such eigenstates come together, work to form a shaft-like mappable tracing that may be extrapolated as a shaft-like appendage to the so-eluded-to general homotopic index.  This just mentioned compilation of cohomological indices acts over time, in so as to form a kinematic display that acts as a series of covariant cyclic permutation -- that works to form an eigenbase that may be implemented as a revolution of proximal ordering - when it comes to the nth delineation of what would here involve the kinematic activity of the so-mentioned two-dimensional string, in this given arbitrary case that I am discussing here.  As the so-mentioned eigenbase of homotopic cohomological-based index is being redefined, over the succession of each iterative and reiterative covariant-based occurrance of group instanton, the three so-mentioned superstrings of discrete energy permittivity that I have mentioned here in this case will here involve a discrete genus of overall wave-tug permittivity -- that will work to cause all three of such directly associated superstrings to bear a condition of being detectable as being proximal in the globally distinguishable.  Yet, when the three here mentioned superstrings of such a case scenario are not initially detectable as being proximal in the globally distinguishable -- in such a manner to where such so-stated superstrings will gradually  work to bear a direct Ward-Cauchy kinematic basis of differentiation, that would here involve the same tense of imagination (the directly associated wobbling of the correlative Fadeev-Popov-Trace eigenstates, are to alter, in so as to then be of the same Real Riemannian Gaussian Translation, amongst the three so-eluded-to discrete units of energy, to where all three directly associated strings will then act as three subspaces that are then of the same universal setting) -- the here directly involved superstrings' unique differential clause, in terms of the correlative covariant wave-interaction,  will gradually work to make these so-stated directly associated strings to eventually act as being adjacent in the globally distinguishable, over time.
I will continue with the suspense later!  To be continued!  Sincerely, Sam.

The Kaeler Relationship To Ghost Annhilation

When a Gliossi-Sherk-Olive ghost-based cohomology of any significant scalar magnitude of Hodge-based index is scattered annharmonically by relatively reverse-holomorphic norm-state projections -- there is a correlative Nielson-Kollosh ghost-based cohomololgy of a significant scalar magnitude of Hodge-based index that is, as well, scattered annharmonically by relatively reverse-holomophic norm-state projections, off of the relative Real Reimmanian Plane.  There is, at this general group metrical point in activity, a complementary-based group attractor that works to pull the residue of the so-eluded-to annharmonically scattered Neilson-Kollosh-based cohomological pattern out of the relatively Njenhuis Plane -- from which the so-stated Neilson-Kollosh ghost-based pattern was formed by gravitons and gravitinos -- into the relative Real Reimmanian Plane, where the so-stated Gliossi-Sherk-Olive ghost-based cohomological pattern that I have here eluded-to was initially both formed and scattered into a certain quantum of Fock Space residue.  Likewise, there is, simultaneously, via the vantage-point of a central conipoint, a complementary-based group attractor that works to pull the residue of the so-eluded-to annharmonically scattered Gliossi-Sherk-Olive ghost-based pattern -- out of the relatively Real Reimmanian Plane and into the correlative Njenhuis Plane, where the so-stated Neilson-Kollosh ghost-based cohomological pattern that I have eluded-to was initially both formed and scattered into a certain quantum of Fock Space residue.  It is, in both just eluded-to cases, one covariant, codifferentiable, and codeterminable ghost-inhibitor for each of such so-stated cases, when taken individually, per case, that works to act upon both of the so-eluded-to genus-based formats of group attractor indices -- in so as to cause such an exchange of the residue of the so-stated ghost-based cohomological indices.  When such a significant quantum, as I have here eluded-to, of the residue of ghost-based cohomological indices, is recycled in the manner that I have just mentioned -- this genus of activity will here work to form an antiholomorphic Kaeler conidition -- via the affect that such a genus of activity works to bear upon the relatively local Rarita Structure eigenstates.  This so-stated affect works to involve the Ricci Scalar -- since the Ricci Scalar happens along the topological surface of the activity of the correlative Rarita Structure eigenstates.  Such an eluded-to initialization of an antiholomorphic Kaeler condition works to cause what is known of as the Kaeler Metric -- at the here given arbitrary local substringular neighborhood.  This will then work to initiate the Wick Action -- which will ensue to cause a Gaussian Transformation, in so as to allow for both the continued kinematic differentiation of active superstrings, as well as causing discrete energy to reattain their correlative multiplets of the fractal of such discrete energy.  To Be Continued!  I will continue with the suspense later!  Sam Roach.

About a Special Ghost Inhibitor

When a superstringular-based phenomenon is scattered harmonically, in so as to form a cohomological-based index, the just eluded-to scattering is of a Reimman scattering.  When the just mentioned superstringular-based phenomenon is scattered enharmonically in so as to annihilate the just mentioned cohomological-based index, the just eluded-to scattering is of a Rayleigh scattering.  So, when one substringular entity of relative reverse-holomorphic-based norm-state projection works to involve a Rayleigh-based scattering, in so as to alleviate the eluded-to condition of a mappable tracing of the physical memory of both the existence and the activity of a given arbitrary substringular entity, this activity of such a genus of a Rayleigh-based scattering will tend to trigger a genus of a ghost inhibitor, that acts upon the holonomic substrate of the so-eluded-to ghost-based cohomological-index -- via the pulling in of wave-tug/wave-pull, that is here due to the eminent activity of a certain genus of a group attractor -- in so as to work to exchange the residue of the phenomenology of GSO ghosts with the residue of the phenomenology of Neilson-Kollosh ghosts.  To Be Continued!!! Sam.

A Little Bit About Other Formats of Scattering

Often, a substringular scattering that is acted upon from an outside source involves both a Reimman scattering and a Rayleigh scattering -- at one general given arbitrary locus.  For instance, let us say that one orbifold eigenset were to strike another orbifold eigenset, in such a manner in so that there is an initial Rayleigh-based scattering at the interial Poincaire-based locus of the so-eluded-to scattering, and, to where, there is a latter happening of a Reimman-based scattering at the exterial Poincaire-based locus of the same general genus of the so-eluded-to scattering.  Here, the interial so-mentioned scattering involves an enharmonic scattering of superstrings, and, the exterial so-mentioned scattering involves a harmonic scattering of superstrings.  The so-mentioned enharmonic scattering works to involve adjacent eigenstates of the said re-displacement of superstrings that work to bear an odd chirality of group related metric -- through the tensoric intricacies of the here spewn eigenbase of Lagrangian setting, over time.  This is while the so-mentioned harmonic scattering works to involve adjacent eigenstates of the said re-displacement of superstrings that work to bear an even chirality of group related metric -- through the tensoric intricacies of the here spawn eigenbase of Lagrangian setting, over time.  This may be more pictorially described in this manner:  The enharmonic so-mentioned scattering in this case works to form a chaotic delineation of re-displaced eigenstates -- in the form of a set of re-delineated superstrings that are not evenly redisplaced, or are outside of any particular pattern of re-established positionings -- as the so-mentioned superstrings are pulled out of an initial Ward-Caucy tense of order,  that would have existed here before the so-eluded-to scattering.  On the other hand, the harmonic so-mentioned scattering works to form a tense of a re-convened eigenbase  of delineation of re-displaced eigenstates -- in the form of a set of re-established positionings -- as the so-mentioned superstrings are pulled back into the initial Ward-Caucy tense of order, that, again, would have existed here before the so-eluded-to scattering.  This would only happen if the initial disorder that would here be caused by the Rayleigh scattering was brought back into order by the effects of an exterior-based source -- that acted upon the so-mentioned conditions of chaos, in so as to bring a state of optimum rest, in so as to scatter the so-stated delineations of chaos back into order.  Yet, eventually, such a tense of a chaotic-based scattering being scattered into a more orderly distribution by an outside source, will tend to bear a more heightened aptitude of being brought back into a condition of chaos once again.  For instance, the Big Bang -- when it created the multiverse -- formed an extreme initial degree of chaos, of which eventually was brought into some local tenses of heightened order.  Yet, the tendency of the just mentioned order is in the direction of a heightened capacity to go back into a state of disorder.  So, as long as there is no exterior influence upon an initial scattering in the substringular, the tendency is, rather, to go from an initial Reimman scattering of orderly re-displacement into a latter Rayleigh scattering of a chaotic re-displacement.

The third part of Session 3 of course 18

The tori-sector-ranges -- during the gauge-metric in-between group instantons, in which both the Bases of Light are majorized and the space-hole is in engagement -- are aligned in such a manner in so that what is to be each ensuing predominant layer of reality (predominant tori-sector-range), is in the forward-holomorphic positioning from the vantage point of forward-time-based momenta eigenstates, while, this is in the reverse-holomorphic positioning from the vantage point of backward-time-based momenta eigenstates.  For every one majorization of an eigenbasis of an overall Basis of Light that exists in forward-time-bearing momenta holomorphicity, there is one majorization of an eigenbasis of an overall Basis of Light that exists in backward-time-bearing momenta holomorphicity.  So, there is a tendency to where, for every holomorphic-bearing eigenstate, there is an antiholomorphic-bearing eigenstate -- as such just eluded-to eigenstates are propagated through their correlative Lagrangian-based paths over a successive series of instantons (time).  Forward-moving time, for each individual tori-sector-range -- is directly interconnected to backward-moving time, for each individual tori-sector-range -- via those segments of inter-woven discrete substringular field core-density (an interconnection of organized mini-string) that are Ward-Caucy bound, by both the existence and the activity of the correlative substringular encoders.
Just touching base today!  To Be Continued!!! I will continue with the suspense later!  Sam.

Conical Semi-Groups Versus Torroidal Semi-Groups, Displacements

Let us say that one were to consider one conical-shaped orbifold that holomorphically struck a torroidal-shaped orbifold, at a spot other than at the general locus of its annulus, to where the latter general format of orbifold -- of which were to here be approaching the so-eluded-to conical-shaped orbifold, at the same velocity, while in the process, was moving in the directly antiholomorphic directoral-based Hamiltonian mappable tracing, over time.  Let us, furthermore, say that both the so-stated conical-shaped orbifold and the torroidal-shaped orbifold that I have mentioned here were to bear the same Hodge-Index of Hamiltonian-based composition -- both in terms of the overall intrinsic rest energy quanta, and, also in terms of their intrinsic Lorentz-Four-Contraction, in so that the degree of compactification of both of the orbifolds that I have mentioned here were to be the same -- in terms of the resultant of the Lorentz-Four-Contractions of both of the said orbifolds, as both of the so-eluded-to semi-groups are to here approach each other in a Ward-Caucy manner that relates to a tense of 180 degrees.  So, here, the resultant genus of Polyakov-Action of both of the so-stated orbifolds are to be of the same parity -- as each of the said orbifolds are to here approach each other on a common Real Reimmanian plane, that curves as to the intrinsic curvature of space-time-fabric, and not of a Wilson Line-based plane of binary approach.  Here, the conical-based orbifold structure that I have eluded-to will tend to scatter the torroidal-based orbifold structure in a Rayleigh scattering -- as the two so-eluded-to orbifolds are to here strike each other upon the general gauge-metric, in which the two said semi-groups are to then work to bear a viable Gliossi-based Yakawa Coupling.  Yet, if everything here were to be the same, except that both of the so-eluded-to orbifold eigensets that are to here be involved were to be of a torroidal-based nature, then, the scattering will, instead, be of a Reimman scattering.  To Be Continued!  I will continue with the suspense later!!! Sam.

Some Stough As To Reimman Scattering Versus Rayleigh Scattering

When one given arbitrary substringular phenomenology is scattered harmonically, such an eluded-to semi-group is then here undergoing a Reimman Scattering.  When one given arbitrary substringular phenomenonlogy is, instead, scattered annharmonically, such an eluded-to semi-group is then here undergoing a Rayleigh scattering.  A Reimman Scattering -- in the substringular -- is one in which one given arbitrary group of superstrings that operate to perform one specific function (a given arbitrary  orbifold eigenset) is scattered in such a manner, in so that the adjacent eigenmembers of phenomenolgy that are redistributed by the so-stated scattering will bear an even chirality, as well as that these so-eluded-to eigenmembers that are adjacent are here tending to bear a trivial isomorphism -- as the so-stated given arbitrary orbifold eigenset that is here scattered is re-distributed into a different delineation, over time.  Whereas, a Rayleigh Scattering -- in the substringluar -- is one in which one given arbitrary  group of superstrings that operate to perform one specific function (a given arbitrary orbifold eigenset) is scattered in such a manner in so that the adjacent eigenmembers of phenomenology that are redistributed by the so-stated scattering will bear an odd chirality, as well as that these so-eluded-to eigenmembers that are adjacent are here tending to bear a non-trivial isomorphism. -- as the so-stated given arbitrary orbifold eigenset that is here scattered is re-distributed into a different delineation, over time.  Such just mentioned scatterings (that are either of a Reimman Scattering or that are of a Rayleigh Scattering) may be of either a euclidean-based perturbative genus, or such scatterings may be of a Clifford or euler-based perturbative genus.  A prime example of a general format of a Reimman Scattering, is the process of the formation of cohomolgical projections, over time, by the mappable tracings -- that are multiplicitly pulled into existence by the kinematic activity of substringular activities, in the process of the integration of ghost-based indices, while, a prime example of a general format of a Rayleigh Scattering, is the process of the vanquishment of cohomological projections, over time, by the mappable tracings that are multiplicitly pulled into existence by the kinematic activity of substringular activities, in the process of the reverse-derivation of ghost-based indices.
Next post, the tendencies of scatterings due to both the motion of either torroidal-based morphologies that are kinematically delineated, as redistributed orbifold eigensets that are displaced over time, and/or the motion of conical-based morphologies that are kinematically delineated, as redistributed orbifold eigensets that are displaced over time.
To Be Continued!  I will continue with the suspense later!!! Sam Roach.

A Little About The Displacement of the Substringular

When one considers two semi-groups that collide with an equal velocity upon contact, this of which  acts as two relatively small groups of superstringular phenomenology that are alike -- except for the condition that one of the two just mentioned superstringular semi-groups bears a relatively homeomorphic pattern of Lorentz-Four-Contraction, of which is more compactified, in general, than the other of the two so-eluded-to semi-groups that I have here mentioned -- then, the first of such eluded-to semi-groups of superstringular phenomenology will tend to act as a holonomic substrate that will be able to produce more of a displacement upon the second of such eluded-to semi-groups, again, upon contact, in so long as both of the here mentioned semi-groups work to bear the same differential pattern of general morphology, and, in so long as both of the here mentioned semi-groups are of the same Hodge-based scalar magnitude of Hamiltonian Ward-Neumman-based quanta, and, in so long as both of the here mentioned semi-groups -- that will here act as two colliding respective holonomic substrates, work to bear the same genus and format of conformal invariance, upon contact.  This will then, here, work to indicate that both of the here eluded-to structures of superstringular phenomenology will bear two different resultant tenses of both their Lorentz-Four-Contraction, as well as bearing two different tenses of the scalar magnitude as to the extent of their two distinct respective gauge-metrics, when this is in consideration of the correlative eigenstates of their Polyakov-Action-based activity.  This also only tends to be true if both of the here mentioned semi-groups will here be both approaching each other at the same velocity, in relativistic terms, right before contact -- via the presence of a binary Hamiltonian operand, that acts as the mappable path of a homeomorphic binary-based Lagrangian, as well as both of these so-eluded-to semi-groups striking each other with the same genus of their overall permittivity-based index -- as taken from the vantage-point of a central conipoint.  Such a displacement may either be of a Wess-Zumio manner of metrical scalar genus, or, such a displacement may, instead, be of a more perturbative format -- in so that the displacement will then here scatter the eigenbase of the Hodge-based group index of the original composition of the initial structure of the "weaker" of such holonomic substrates, that here worked to comprise the Hamiltonian operator that acted as the here mentioned semi-group that I had initally eluded-to as being more likely to be overtly displaced -- at the here eluded-to general locus, of what may either be a euclidean or a Clifford-based scattering of one semi-group of phenomenology by another semi-group of phenomenology.  I will continue with the suspense later!  To Be Continued!!! Sam Roach.

Part Two of What may be my Third Session of Course 18

The condition of each individual layer of reality of each set of parallel universes, as existing in a completely diversified manner of delineatory index -- in a granular-based flow of homotopically-based indices, in such a manner in so that each of the so-stated layers of reality of each set of parallel universes -- may be termed of as an extremely staggered tori-sector-range, to where this is related to what is termed of as the Gliossi-Sherk-Olive-Theorem.  Under the just mentioned multiplicit Ward-Caucy conditions, each layer of of reality, or, in other words, each tori-sector-range of each individual set of parallel universes, is intricately woven into the general fabric-based boundary conditions of all of the other parallel universes of a given arbitrary set of parallel universes, in so as to work at forming an inter-relationship of all of the layers of reality of one given arbitrary set of parallel universes, in retrospect to one another -- in an interdependently respective eminent manner.  The general condition of those directly applicable ghost anomalies -- as well as their directly associated cohomological-based projections -- as being formed as the multiplicit mappable tracing of the physical memory of the correlative superstrings of discrete energy permittivity -- is the basis of  what is formed of as a result of this genus of activity,  to where this works to form what are known of as Gliossi-Sherk-Olive ghosts.  The integration of such just-eluded-to ghost-based indices works to form those cohomologica-based entities that are directly related to the extrapolation as to the what, where, and how, those so-stated superstrings of discrete energy permittivity had kinematically differentiated, over a sequential series of group instantons.

Some Additional Help

When one given arbitrary relatively more variant-based substringular motion of superstrings strikes a riven arbitrary relatively more conformally invariant-based substringular motion of superstrings -- over a given arbitrary set sequential series of group instantons -- the so-stated more conformally invariant set of substringular phenomenology will tend to bear more of a potential to be displaced, than the so-stated more variant set of substringular phenomenology.  As this so-eluded-to set of conditions happens over time, the relatively more conformally invariant set of substringular phenomenology that I have just eluded to will tend to bear less of an overall overt basis of Lorentz-Four-Contraction, while, the relatively less conformally invariant set of substringular phenomenology that I have just eluded to will tend to bear more of an overall overt basis of Lorentz-Four-Contraction.

Part One of the Third Session of Course 18 -- The Ricci Scalar and the Kaeler Metric

Any given arbitrary set of superstrings of discrete energy permittivity, that are of one layer of reality -- that would here work to describe all of the superstrings that would then appertain directly to both one layer of reality, that would thus exist, as well, to where this here is  being of the same set of parallel universes --, when one also considers their directly corresponding counterstrings, and their correlative Fadeev-Popov-Trace eigenstates -- that are inextricably bound to their correlative light-cone-gauge eigenstates --, tends to kinematically differentiate, over time, within a realm, that may be physically described of as the Ward-Caucy bounds of their directly associated tori-sector-range.  There then tends to be, when one bases this description as to what I mean by of as a tori-sector-range, as many layers of reality, or tori-sector-ranges, in any of the three respective sets of parallel universes that one may here work to consider, in any given arbitrary case, as there are tenses of reality that differ to at least some sort of extent, from within whatever set of universes that one may directly consider -- in the just-eluded-to genus of an extrapolatory consideration.  There are initially 159,000 layers of reality from within the Ward-Caucy bounds of any specificallly considered set of parallel universes -- from before any fraying of space-time-fabric had started to occur -- before any of the damage that was due to any black-hole had worked upon the here eluded-to set of parallel universes, that one may here be considering, under any given arbitrary extrapolation as to the number of tori-sector-ranges that would then exist at the so-eluded-to genus of consideration.  This is all for now!!! To be continued!  Sam.