A Little About The Norm-Projections That Help Start Gaussian Transformations

The Wick Action is put into play by the activity of gluons. The activity of gluons by which certain sub-atomic particles are stuck together is known of as the strong force.  Gluons work to stick the respective sub-atomic particles together that the said gluons are most directly associated with via the help of a perturbation in the Ricci Scalar that involves an Anti-De-Sitter/De-Sitter gravitational alteration.  Just as the quaternionic-instanton-field-impulse begins to happen directly before instanton, what are to be gluons during the ensuing respective instanton undergo an Anti-De-Sitter gravitational pull that initially "flaps" the concavity of what are to be the Hausendorf Projections that will form Wick Action eigenstates, during the same general region during the same duration of instanton, from being directly concave toward each other toward being directly concave away from each other.  The relatively simultaneous activity of the mentioned Anti-De-Sitter gravitational directoralization of the Ricci Scalar initially -- as the ends of the corresponding mentioned Hausendorf states are flapping -- works to hold the related Hausendorf norm-states in a relatively and covariant still position until the beginning of the ensuing local instanton.  Just as the said ensuing instanton that we are arbitrarily dealing with here begins, the ends of the Hausendorf norm state eigenstates  that are to work together to form a projection known of as a Wick Action "flap" back into a condition of being concave toward each other on account of the alteration of the Ricci Scalar in regards with the relatively local gluonic force from going back into a De-Sitter gravitational mode.  At this point, the respective Hausendorf eigenstates that are to integrate in so as to form the Wick Action are relatively loosened from a localized covariant-based virtual standstill into being thence pulled into the direction of a Campbell-Hausendorf projection that is known of as a Landau-Gisner Action.  The end of the initially touched eigenstate of the mentioned Landau-Gisner Action Action overall eigenstate is of a planar configuration that bears a Hodge volume that is 6.25*10^18 times the Hodge volume of a fully contracted Higgs Action eigenstate.  At the respective relatively norm-to-reverse-holomorphic end of the said Landau-Gisner Action that we are arbitrarily discussing in this given case at the relatively holomorphic end of where the said Action is undergoing a Fischler-Suskind-Mechanism eigenmetric, the end of the Campbell-Hausendorf projection here is correspondingly concave-up.  Directly to the relatively reverse holomorphic end of the just mentioned relatively concave-up holonomic geometry -- connected via mini-string -- is another of such prior mentioned planar Hodge-based volumes that also consist of tightly-knit and integrated first-ordered-point particles.  Such an interconnectioin continues as such until a planar end of a Campbell-Hausendorf norm-state is avainable to lift a respective Klein Bottle eigenstate via its corresponding Higgs Action eigenstate.  Any given arbitrary well-functioning Wick Action eigenstate touches its corresponding Landau-Gisner Action eigenstate in a Gliossi manner at 22.5 degrees from a Wilson Line that one may subtend as colinear -- in a Laplacian manner -- in delineation across the relatively norm-to-holomorphic end of the most holomorphically-placed end of the said Landau-Gisner Action that is to undergo its associated Fischler-Suskind-Mechanism.  This -- via the particular twining and motion of that mini-string that binds the whole said Mechanism -- causes the flush leveraging of the Higgs Action to move the Klein Bottle, while also causing the respective Higgs Action eigenstate involved in any given particular case to angle at 22.5 degrees  from straight up-and-down holomorphically in such a manner so as to move the corresponding Klein Bottle eigenstate to the left -- while causing the same Higgs Action eigenstate to angle at 22.5 degrees from straight up-and-down reverse-holomorphically in such a manner so as to move the corresponding Klein Bottle to the right.  Enough for now!  Sam Roach.        

A Little Clarification As To The Light-Cone-Gauge

The last three Planck-based motions of the Klein Bottle in any given arbitrary Kaeler-Metric eigen-based activity is a positional readjustment that allows the Klein Bottle -- via the Higgs Action -- to be able to move to a locally-based different general spot so that a Gaussian Transformation may occur at a slightly different location during an ensuing Kaeler-Metric eigen-based activity in terms of the utilization of the same Klein Bottle eigenstate.  This way, the same Klein Bottle eigenstate is able to be used for local Gaussian Transformations that are not of the same holonomic substrate in the same general region.
There are countless Klein Bottle eigenstates that multiplicitly move via the Kaeler-Metric eigencondition via one Higgs Action eigenstate per Klein Bottle eigenstate.  This way, relatively localized Higgs Action eigenstates are able to form relatively localized Gaussian Transformations indirectly so that local changes in norm-conditions that are essential for the freeing up of space in a general region may be more directly associated so that there is no chance for the inability of superstrings -- that are in need of reattaining permittivity so that the said strings may be the energy that these need to be so that superstrings and thus discrete reality may exist -- to lack the kinematic interchanges that are necessary so that Gaussian Transformations may happen to the said superstrings so that the said here given arbitrary norm conditions may occur so that such a reattaining of permittivity in discrete units of holonomic-based energy may occur.  The implied Klein Bottle eigenstates thence exist all over the place in their respective world-tubes so that wherever superstrings are relatively at, there is a basis of substrate in which the respective Higgs Acion eigenstates may be able to move the respective Klein Bottle eigenstates in such a manner so that Gaussian Transformations may occur for the reasons mentioned before.  Therefore, Wick Action eigenstates, Landau-Gisner Action eigenstates, and the holonomic substrate of Fischler-Suskind-Mechanism eigenstates also are multiplicitly displaced around the general world-tubes so that there may be a definitive basis for the ability of the Kaeler-Metric eigenconditions to happen in such a manner so that the necessary Gaussian Transformations may occur.  I will continue with the suspence later!  Sincerely, Sam.

The Second Part Of The Tenth Session Of Course Ten

The Laplacian mapping of the path that relates to what I was last describing in the first part of session 10 (the path of the orbifolds in a timeless fret that is here to be considered) curves in part on account of the corresponding Njenhuis wave-tug permittivity eigenforces and the related Njenhuis wave-tug impedance eigenforces that had happened over a previous Fourier Transformation that had directly interacted with the condition to be mapped that I have just described.  This mapping described alters over a Fourier Transform that subsequently occurs over a sequential series of instantons in such a manner that indicates a relatively gradual change in the corresponding norm-conditions that works to eventually allow for those Gaussian Transformations that act in such a manner so that substringular room may be freed up so that space-time fabric may be kinematic in order for energy to exist so that reality may persist.  This activity that I just described happens in such a manner so that the Campbell/Hausendorf Projections, the Campbell Projections, the Hausendorf Projections, and the Zero-Norm Projections that are formed on account of this may here arbitrarily form a hermitian motion either directly or indirectly upon those fermionic superstrings that act as discrete units of kinetic energy permittivity in an electron to form photons via the Greene Function in a manner known of as the Fujikawa Coupling.
In other related cases, such an activity may form other types of Yakawa Couplings.
Yakawa Couplings are activites in which superstringular topology either touches, rubs, and/or curls upon other superstringular topology.  A direct touch of a substringular phenomena upon another substringular phenomena is known of as a Gliossi Action.  When such a Gliossi Action produces a torque in one or more related topological sources that are directly involved in the Gliossi Action, then such a Gliossi touch is said to bear cohomology.  Such an activity of orbifolds that works to allow for the opening and/or the closing of superstrings alters both the Laplacian and the Sub-Fourier differential translation of the Clifford Expansion delineaions of light-cone-gauge eigenstates that happen during the corresponding eigenmetrics in which such a type of expansion is happening in over the course in which the related superstrings undergo such an activity over their affiliated durations that involve  BRST in the multiplicit loci in which this is happening.  The torsioning of the affiliated Clifford Expansion eigenconditions of light-cone-gauge eigenstates helps to cause part of the reason as to why space-time-fabric is curved in relationship to the existence and the activity of electromagnetic energy.     
I will ellaborate more in future sessions.  You have a phenomenal day!  Sincerely, Samuel Roach.

Part One Of The Tenth Session Of Course Ten

Let's say that there were, in the following case scenario, three covariant substringular groups that are here going through a Fourier Transformation that is here perturbated in a Njenhuis manner in such a way to where the three said groups which here represent three orbifolds work to produce a alterior perturbation in the corresponding covariant differentiation that will potentially alter any potential Kaluza-Klein light-cone-gauge topology in the said three orbifolds to be brought into having a Yang-Mills light-cone-gauge topology.  Yet here, the homotopic residue of each mentioned substringular group will maintain its  Fourier-based generation of substringular field during the duration in which the said three mentioned groups propagate along the Ultimon Flow -- when one considers the integration of both the Real Reimmanian-based time that involves the reiterating of instantons along with the Imaginary-based time that exists in-between the durations of the said individual instantons over the course of the iteration and the reiteration of the integrated sequential series of instantons that form the time that involves the mentioned Fourier Transformaion illuded to here.  Homotopic residue is the mini-string segments that begin to break off while yet reconnect to other topology during what I term of as the space-hole.  The space-hole is the duration that happens right before the instanton-quaternionic-field-impulse-mode in which topology virtually disconnects in just of a manner in so that homotoy may be altered in just enough of a degree in order that norm-conditions may be able to change in the manner that these need to change so that the proper Gaussian Transformations may happen so that the substringular may be spontaneously and perpetually kinematic so that energy may be able to persist.  The prior activity that I was describing before I mentioned what homotopic residue is happens so thawt the previously mentioned homogeneous wave permittivity will allow for the commutation of spin symmetry via the indices that are relatively local to all three of the described substringular groups at one general group metric or another on their way through the Lagrangian-based operand that each group is kinematically pulled into through their motion along the Continuum.  Such an activity allows for the said three substringular groups to here differentiate in a timewise manner with what is in this case an even chirality that exists in an isometric fashion among the vibratory operation of the homotopic residue that respectively exists in correspondence with the three said substringular groups when in covariant relation with each other.  This prior activity is happening in holonomic proportion, in terms of their corresponding Hodge-Indices and the parity of their respective fractal of angular momentum, in such a manner so that their related norm-conditions that are in transition are here to be in covariance with the fractal of angular momentum of each sector of the described homotopic residue.  In the meanwhile, the tri-local substringular encodements that help to determine the positioning of the corresponding superstrings along with helping to determine the positioning of said superstrings homotopic residue, here works to converge the coniaxial that is related to the conipoint that helps to define the relativistic center of the general activity that I am describing here so that the locus of the related orbifolds that represent the three substringular groups may be in isometric and Hodge proportion to the euclidean-based even distribution of their wave propagation and their respective residue over what may be described here as an inverse of a Clifford Expansion that brings the three orbifolds into an interactive-based region.  Those semi-groups that here arbitrarily commute a kinematic discharge of phenomena that is related to the superstrings that comprise the said orbifolds as the said orbifolds exist in relation to one another will here form spin-symmetries that become covaliant via wave coaxials that kinematically differentiate thru Lagrangians that occur over an arbitrary Fourier Transform.  I will continue with the suspence later!  Part Two Soon!  Sincerely, Sam.           

The Ninth Session Of Course Ten

What general type of a perturbation series would propagate if certain strings of covariant traits were to aquire topological sways, and how would this alter the angular momentum of that homotopic condition whose phenomenology is defined by the interaction of those covariant traits which act in an eigen manner toward the pertainent differentiable semi-groups?  (The semi-groups here are norm- states that act as catylists to the formation of those strings which encode for the mentioned covariant traits)?  As an arbitrary example:  A superstring is reiterated within the same neighborhood, or, in other words, within the same general substringular region.  Zillions of related strings do the same here too.  A minority of the two-dimensional strings related here iterate and reiterate in a relatively side-to-side manner on a slightly differentiable coaxial basis.  These strings maintain an even function of polar shift when one is to consider the Ward amplitude of all of the resultant Real Reimmanian and Njenhuis tensors that inter-relate in a manner that forms a unitized group tree-amplitude diretoral.  This just mentioned activity operates to allow the corresponding superstrings to not get "kicked out" of their association with the other superstrings that also help to define the basis of their respective covariant traits.  The change in the resultant holomorphic index, thus caused, commutes phase change in the nodation of the anharmonic oscillation pattern that may be mapped through a Lagrangian over an affiliated Fourier Transformation.  This causes a change in wave connection and wave-tug between the other superstrings and the other mentioned inter-related strings.  This phase alteration repositions the parallax of the consequently affiliated homotopic differentiation by setting up a buffer in the related semi-groups.  This activity localized as a supplement in the Imaginary tense toward the change of angular homotopy that is caused by the coaxial twists of the corresponding superstrings.  The buffer mentioned here is produced by the harmonic sway of those wave connections which were relocalized by the illuded to propagation of axions.  Such axions were generated by the tensors that here work to cause a euclidean repositioning during every instanton in which the related superstrings are in the process of being spontaneously torqued in a cohomoligical manner.  This angular momentum change would, by interacting with the mentioned "buffer", diverge the local condition of conformal invariance of the interactive traits that had been just going on previously, yet, the said change in angular momentum would then converge the association of the kinematic differentiation of the given covarince.  This is since the codifferentiation that happens with the "buffer" would act as a "check and balance" to the inertial Dirac of the given condition of homotopy.  If, after a discrete accumulation of, differentially speaking, relatively less conformal invariance, and, if the condition of homotopy has undergove global kinematics via alterations that are due to the acitivities that happen during the "space-hole", (What I call the "space-hole" is the virtual fraying of topology that happens during Ultimon Flow right before the instanton-quaternionic-field-impulse.), then the series described diverges from having a local basis of static equilibrium.  It is then that the given buffer is said to be a member of a potentially spurious eigenbasis.  Sam Roach.         

Session 8 Of The Tenth Course Of My String Theory

Let us examine the reiteration contributions of gravitons, gravitinos, tachyonic pulse, dilatons, and dilatinos in respect with the wave-tug of two given arbitrary superstrings that may be mapped in a Laplacian manner via its corresponding world-sheets operands that covariantly interact upon each other, based on a convergent sequential series integration that forms a Fourier-based mapping that consists of taking the individual partial snapshots as to where, how, and when the related world-sheets that appertain here to the mentioned substringular phenomena differentiate over a discrete duration of time in such a manner in that these said world-sheets in this scenario involve both of the mentioned superstrings and their related group semi-attractors -- the attractors of which differentiate in the neighborhood of the two superstringular-related fields that appertain to the fields of strings that form discrete energy permittivity.:
After several iterations of instanton that involve both of the said superstrings in this case, both of the said superstrings of energy permittivity form a logarithmic pattern of expansion and contraction on account of the associated perturbation of the scalar amplitude of the related Polyakov Action eigenmetrics that hence interact with the related Clifford Expansion of the light-cone-gauge that happens per BRST.  This kinematic variaition of parameters in the Ward-Caucy bounds appertaining to the Lorentz-Hamiltonian flow of the affiliated Clifford Expansion eigenoperations forms the semblance of a variable homotopic periphery that has a tendancy of moving in the direction of a hermitian flow in terms of the Ward Neumman alterations that appertain to the kinematic alteration of the Lorentz-operators that influence the associated superstrings in so that the changes that are here applicable to the changes in the mass, time, and length of the mentioned superstrings relative to E.M. bear a Yau-Exact flow in Fourier Translation instead of the mass, time, and length altering in a spurious manner.  The mentioned Polyakov eigenoperations here will consequently wobble from side-to-side during the applicable Imaginary Exchange of Real Residue in so that the coniaxial of the Laplacian-basis of the two said superstrings will be relatively maintained.  In the meantime, the topological integrands of the loci of the Hamiltonian operators that effect the kinematic activities of the said strings will tend to bear a holomorphic field that involves eigenindices which majorize in such a manner so that the said eigenindices will bend the ground conditions of the two superstrings' fields in this case scenario, to where this will add a degree of bilateral Njenhuis tensorism to the Imaginary Ward Caucy conditions of the said strings' holomorphic fields.  This is considering the Dirac function that is associated with the elastic modulae of the said strings holomorphic fields.  On account of this, any smooth torque that is applied to the radial index propagation of each of the two strings holomorphic field generations will redistribute the coniaxial settings of each of the two said superstrings, and this will alter the Lorentz-Four-Contractions effect of relativity upon the said strings in terms of their relativistic velocity and their general limit of velocity.  If the corresponding gravitational particle contributions are Diraced by an acute propagation of group integrands via a kinematic activity that involves a Lagrangian that is delineated thru as is according to a given arbitrary tree-amplitude here, the motion of the two said  covariant superstrings will integrate their motions in a convergent manner over the described related Fourier Transformation thru the whole general operation that I am describing here.  Sam Roach.  

Session Seven Of Course Ten On The Light-Cone-Gauge

What are the ramifications of Yakawa Couplings in terms of how these, in certain circumstances, effect light-cone-gauge eigenstates?  This here is going to be something similar but different from something that I wrote for Course Nine.  Let us say that there are here two sets one-dimensional superstrings and also two sets of two-dimensional superstrings that codifferentiate over a Fourier Transformation in a covariant manner in the scenario that I am about to discuss.  One of the said sets of one-dimensional superstrings along with one of the sais sets of two-dimensional superstrings are in the process of going through a significant perturbation, when one is to compare what these two sets of superstrings are going through over a given arbitrary duration that involves a sequential series of timebound iterations that are consecutive and Caucy Ward Bound over the whole Fourier Transformation that I am relating in this case.  Each of the said two groups of superstrings that are relatively interbound in terms of being both covariant -- as well as going through a relatively significant perturbation --  also bear a certain degree of covariant codifferentiation over the same general duration of Fourier Transformation with the other two sets of superstrings that I initially mentioned near the beginning of this scenario, except, the other two sets of superstrings involved here are not going through a relatively significant perturbation when compared with the initial two  mentioned groups of superstrings.The two-dimensional stringular groups that I initially mentioned  bear a kinematic homotopic residue, in spite of the condition that one of these groups here is altering in terms of its relative Ward-Caucy condtions while the other substringular groups is not.  Such a kinematic homotopic residue involves a propagation of a sequential series of Laplacian-based differential symmetry between the point-fill, spin, and roll superfield tensors whic quantify as a homogeneous wave permittivity that is bidirectoral in terms of the resulting kinematic operation of such superstrings over a deffinitive Fourier Transform.  The relatively invariant stringular groups bear a deffinitive inter-relationship with each other in spite of the conditon that two of  these groups is going through a perturbation in their Ward-Caucy bounds while the other two groups are relatively unperturbated in their Ward-Caucy bounds over a duration that involves the motion of the said supeerstrings over a discrete period of time.  The more that a Wilson Line develops -- alligning the parity between those strings which would converge the holonomic discharge of wave interaction between the two said altering groups with the two said relatively unperturbated groups -- the more that the conformally invariant stringular groups that I had metioned earlier that are being altered will be one of the superstringular groups of its corresponding tori-sector that will eventually dissociate from having a direct correspondence with the groups of superstrings that are here not being altered as I previously described.  This is partially on account of the condition that the Polyakov Action and the activity of the light-cone-gauge eigenstates is altered when two relatively less related superstrings are brought into too much allignment with two relatively more related superstrings.  This is considering here that the condition of the perturbation in the said two said substringular groups that I had mentioned involves the same general format of alteration in Ward-Caucy bounds.  But here, the said homotopic residue of each stringular group that undergoes such a change will maintain its generation as it propagates along the Ultimon.  This is so that the previously mentioned homogeneous wave permittivity that is involved here will respond in such a manner so that the commutation of spin symmetry via the indices that are local to both sets of stringular groups at one metric or another on their way around the Ultimon will here differentiate with a basis of chirality that hermitianly distributes the substringular residue as it vibrates in proportionality to the norm-conditions that relate to the transition of the angular momentum of each segment of the related residue.  As bi-local stringular encodements converge their trait-based residue ("traits" here referring to the residue of their intrinsic vibrations) in proportion to the even distribution of their wave propagation, the described semi-groups isometrically commute their mentioned kinematic phenomena-based discharge in a manner that bears a symmetric parity.  The spin symmetries that become covalient via "wave-axials" of the kinematically differentiating respective Ward-Caucy curvatures here are then the action of Yakawa Couplings that bear some sort of cohomological inter-relaion with the light-cone-gauge in terms of the respective Gliossi interactions that happen over time.  Sincerely, Sam Roach.

The Glossary That Goes To Courses Nine And Ten

1)  Substringular Real Residue -- Substringular residue that happens during BRST.  

2)  Substringular Imaginary Residue -- Substringular residue that happens during Ultimon Time.

3)  BRST -- Substringular activity that happens during that part of instanton when the Polyakov Action and the Bette Action are happening simultaneously.

4) Iteration -- The globally distinguishable noticeable pulses when the noticeable time known of as instanton happens.  

5)  Ultimon Time -- Time that happens in-between iterations.  Such time may be expressed by Imaginary Numbers.

6)  Real Exchange -- Substringular exchange that happens on the Real Reimmanian Plane.

7)  Imaginary Exchange -- Substringular exchange that happens off of the Real Reimmanian Plane.

8)  The Core Of BRST -- The Real Residue that is exchanged during the Imaginary Exchange, of which happens during BRST.

9)  The Light-Cone-Gauge -- The connections between Planck-Phenomena-Related phenomena and their corresponding superstrings.

10)  Fock Space -- Substringular phenomena that exists besides substrings, counterstrings, Planck-Phenomena-Related phenomena,  stringular encoders, stringular encoder counterparts, and heterotic strings.

11)  Gravity -- As a force that is weaker than the "strong" force as well as weaker than the electromagnetic force, gravity is that general category of phenomena that pulls phenomena into order so that the whole of phenomena may be able to inter-relate and codifferentiate through time.

12)  Dilatons -- Transversal indices that quantize to become transversal-based gravity.  These are formed by posivive-norm states that are scattered by negative-norm states that are "scraped" off of their respective world-sheets, such world-sheets being comprised of by Gliossi-Sherk-Olive-Ghosts, in such a manner in that these are moved off of the Real Reimmanian Plane to help in the formation of gravitational particles.

13)  Negative-Norm-States -- Antiholomorphic Fock Space that works to scatter world-sheet indices in such a manner so that the corresponding ghost anomalies that had directly before comprised the related world-sheets may be able to redistribute so as to both free up room for the motion of superstrings, as well as thus providing a basis for the formation of gravitational particles.

14)  Positive-Norm-States -- Holomorphic Fock Space that moves in such a manner so as to form ghost anomalies that comprise a physical-mapping known of as world-sheets that act as a substrate for both an indication as to where and how superstrings had just iterated, as well as providing a substrate for negative-norm-states to scatter these so that gravitational particles may subsequently form indirectly because of this.

15)  Dilatinos -- Spin-Orbital indices that are formed by the scattering of Gliossi-Sherk-Olive-Ghosts that quantize to form the spin-orbital-basis of gravitational particles.

16)  Gravitons -- The transversal particle/wave discrete phenomenology that is due to the transversal kinematic translation of gravitational particles.

17)  Gravitinos -- The spin-orbital particle/wave discrete phenomenology that is due to the spin-orbital kinematic translation of gravitational particles.

Session Six Of Course Tex

What about substringular singularities?  During the iteration of instanton, Real Reimmanian residue is released and obtained, and, other Real Reimmanian residue that exists in-between superstrings and their counterparts has an Imaginary Exchange that occurs over the duration of BRST that happens during the said iteration of instanton.  The Imaginary Exchange of Real Reimmanian residue may be described by odd functions -- one odd function per individual exchange that exists in-between a substringular first-ordered point particle and its corresponding counterpart.  Odd functions describe activity that is explained in part with Imaginary numbers.  Ultimon Flow mainly happens outside of the duration of instanton on account of the condition that it involves the flow of substringular phenomena when superstrings are not basically at a standstill.  The "time" that happens during Ultimon Flow is imaginary here to us, although this "time" is very actual.  Ultimon Flow outside of the iterating of instanton may be described by odd functions.  Some phenomena that work to describe part of the Ultimon-related time outside of instanton are to be described by singularities which would at first seed to appertain to a degree of relative infinity in terms of the amplitude of some of the corresponding scalars and tensors that are related to the prior mentioned residue.  Phenomena that are smaller than superstrings may be described by singularities that appertain to a degree of relative the infinitessimal in terms of the amplitude of some of the corresponding scalars and tensors that are related to the prior mentioned phenomena.  Yet, the residue of world-sheets and other substringular phenomena that appertain to Ultimon Flow that is outside of the duration of instanton, as well as the description of lengths and other scalars that involve less distance than the Laplacian-mapping of less than: the Planck length (for transversal mapping); and/or the Planck radius (for radial mapping) -- are very Real and very crucial to understand.  The Imaginary Exchange of Real Residue has singularities that apperatin to the relatively infinitessimal in terms of aquainting the Hodge-Indices of the relative bottoms of certain first-ordered point particles that exchange their Hamiltonian-based momentum with the tops of certain other first-ordered point particles.  These condtions involve numbers, that, in terms of the Dirac operations that include the Clifford-Expansion activity that often includes what happens during Polyakov Action eigenmetrics which occur during BRST, may be described by odd functions.  This is due to the condition that the very indiscretely small and the indiscretely large involve alterations in certain Ward-norm-conditions that are respectively either above the scalar range of "normal" computions or below the range of "normal" computation.  Activity that happens off of the Real Plane involves Ward tensors that are to be Imaginarily computated.  The very small work to define the very large, and thus the singularities and odd functions of the very small work to form not only our normal globally distinguishable space, yet, this acitivity also works to describe the singularities and odd functions of the very large.  We exist in a world that observes energy based on Planck phenomena-related phenomena to our perception.  The norm gradients that integrate in-between  infinitessimal and  infinite singularities, as well as the norm gradients that integrate between Njenhuis tensors, to define the workings of the globally distinguishable.   Sam.       

A Tad Bit Of Clarification

What I meant by "types" of substringular angles is that, as to the number of substringular angles that exist between two different superstrings that are Gliossi relative to one another, there are 10^81 types of angles.
Sincerely,
Samuel David Roach.    

Session Five Of Course Ten

The spherical shape of a two-dimensional superstring's field may be considered as many disc-like field partials.  These field partials interact with the field partials of light-cone-gauge eigenstates.  One of these disc-likle partials may be viewed of as either a washer or an annulus shpae.  Take the conter annulus of a three-dimensional stringular field that corresponds to a two-dimensional superstring.  We will here consider the annulus section of the said three-dimensional stringular field on account of the condition that this mentioned section is the substrate of the fractal of angular momentum of the field that I have been discussing.  The holonomic part of the annulus here bears the angular momentum indices of the three-dimensional substringular field during an iteration of instanton.  On the other hand, the interior of the said annulus bears the fractal of a magnetic field in this case, since, it is in this said section of the three-dimensional field that I have been discussing in which the radial momentum of the said field exists.  The interior of the said annulus also bears the spin-orbital momentum of the given three-dimensional field of the corresponding given two-dimensional superstring, since, the radial component of the field as well as the spin-orbital momentum component of the field both act as part of the vibratorial component of the said field.  The discs I mentioned of the substringular field here that I have described integrate in a Gliossi-Hodge manner to form the overall field of the given two-dimensional superstring.  The Laplacian integrand-based discs that contain the central annulus of the described field work to form the central- field-indices of the overall field of the said two-dimensional superstring.  The integration of the said disc-like phenomena that come together to help form the said three-dimensional substringular field of the said two-dimensional superstring works to form the integration of the cohesive partial fields of the described overall general field networking that exists in the substringular neighborhood that exists in the given general locus.  This general field is the set of mementum indices that interact with the field partials of the corresponding light-cone-gauge eigenstates in order to synchronize in kinematic codifferentiation in such a manner so as to help cause the operation of the said two-dimensional superstring that here, in this given arbitary case, acts as a propagatorial operator in space-time-fabric.  Such propagation is caused, in part, by the spring-like activity that is due to the operation of the local light-cone-gauge eigenstates.  I will continue with the suspence later!  God Bless You, and I will write some more soon!
Sincerely, Samuel David Roach.

The Second Part Of The Fourth Session Of Course Ten

The orbital components of any given light-cone-gauge eigenstate acts as activated reigns that helt to push the said light-cone-gauge eigenstate via the activity of the said respective local reigns.  The overall forward momentum of light-cone-gauge eigenstates are equal in terms of the holomorphicity of the action that relates to its corresponding Clifford Expansion, except that the directoral permittivity of the corresponding momenta may vary by the type of superstrings that these light-cone-gauge eigenstates are attached to.  Light-Cone-Gauge eigenstates of an angular momentum guides its general transversal directoral permittivity.  Light-Cone-Gauge eigenstates attached to any given one or two-dimensional superstrings of what I term of as the "upper" half of the Royal Arc have more of a radial momentum that guides its directoral permittivity on account of the condition that the "upper" half of the Royal Arc appertains to the region in which positive moving time is kinematic per iteration of instanton.  Light-Cone-Gauge eigenstates that are attached to any given one or two-dimensional superstrings of the "lower" half of the Royal Arc have more of a sinusoidal push momentum that guides its directoral permittivity on account of the condition that what I term of as the lower half of the Royal Arc appertains to the arena in which backward moving time is kinematic per iteration of instanton.  I can only describe so much of the picture of the substringular at once. 
I will continue with the suspence later!  Sincerley, Samuel David Roach.     

Part One Of The Fourth Session Of Course Ten

Light-Cone-Gauge-Symmetry involves the differential chirality between the light-cone-gauge eigenstates that are attached to those one-dimensional superstrings that are a form of energy permittivity ,and, this symmetry also involves the differential chirality that exists among the light-cone-gauge eigenstates that are attached to those two-dimensional superstrings that are a form of energy permittivity.  This symmetry allows all of the superstrings to tend to travel at light-speed and below, in so long as the corresponding respective given superstrings obey Noether Flow.  Superstrings obey Noether Flow if these strings are orientable during either the Bette Action and/or during the Regge Action.  If a superstring is unorientable during both the Bette Action and also during the Regge Action, then, the said given arbitrary superstring will be tachyonic during the duration that exists in-between the initial iteration of instanton in which the said string was unorientable until the next corresponding iteration of instanton.  The mentioned general form of symmetry allows for all of the superstrings that are affiliated with the said tendancy of Noether Flow to travel through the general kinematics that are associated with "Ultimon Speed" during the course of that related Ultimon Flow that corresponds to the respective activity that happens in-between one iteration of instanton until the ensuing iteration of instanton.  The transveral components of any given first-ordererd-light-cone-gauge eigenstate pulls the whole respective said light-cone-gauge-eigenstate phenomenon around the Ultimon in a radial manner -- via the cross-sectional basis of the mentioned said light-cone-gauge eigenstate that is related to the initial Laplacian differential geometry that exists among both the respective second-ordered-light-cone-gauge eigenstates with correspondence to the initial Laplacian differential geometry that exists among the respective first-ordered-light-cone-gauge eigenstate during the course of that eigenmetric of BRST that exists during the iteration of instanton in which one is able to map the respective said "snapshot" of how such a mentioned differential geometry covariantly interacts with its local environment.  I have more to say about this later.
I will continue with the suspence later!  Sincerely, Samuel David Roach.    

The Third Session Of Course Ten

Stringular fields of one-dimensional superstrings are disc-like, and stringular fields of two-dimensional fields are spherical-like.  The light-cone-gauge eigenstates intaeract with substringular fields -- and are joined together with these.  Superstrings tend to be centered in their substringular fields.  World-Sheets are enacted upon by these fields by acting conformally invariant with the Ward-Caucy boundaries and the other related Ward conditions of the radial and transversal differentiation of the fileds of one and two-dimensional substringular fields.  The corresponding ghost anomalies that form during the Fourier-metric differentiation of the said substringular fields form as core stringular ghost fields that are surrounded by core stringular ghost anomailies.  The ghost anhilators that form disperse the ghost anomalies by normalizing the point commutator fields that are distributed by the related ghost anomalies.  The said ghost anomalies that are thus formed are due to the differentiation of the said corresponding world-sheets upon the positive-norm-states that surround the related superstrings, as well as the related stringular fields.  The ghost annhilators are the negative-norm-states that happen to move in the reverse-holomorphic directoralization of the respective positive-norm-states.  Positivt-Norm-States are comprised of the point commutator orientation that I have discussed before, and, these here are near the respective superstrings and their respective substringular fileds that are in the general direction -- as may be derived based on the norm-conditions that correspond between these both during the same general metric.  The negative-norm-states are comprised of the same general type of phenomenology as positive-norm-states, except, these move in the reverse holomorphicity (reminder).  The zero-norm-states are the loose point commutators that work to open two-dimensional superstrings at certain times, while these at other times work to close one-dimensional superstrings.  Every point commutator is a first-ordered-point-particle that is not in either a superstring, a counterstring, or a Fadeev-Popov-Related-Type-Ghost when considered during BRST in their respective world-tubes.

Part Two Of The Second Session Of Course Ten

As the superstrings iterate, the light-cone-gauge quanta that I described in the first part of this session a while ago act as reins that cause the Planck phenomena to dance into their ensuing iteration.  The spin, orbital, and transversal responses of the corresponding Planck phenomena send mini-stringular impulses that cause the Imaginary Exchange of the said related substrings.  The Imaginary Exchange of the substrings mentioned here push the light-cone-gauge quanta inward to spring the substringular into the process of Ultimon Flow-based action as the light-cone-gauge eigenstates that I am here reffering to spring outward.  This happens in such a manner so that the light-cone-gauge-related Fock Space gears the positive-norm-spaces to form ghost anomalies at the points where the said superstrings and their fields were.  As ghost anomalies have formed, the negative-norm-spaces are pulled orphoganally by the positive-norm-states so as to annhilate the ghosts that had recently formed.  This produces residue in the form of the dilatons and the dilatinos that quantize to form basic quantum of gravitational particles.  I will continue with the suspence by typing out the third session of this course soon.  You have a phenomenal day!  Sincerely, Samuel David Roach.