A Helpful Tidbit

The relative spacing increments of gauge-bosons -- which work to form the respective delineations of the so-stated gauge bosons, upon the just-eluded-to second-ordered light-cone-gauge eigenstates -- depends upon certain factors.  First, there is the factor as to the directly prior sequential series of Lorentz-Four-Contractions that had just recently, in any given arbitrary case that one may here be dealing with, been implemented upon the directly corresponding respective said second-ordered light-cone-gauge eigenstates.  For instance, if any certain given arbitrary superstring has just decreased, in a strong euclidean manner -- in terms of the scalar amplitude -- in its directly associated Lorentz-Four-Contraction, then, this manner of a strong decrease in contraction will here work to form such an alteration in the correlative Clifford Expansion of its respective delineations of its corroborative light-cone-gauge eigenstate, in so as to tend to "toggle" the directly corresponding gauge-bosons, from the here eluded-to initial staggering of delineation, into a distribution-based toggling that would then here work to pull the said gauge-bosons in the relative reverse-holomorphic direction.  Another condition that often may work to perturbate or alter the respective relative delineation of gauge-bosons from their initial distribution characteristics, in a sequential series of instantons, would be the isometric torsioning of a superstring.  If a superstring is pulled or tugged -- even if both the respective Lorentz-Four-Contraction is here to remain constant, and the respective conformal dimension of both conditions of such a superstring are here of the same Hodge-based index, the just-eluded-to torsioning may often work upon the respective relative delineatoroy index of the just eluded-to superstring.  The alteration of the delineatory index of a superstring, over time, can work to alter the distribution of the correlative gauge-bosons that work to act upon their respective second-ordered light-cone-gauge eigenstates.  One other factor that I will mention here, that can work to alter the delineation of gauge-bosons upon their stagger-based distributions -- upon their relative topological-based locus of their correlative second-ordered light-cone-gauge eigenstates, is any given arbitrary change in the Hodge-based conformal dimension of the said given arbitrary superstring.  For instance, if a superstring goes from a bosonic-based topology of holonomic substrate into a fermionic-based topology of holonomic substrate, or vice-versa, then, this alone will cause a shift in the whole general basis of the respective so-eluded-to format of the delineations of the so-stated gauge-bosons -- upon the general topology of the respective given arbitrary superstringular  phenomenon of such a case.
To Be Continued!  Sam.

Part Four of the Ninth Session of Course 17 About the Ricci Scalar

If the permutations that were to exist in such a manner, in so as to bind one or more smaller bases of cohomology -- are not of a hermitian nature, then, these so-stated permutations here do not directly involve a smooth topology.  Often, a permutation that works to bind one cohomology to another, works to pull the initially inferred cohomological projection off of the respective relative Real Reimmanian Plane -- thus forming a Njenhuis-based projection of an integration of cohomological ghost-based indices.  Such permutations here, that are off of the initial Ward-Caucy bounds of the initially stated basis of cohomological projection, are perturbative -- in a Laplacian-based manner -- to the Gaussian format of the so-stated initial cohomological projection.  No matter how hermitian both cohomological-based projections are individually, the overall insinuated binary cohomology that would thus form would not be completely hermitian, and thus such a binary cohomological stratum would never by Yau-Exact -- due to the so-eluded-to perturbative permutation that would here work to bind the two so-stated initially smaller cohomological stratum.  If such a cohomological-based stratum were to then be perturbated spontaneously into a phenomenon that would not bear Yau-Exact individually based superstrings (if the directly associated superstrings that were to work to comprise the so-stated physical stratum, that worked to form the just mentioned binary cohomological pattern, were to alter into a condition of being not Yau-Exact), then, such a phenomenon would not then work to describe the physical memory of a phenomenon of mass.  This would then mean that this phenomenon, at this point, would not directly bear the essence of any given arbitrary Calabi-Yau manifold.  This would then mean that the correlative Ricci Scalar eigenstates that are then here to interact with the so-eluded-to superstrings, that were to work to form such an altered cohomology, would then not interact with the so-stated cohomological stratum in the manner that gravity tends to interact with a mass in.  Such a net cohomological stratum is a description of either scattered energy or scattered electromagnetic energy, depending upon how the directly involved Chern-Simmons singularities vibrate -- otherwise, either harmonically or annharmonically, respectively.  If the Chern-Simmons singularities that are here of a given arbitrary case, do vibrate -- with relative harmonics, in spit of the permutations, then, the Ricci Scalar eigenstates of such a case is appertaining to a condition of scattered kinetic energy.  Yet, if the directly correlative Chern-Simmons singularities of such a case vibrate with relative annharmonics, then, the Ricci Scalar eigenstates of such a case is appertaining to a condition of scattered electromagnetic energy.  To Be Continued With 10!!!

Part Three of the Ninth Session of Course 17 About the Ricci Scalar

When two or more cohomologies are bound -- in an orthogonal-based manner -- then, the directly affiliated  coalescing of the correlative world-sheets involves permutations at the so-eluded-to binding cite, that are formed by the holonomic substrate of one genus and format or another of a norm-state projection.  Such permutative-based holonomic substrate eigenstates may either be of a cyclic-based format of permutation, or, such permutative-based holonomic substrate eigenstates may also, instead, bear a Majorana-Weyl invariance -- to where the specific locus-based cite of the so-eluded-to permutation-bearing norm-state projection may either be of an indistinguishably different differential genus, that may vary in its Ward-Caucy conditions, or, the specific locus-based cite to the so-eluded-to permutation-bearing norm-state projection may be of a steady-state genus of spatial interconnection, that does not vary to the same so-eluded-to extent.  Either way, the binding cite, that would here work to interconnect two specific smaller-based cohomologies, into a more overall specific larger-based cohomology, will bear at least some sort of torsional-based spike -- that works to form a tense of necessary Chern-Simmons singularity -- that works to form a higher tense of a harmonically scattered genus of norm-state-projection, in so as to bear more of a viable ability for any given arbitrary reverse-mode of norm-state-projection (a compatable norm-state projection that bears an opposite kinematic basis of holomorphic topological sway) to act upon the initially stated general format of cohomological index, so that the just stated cohomology may be annharmonically scattered into that general format of substringular residue that is then pulled off of the here relative Real Reimmanian Plane -- into the correlative plane of gravitons and gravitinos.  Such residue of Gliossi-Sherk-Olive ghosts -- that is then pulled into the respective plane of gravitational particles -- is utilized, over a more broad-based sequential series of iteration of group instanton -- in so as to eventual be utilized indirectly to form Neilson-Kollosh ghosts -- in so as to form a substringular residue from the annharmonic scattering of the just mentioned ghosts, that is then pulled back into the initially mentioned relative respective Real Reimmanian Plane.  This is the general process of the exchange of cohomological residue that happens in so as to form the general holonomic substrate that the Rarita Structue eigenstates must work upon most directly, through the activity of the correlative Schwinger Indices -- in order for the Ricci Scalar to be able to take effect.  To Be Continued!  Sam.

Part Two of the Ninth Session of Course 17 About the Ricci Scalar

A Rham cohomology is a cohomology that is completely hermitian.  This means, then, that the singularities of a Rham-based cohomology are Yau-Exact.  This also means that either a superstring, an orbifold, or an orbifold eigenset, that is working to form a Rham-based cohomology, is Yau-Exact -- as such a respective given arbitrary superstring, orbifold, or orbifold eigenset is operating in such a manner -- in so as to form a Rham-based cohomology.   Although a Doubolt cohomology is often of a hermitian-based nature -- if a Doubolt cohomology is ever Yau-Exact, then, the projection of at least part of such a cohomological-based nature bears Njenhuis-based projections, that are part of the so-eluded-to cohomology -- under the just mentioned general substringular situation.  Yet, if a Doubolt cohomology bears no Njenhuis attenuations that work to comprise such an integration of ghost-based indices, then, the so-eluded-to general format of such a cohomology will then not be Yau-Exact.  This then means, that, a purely Real Reimmanian-based Doubolt cohomology will either bear Lagrangian-based Chern-Simmons singularities, and/or, such a general genus of cohomological stratum will bear metrical-based Chern-Simmons singularities.  So, if two world-sheets that work to form a ghost-based cohomological pattern work to form two orthogonal ghost-based stratum -- to where one end of either a Real Reimmanian-based projection of cohomological-based stratum and/or a Njenhuis-based projection of cohomological-based stratum is normal to the other respective end of either a Real Reimmanian-based projection of cohomological-based stratum and/or a Njenhuis-based projection of cohomological-based stratum, then, such an overall cohomological-based pattern -- that is put together, via a linking that may be formed by the activation of a norm-state projection, that puts the two initially stated cohomological-based projections together into an overall ghost-based stratum, will always work to form some sort of Doubolt cohomological pattern.  This is because, the activity of two cohomological-based projections -- being tied together in a 90 degree-like manner, works to form at least some sort of spurious and/or spike-like torsioning at the linkage, that works to put the two so-stated general formats of cohomological-based stratum together.  This is partially due to the condition that adjacent superstrings that are of the same universe, iterate in such a manner in so that these are differentially geometric -- the relative one to the other -- in a 90 degree manner.  Ghost-based indices are the mapped-out tracing of world-sheets.  World-Sheets are the trajectory of the projection of superstrings.  Cohomologies are ghost-based indices that are put together, in one manner or another.  Cohomologies are thus the physical memory of the where, how, and what -- that superstrings had just done, in any given arbitrary case.  Therefore, any binding of one or more orthogonal projections of cohomological-based stratum -- whether one or more of such cohomological-based patterns are Yau-Exact or not, in and of themselves, will always work to form an overall cohomological-based pattern that will then be of a Doubolt nature.  This is why all norm-based interconnections of one or more cohomological-based stratum will always work to form some sort of Chern-Simmons singularities.  This does not, however, work to discredit the condition that all superstrings that bear Yau-Exact singularities -- in any one individual ghost-based projection, that is considered in a unitary-based manner -- work to form the condition of the directly corresponding superstrings that had worked to form such singularities -- as being Yau-Exact.  Such Yau-Exact superstrings work to form manifolds, as to their conformally invariant base of iterating over a sequential series of instantons, that are known of as Calabi-Yau manifolds.  Calabi-Yau manifolds are the multiplicit Gliossi-Sherk-Olive stratum, that directly appertains to the existence of a superstring of mass, that  is to then here exist, in one manner or another, in a tense of Majorana-Weyl covariance.
I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

Part One of the Ninth Session of Course 17 on About the Ricci Scalar

Chern-Simmons singularities are not always existent directly in-between locants in which orbifolds and orbifold eigensets are specifically delineated.  Let us first look at what, in general, happens -- when a world-sheet is mapped-out as a tracing as to the exsitence of both what and how a given arbitrary superstring had kinemtatically differentiated over time.  We will then consider the just mentioned extrapolation by examining the general cohomology of a specific given arbitrary tracing of a mappable region in which a specific given arbitrary respective superstring had moved kinematically over a correlative sequential series of integrable integrations of group instanton.  The so-eluded-to cohomology that we are here considering initially exists as a given arbitrary Rham-based cohomology.  This, as an ansantx, means that the initial increment of traceable mapping of the correlative world-sheet, that works to form the here considered ghost-based cohomology, is delineated as a Yau-Exact substringular distribution over time -- to where the directly associated singularities that are thus formed by such a cohomology are then here of a Yau-Exact nature.  This also means that the so-eluded-to cohomology is on the relative Real Reimmanian Plane -- over the correlative duration in which such an eluded-to ghost-based integration of indices is being formed, as a physical memory as to both the existence of what and where and how the directly affileated correlative group of one or more superstrings -- that here operate in so as to perform a given arbitrary specific function in the substringular, over a correlative given arbitrary group covariant action, over time.  The given ghost-based cohomology, that is here a mappable tracing of a world-sheet -- that works to indicate both the how, what, and where the so-stated set of superstrings of a common functional operation -- will, in the situation in which I am here addressing, conjoin with another respective given arbitrary world-sheet-based tracing, at an orphoganal-based manner, that will then elemetarily bind at a given arbitrary 90 degree-based differential-geometric-based webbing.  This will thus happen as a relatively local binding cite, that acts as an addition to the initially mentioned cohomology that I had mentioned at the beginning of this post.  Since the topological-based directoral-sway of such a spike in the substringular would thus form a change in derivatives, that is higher in Hodge-based index than the number of physical spatial dimensions that the general mappable tracing is being delineated through -- over the binary-based Lagrangian format, that would here involve the Laplacian-based exrapolation of the tracing of the overall cohomological pattern, of this given arbitrary case, over time, then, the just described general cohomology that is thus formed will bear at least some Lagrangian-based Chern-Simmons singularities.  This will then happen, even though the individual initially-mentioned "mers" of such a cohomology may be smooth enough in topological sway, on their own, in such a manner in so that the two eluded-to segments of such a cohomology may be of a Rham-based cohomology in and of themselves.  (This is before the covariant-based conjoining is here to be considered, for the overall mappable tracing, that is to then involve both of the eluded-to segments.)  This would then work to form an overall mappable tracing that would then be of a Doubolt nature, when the overall tracing is to be extrapolated, as an integration of both of the so-stated segments -- over the mapped-out Lagrangian that is to here involve both of the eluded-to respective segments that I have here described, in general.  This would then make the so-eluded-to overall just mentioned cohomological pattern of a manner that is thus not Yau-Exact.
I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

Part Three of the Eighth session of Course 17 About the Ricci Scalar

Njenhuis-based perturbative oscillations are vibrations that are off of the relative Real Reimmanian Plane.  So, a singularity that is not hermitian, yet is also not perturbative in a Lagrangian-based tense -- is either not topologically smooth, on account of some degree or other of Njenhuis projection, or, its annharmonic vibration is on the relative Real Reimmanian Plane.  Chern-Simmons singularities are thus never Yau-Exact, and thus, superstrings that -- over a specific duration in which these may here be considered -- display Chern-Simmons singularities, that are, at such a metrical-based involvement, never Yau-Exact then.  Chern-Simmons singularities are either not topologically smooth, or else their vibrations are annharmonic -- if not both.  Generally, Chern-Simmons singularities are not topologically smooth.  Partially hermitian Chern-Simmons singularities are often of this sort, due to permutations in the field of the given singularities.  Partially perturbative singularities are often singularities that vibrate harmonically, yet off of the Real Reimmanian Plane -- during the correlative iterations of group instanton that appertain to the conditionality of such a tense of singularity.  Only Ricci Scalar eigenstates that directly appertain to the activity that appertains to a mass, are completely hermitian, and thus, only Ricci Scalar eigenstates that directly appertain to the activity that appertains to a mass bear Yau-Exact singularities.  This is why any discrete quantum of mass -- that behaves as a mass -- is considered to be Yau-Exact.  A Yau-Exact quantum exists in manifolds known of as Calabi-Manifolds.  This general format of a Calabi-based manifold is the cohomological extrapolation of the mappable tracing as to what, where, and how the ghost-based indices of the existence of superstrings of mass had behaved over any extrapolation of any given arbitrary Sterling Approximation of any given superstrings of mass -- as these have then here respectively behaved over any correlative time-line.  To Be Continued!!!Sam Roach.

A Post of Explaination

Even if a superstring is to smoothly alter the rate of its pulsation from its vibrational oscillation, from one iteration of group instanton to the next -- in a successive series of the so-stated instantons -- the superstring is said to bear spurious Chern-Simmons singularities.  (The said given arbitrary superstring will then here bear metrical-based singularities.) So, if a superstring were to go from an optimum vibrational-based eigenstate of pulsation, to one genus of elongated pulsation in its next locus of vibrational oscillation, to the next genus of elongated pulsation in its next locus of vibrational oscillation -- in the course of three successive iterations of group instanton, to where such a rate of perturbated pulsation is smooth, yet accellerated, then, the so-eluded-to superstring will bear correlative metrical-based Chern-Simmons singularities.  In the course of what I have just here explained, the superstring will go from an otherwise so-to-speak Yau-Exact basis of singularity in its first respective iteration, to having a non-hermitian metrical-basis of singularity -- that would here involve a 0+ singularity, to having a non-hermitian metrical-basis of 0+^2 singularity, in relation to the initial optimum vibrational oscillaton-based pulse -- over the course of three consecutive iterations of group instanton, in this given arbitrary case. So, if instead, the said respective given arbitrary superstring did as before, yet, afterwards, went into a pulsation that jerked into one genus of abridged vibrational oscilation from the so-eluded-to rate of pulsation, into pulsating into two geni of abridged vibrational oscillation from an optimum rate of pulsation, in the course of the then proceeding iteration of group instanton, then, the singularities would go from bearing a spurious attribute of 0+, to 0+^2, to infinity+, to infinity+^2, over the course of five consecutive respective given arbitrary iterations of group instanton.  This would, in and of itself, work to indicate metrical-based singularities that are independent of any potential Lagrangian-based singularites, that could also be involved here.  A metrical-based singularity is also known of as a spurious Chern-Simmons singularity.  Yet, this does not rule out the potential condition that spurious Chern-Simmons singularities may often be effected by Lagrangian-based singularities.  This would be dependent upon the directoral permittivity and the directoral impedance, of the flow of both the so-eluded-to metrical-based singularities and the eluded-to Lagrangian-based singularities -- that would thus be involved here.  This would mean that there are possibly Hodge-Indices of singularity that may be either added as integer-based additives of singularity, or, added as irrational-based additives of singularity -- depending upon both whether or not metrical-based singularites and their correlative Lagrangian-based singularities are trivially isomorphic or not, and, whether the so-eluded-to singularities are more appertaining to either the Hamiltonian-operation of its Planck-Length or the Hamiltonian-operation of its Planck-Radii -- or appertaining to both the Hamiltonian-operation of both its Planck-Length and its Planck-Radii.
I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

Part Two of the Eigth Session of Course 17 About the Ricci Scalar

Hermitian singularities are said to be Yau-Exact, if these are non-perturbative -- over the course of the respective iterations of instanton, that these are smooth and harmonic in respective vibration towards -- in the process of both their Lagrangian-based nature and their metrical-based nature, over time.  For instance, if a substringular-based singularity -- that is appertaining to the differential geometric resultant of the kinematic activity of any given arbitrary superstring -- does not change in more derivatives than the number of dimensions that it is moving in, and also, if the said respective given arbitrary superstring of this same case does not alter in the rate of its correlative pulsation over time, then, this said given arbitrary superstring that displays such a singularity, will then neither bear any Lagrangian-based singularities, nor, will it bear any metrical-based singularities. Such a superstring, over the respective eluded-to iterations, is said to be Yau-Exact.  Conditions of a substringular singularity being Yau-Exact, are considered per successive individual respective iterations of group instanton.  If such a similar singularity is hermitian in its Lagrangian-based format, while yet, it is perturbative in the rate of its pulsation, then,  -- during the given correlative successive iterations, that such an eluded-to extrapolation is being considered -- the so-stated singularity will not be harmonic in its metrical-based vibration, over the course of the directly correlative iterations of group instanton, that appertain to the directly affiliated successive series of group instanton.  So, if such a series of  substringular iterations is not hermitian in its metrical-based motion, over an affiliated successive series of correlative instantons -- even though it may here be hermitian in terms of its Lagrangian-based motion, then, the directly affiliated superstring that had formed such a so-stated singularity will not be Yau-Exact.  Also, if a similar singularity bears completely hermitian metrical singularities, although, in this case, it does not bear hermitian-based Lagrangian singularities, (on account of the correlative respective given arbitrary superstring changing in more spatial derivatives than the number of spatial dimensions that it is moving in), then, the superstring that were to bear the just mentioned format of singularity is also said to not be Yau-Exact.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of the Eighth Session of Course 17 About the Ricci Scalar

Besides hermitian-based singularities, with reference to either superstrings, orbifolds, and/or orbifold eignsets,  -- there are Chern-Simmons-based singularities with reference to either superstrings, orbifolds, and orbifold eigensets.  Any given arbitrary superstring -- that is directly associated with the Yakawa Couplings, of which appertain to a discrete phenomenon of mass -- happens to exist, over time, in a vibrational-based context, that would here be directly associated with a manifold that is known of as a Calabi-Yau manifold.   Superstrings of mass bear Yau-Exact singularities.  A Calabi-based manifold is an attribute to the ghost-based manifold of any given arbitrary superstring, that here eludes-to the condition of the interaction of electromagnetic energy with that superstring, over time.  This is due to the prevaliant fact that all physical phenomena exist, to some extent or another, in relation with both the existence and the motion of electromagnetic energy.  So, Calabi-based manifolds elude-to the existence of the scattering of electromagnetic energy upon the multiplicit contextual holonomic substrate of superstringular phenomena of discrete energy.  This, then, works to indicate the condition of hermicity, that superstrings of mass show attribute to over time, as a mass that may be arbitrarily considered here, in a given case, to then bear such a conditionality as these then moving through their correlative Lagrangian-based paths -- in whatever kinematic-based format or genus that these may here happen to be differentiating in -- in the directly inferred Fourier-based differentiation.  Hermitian-based singularities are smooth in Lagrangian-based translation, over any directly associated mappable tracing in which such an eluded-to kinematic-based superstring is moving through any given arbitrary path, to where there is no spike in the Ward-Caucy-based curvature in which such a so-stated superstring is going through, in any directly associated integrable sequential series of group instanton.  Also, if any given arbitrary superstring is of a hermitian-based nature, the pulsation of its vibrational-mode -- when one is to initially compare the gauge-metrics of such a pulse in one iteration of BRST,  while then comparing the ensuing genus of gauge-metrical activity of the said given arbitrary superstring over a specific directly affiliated sequential series of iteration of BRST, -- to where the rate of the so-eluded-to pulsation of the holonomic substrate of the correlative eigenstate of Calabi-based manifold is happening -- in a manner that neither accelerates nor decelerates -- over the set metric in which such a specified given arbitrary superstring is kinematically moving in its correlative Lagrangian path over time.  Yet, if the rate of the just mentioned pulsation of the said superstring is to abruptly accelerate and/or decelerate over any specifically considered given arbitrary duration of time, then, the so-eluded-to spike in the harmonics of its Gliossi-based vibration will then here be considered to bear what is known of as a spurious condition.  This is the basic idea as to what a metrical-based Chern-Simmons singularity is based upon -- in premiss.  If a superstring bears any Lagrangian-based singularities or metrical-based singularities -- in any specific time period in which such the directly associated Ward-Caucy bounds of the said superstring is being given consideration -- then, the superstring is said to Not be Yau-Exact at that time.  Rham-based cohomologies are Yau-Exact, while, Doubolt cohomologies often bear at least some Chern-Simmons singularities.  The exception is a cohomology that is pulled -- in one manner or another -- off of what the relative given arbitrary Real Reimmanian Plane.  A cohomology that bears Njenhuis-based Lagrangian and/or Njenhuis-based metrical singularities will be of a Doubolt nature -- even if it is of a Yau-Exact nature.
I will continue with the suspense later!  To be Continued!  Sincerely, Sam Roach.

Just A Little Hint

The Ricci Scalar is the  basis of the scalar magnitude of the kinematic activity of gravity.  The Ricci Scalar happens through that physical stratum that works to inter-bind the multiplicit Real Reimmanian Plane with the respective multiplicit Njenhuis basis of the gravitational-based Plane, this general inter-binding physical stratum of which is known of as the Rarita Structure.  Each individual locus of Rarita Structure manifold -- that works to inter-bind one locus of Real Reimmanian-based Plane of superstringular activity, as to those general field-based regions where discrete energy permittivity and discrete energy impedance is Gliossi to, during each succeeding iteration of group instanton -- with the directly corresponding Njenhuis-based field -- where both gravitons and gravitinos interact, in so as to form the basis of the activity of gravity in general -- is known of as the general holonomic substrate of the correlative Rarita Structure eigenstates.  So, there are countless layers of relative Real Reimmanian-based Plane, where discrete energy permittivity and discrete energy impedance work kinematically, in so as to allow for the spontaneous existence of viable energy -- that inter-bind with the correlative countless layers of relative geni of certain Njenhuis Plane eigenfields, where both gravitons and gravitinos exist and act in so as to form the Gliossi-based field as to where the discrete operators of the basis of gravity exist.  So, the general genus of structural phenomena, that act as the holonomic substrate that works to cause the motion of discrete energy to be inter-dependent with purely gravitational-based particles -- in so as to create that general format of activity, that causes the ability of phenomena to be able to both be brought together and to be able to stay together -- is called the Rarita Structure.  It is the core Gliossi-based activity of the light-cone-gauge, that works most succinctly as the general tense of that vibrational force that causes the wave-based modem of the multiplicit Rarita Structure -- that acts as the result of the direct Yakawa Coupling of certain heterotic strings (E(6)XE(6) strings) with the correlative second-ordered light-cone-gauge eigenstates -- in so as to allow for such interaction to occur.  This is an interdependent general function, that operates alongside of the Hamiltonian-based operation of discrete energy.  The respective holonomic substrate of both discrete energy permittivity and discrete energy impedance, is the basis of the particle-like operation of substringular energy, while the counterstrings and the light-cone-gauge eigenstates respectively act as the basis of the holonomic substrate of the wave-function of the said respective discrete energy permittivity and discrete energy impedance.
I will continue with the suspense later! To Be Continued!!! Sincerely, Sam Roach.

Part Four of the Seventh Session of Course 17 About the Ricci Scalar

The individual units or ghost-based indices that work to comprise any given arbitrary Real-based cohomological stratum, work to form the base integrand of whatever the specific genus of a Ricci Scalar eigenstate -- that is worked upon by the here existent either  Rham or  Doubolt cohomology, that the so-eluded-to Ricci Scalar eigenstate -- in so happens to be interacting with.  This happens, while the integration of such here eluded-to cohomological units work to define the magnitude of the Real Reimmanian eigenbase of the said Ricci Scalar genus, that is here under question -- that may here be considered to define the net effect of the gravity of the given arbitrary cohomology, of this here respective state.

Part Three of the Seventh Session of Course 17 About the Ricci Scalar

Since world-sheets are a template for a form of topology, known of as ghost anomalies, these -- to some extent -- may be able to be effected by any directly affiliated gravitational pull that is enacted upon them.  Such a gravitational pull happens via the Ricci Scalar -- on account of the physical holonomic phenomenon known of as the Rarita Structure.  Cohomologies are integrable sets of one or more ghost anomalies that are both codeterminable and covariant.  World-Sheets are the projection of the trajectory of superstrings, as the so-eluded-to superstrings are kinematically differentiable over time.  So, ghost anomalies that are of a completely hermitian nature, in so as to form hermitian cohomologies -- whether such cohomologies are of a Real Reimmanian and/or of a Njenhuis nature -- completely bear a tense of integrated singularity, that works to pull the correlative ghost-based indices, that work to comprise the said respective given arbitrary cohomology.  This happens in such a manner, that the given cohomological entity that is here being discussed may act as a physical memory of both the existence and the activity of a Calabi-Yau manifold.  If, instead, the cohomology bears some sort of a Doubolt nature, then, this may happen in such a manner, that the given cohomological entity that is here being discussed may act a as physical memory of both the existence and the activity of either a Calabi-Wilson-Gordon manifold, or, a Calabi-Calabi manifold.  This is as the said cohomology is differentially integrable, as a kinematically vibrating whole -- over time.  If the said cohomology is purely of a Real Reimmanian nature, then, the respective cohomology is of a Rham-based cohomological index.  Yet, if the said cohomology has a bearing that is off of the relative Real Reimmanian Plane, then, the respective cohomology is of a Doubolt nature.  The gravitational pull of the Ricci Scalar upon ghost-based indices -- in so as to pull the multiplicit cohomologies that exist -- in the relative directoral topological sway of the correlative gravitons and gravitinos, that work to form the directly associated eigenstates of gravitational force -- works as a Njenhuis directed physical entity of holonomic substrate, in so as to cause enough of a bearing of gravitational permittivity, so that the superstringular impedance that exists due to the correlative Fadeev-Popov-Ghosts (that are the physical memories as to both the existence and the activity of the correlative Fadeev-Popov-Trace eigenstates), may be able to occur spontaneously over time.  I will continue with the suspense later!  Sam Roach.

Part Two of the Seventh Session of Course 17 About the Ricci Scalar

For each Poincaire that is taken at the physical locus -- where there is a hermitian-based change in either the derivative of the motion of any correlative superstring and/or where there is a change in the pulsation of the motion of any respective correlative superstring, such individually taken respective Poincaire here acts as an index of hermitian singularity.   The entire multi-dimensional entity of the topology of any of such hermitian-based cohomologies is an integration of point particles that works to define the just eluded-to hermitian-based singularities.  The individual hermitian singularities of each of such cohomologies works to act as differential loci of space, that, although these do not define a hermitian topology in and of themselves, these are hermitian -- when the loci of such singularities are taken, relative to the rest of the integration of all of the other Poincaire-based loci, that exist along the Ward-Caucy bounds of the rest of the topology of any respective given arbitrary superstring of which such hermitian singularities appertain to, is taken into a consideration.
In other words, it takes the whole integration of all of the Poincaires along the topology of any given arbitrary superstring over time, in order to work to establish exactly what and where the loci of the individual hermtian singularities of the respective given arbitrary superstring in question are.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of Session Seven of Course 17 About the Ricci Scalar

As you may now know, hermitian singularities happen at general loci besides in places that may be deemed of as in-between orbifolds of an orbifold eigenset.  For example, hermitian singularities also exist at general loci that exist along the topology of a cohomological eigenstate -- that is of a Real Reimmanian basis.  A Real-based cohomology -- whether it is of a Rham-based cohomological index, or if it is of a Doubolt-based cohomological index -- if the so-eluded-to Doubolt-based cohomology is not of a relatively correlative Njenhuis-based nature, has the potential for bearing many indices of superstringular Poincaire extrapolation -- that may be utilized in so as to work to bear all sorts of respective given arbitrary Sterling approximations and sub-Sterling approximations, as an effort to be able to work to determine both the local bearings of certain multivarious superstrings and also in so as to work to determine what the ensuing activities and delineations of certain given arbitrary potentially multiplicit superstrings are to engage in, over a given arbitrary set of sequential series of group-related instantons.  Also, as well, many cohomological settings that are of a Doubolt nature -- due to the kinematic-based sequential-based distributions and delineations of superstrings that bear either a set of norm-state projections that are of a Njenhuis nature, and/or, that bear a set of ground-state projections that are of a Njenhuis nature -- have the potential for bearing many indices of superstringular Poincaire extrapolation, that also may be utilized in so as to work to bear all sorts of respective given arbitrary Sterling approximations and sub-Sterling approximations -- as an effort to be able to work to determine both the local bearings of certain multivarious superstrings that have kinematically moved off of the relative Real Reimmanian Plane.  This general given arbitrary genus of extrapolation may also be utilized in so as to work to determine what the ensuing activity and delineations of certain given arbitrary potentially multiplicit superstrings are to engage in, over a given arbitrary set of sequential series of group-related instantons.  (This may also be done by the utilization of both Laplacian-based and Fourier-based mathematics, in so as to apply the multivarious geni of Poincaire-based tensoric operators -- in an effort to be able to determine both the general given arbitrary loci of certain superstrings in question, and, in an effort to be able to determine the general activity of superstrings over time.  Such format-bearing geni of Poincaire-based extrapolation may be utilized in so as to work to determine both the formation and inter-activity of ghost-based indices -- as of any given arbitrary group metrical duration in which such ghosts are not "torn-down."  The formation of ghost-based indices by the delineation and re-delineation of world-sheets that are projected over time works to form a cohomological-based format that allows for whatever the multi-various needed given arbitrary local Kaeler-Conditions are to be existent, in one specific given arbitrary substringular neighborhood.  So, as ghost anomalies or cohomological settings are annharmonically scattered, in so as to be brought off of the relative Real Reimmanian Plane (as the raw phenomena that work to form both gravitons and gravitinos) -- this re-formated phenomena is then used to form a holonomic substrate that inter-relates with superstrings of discrete energy energy permittivity in so as to form a general basis of the existence of what is known of as the Ricci Scalar.  I will continue with the suspense later!  Sincerely, Sam.

Part Two of the Test Solutions to the First Test of Course 17 About the Ricci Scalar

6)  A hermitian singularity may be one of two different types of general considerations.  A hermitian singularity that is of a Lagrangian-based nature is when there is a change in the number of derivatives -- over a mappable path -- that is equal to or less than the number of spatial dimensions that any respective given arbitrary substringular phenomenon is going through over time.  A hermitian singularity that is of a metrical-based nature is one, however,  to where the harmonics of a superstring that may be taken along its given arbitrary path, over a discrete Lagrangian, works to alter or perturbate its pulse -- by demonstratively, either elongating or abridging its pulse -- in so as to form enharmonic gauge-metrical spikes in the respective given arbitrary initially eluded-to substringular rhythm, which is known of as a spurious substringular condition.

7)  A Rham-based cohomology is a set of integrable ghost-based mappable indices that appertain to a hermitian (purely) or Yau-Exact extapolatable tracing of world-sheets, that is of a Real Reimmanian nature. A Doubolt-based cohomology is one that is not of a Rham-based nature.  A Yau-Exact setting often refers to a Calabi-Yau manifold -- or, a setting of a structure that directly appertains to a superstring of mass that is vibrating in a relatively confined and set local region.  Mass-Based indices are the core holonomic substrate that gravity acts upon.  And, it is the Ricci Scalar which acts as the mechanism that correlative Rarita Structure eigenstates act through, in so as to cause gravity.

8)  Substringular phenomena are hermitian, when the singularities that these work to form -- via either their Lagrangian-based sequential series of delineations, and/or their metrical-based pulsation-based harmonics is hermitian.

9)  Substringular phenomena is Njenhuis when it involves norm and/or ground-state-projections, that veer off of the directly associated relative Real Reimmanian-based Plane.

10) Chern-Simmons singularities are singularities of either a Lagrangian-based and/or are of a metrical-based nature -- that  are not hermitian.

11)  Topology that is of orientable substringular phenomena is what works to obey the general conditionality of the Noether Current.  This is due to the condition that the Ricci Scalar is more "locked-into place" with superstrings that bear a stable or even Grassman Constant.  When a superstring is unorientable during the Bette Action, this works to virtually dislodge part of what the general operation of the Ricci Scalar, upon the said given arbitrary superstring.  If the directly proceeding Regge Slope eigenstate is not hermitian, and/or, if the differential geometry of the so-stated Regge Slope is not arced properly, then, from here, the  Ricci Scalar -- via the local Rarita Structure eigenstates -- works to pull the so-eluded-to superstring into an indistinguishably different Kaeler-based setting, at an augmented locus, that is at a distinguishably different locus.  Such a furthered propagation  causes tachyonic flow.  This is why an unstable or uneven Grassman Constant is a key topological condition as to having a superstring that  either obeys Noether Flow or tachyonic flow.
I will continue with the suspense later!  Sincerely, Sam Roach.

Part One of the First Test Solutions of Course 17 About the Ricci Scalar

1)  The three general forms of energy -- when not including entropic photons -- are electromagnetic energy, plain kinetic energy, and mass.

2)  Electromagnetic energy always has a Yang-Mills light-cone-gauge topology.  (This is when not including entropic photons.)  Mass that is not translated at the speed of light or faster always has a Kaluza-Klein light-cone-gauge topology.  Plain kinetic energy may have either a Yang-Mills or a Kaluza-Klein light-cone-gauge topology.  Electromagnetic energy has partially hermitian singularities amongst the superstrings that work to comprise it.  Plain kinetic energy tends to have partially Chern-Simmons singulariies amongst the superstrings that work to comprise it.  Mass as a mass -- that is not tachyonic -- has purely hermitian or Yau-Exact singularities amongst the superstrings that work to comprise this.

3)  An orbifold eigenset is a set of one or more orbifolds that operate in so as to perform a specific function.

4)  The Ricci Scalar effects mass via the activity of the directly affiliated Rarita Structure eigenstates.  Such a general genus of interaction is here brought into existence by the Gliossi-based delineation of second-ordered Schwinger Indices.  The condition of mass, being involved here -- is due to the consideration of those Calabi-Yau manifolds that are undergoing any given arbitrary eigenmetrics of the Noether Current.

5)  Mass is that general form of energy that is most viabely effected by gravity.  Those bosons -- that are the heterotic strings known of as E(6)XE(6) strings, or gauge-bosons -- work to "pluck" second-ordered light-cone-gauge eigenstates, in so as to form those second-ordered Schwinger-Indices that work to correlate any directly affiliated given arbitrary Rarita Structure eigenstates with superstrings of mass -- in so as to bring the gravitational effect of gravitons and gravitinos upon closed-loops, that are undergoing the respective local Noether Current, this current of which is what works to make gravity take its general effect upon mass. (This is considering, though, the condition that gravity effects all substringular phenomena to some certain amount or another -- yet it is most effective upon the constituent force that works to bind different covariant discrete groups of mass-bearing phenomena.)  Weight is mass times any correlative given arbitrary local acceleration of gravity.  This works to make "weight" that particular term -- which makes the condition that mass is primarily that general format of phenomena that is effected by gravity -- an ansantz.

Test Questions To First Test of Course 17 About the Ricci Scalar (6)

1)  What are the three general forms of energy, besides entropic photons?

2)  What are the similarities and differences between the three said general forms of energy?

3)  What is an orbifold eigenset?

4)  Describe, in general terms, the Ricci Scalar -- in general relation to a mass.

5)  What form of energy is most effected by gravity?  What terms makes this an ansantz?

6)  What is a hermitian singularity?

7)  Describe the Ricci Scalar -- in terms of the general topological settings that have  hermitian singularities

8)  When is substringular phenomena hermitian?

9)  When is substringular phenomena of a Njenhuis setting?

10)  When are Chern-Simmons singularities?

11)  What general format of topology works to keep the Noether current?  Why?

I will continue with the solutions in a couple of days!  To Be Continued!!! Sincerely, Sam Roach.

The Fourth Part of the Fifth Session of Course 17 About the Ricci Scalar

Let us say that a given arbitrary orbifold or orbifold eigenset -- in this case -- is of a harmonic-based Lagrangian nature, over a discrete group oriented metric.  Let us say that all of the Lagrangian-based singularities that are formed by the said orbifold or orbifold eigenset here are of a Real Reimmanian-based nature.  Let us now say that all of these just mentioned singularities are hermitian.  Then, all of the ghost-based indices that are here formed will be of a Rham-based cohomoligical-based nature, over time.  Now, let us say, instead, that all of the Lagrangian-based singularities of the otherwise same said orbifold or orbifold eigenset are of a Chern-Simmons-based nature.  Then, all of the directly corresponding ghost-based indices that are here formed will be of a Doubolt cohomological-based nature here.  Let us now say that the eluded-to said orbifold or orbifold eigenset bears hermitian-based Lagangian singularities that are not of a Real Reimmanian-based nature.  Such singularities would then here be of a Njenhuis-based nature.  Then, the ghost-based indices that are thus formed here will be of a Doubolt cohomological-based nature, in spite of the so-eluded-to hermicity that would here be involved.  Let us say that there is -- in this case -- an orbifold or an orbifold eigenset that bears both hermitian and Chern-Simmons Lagrangian-based singularities, over time.  Or, if the orbifold has both Real Reimmanian and/or Njenhuis-based singularities, or, if there is a combination of the last two scenarios.  Then, the ghost-based indices that would then here be formed by the said orbifold will bear both Rham and Doubolt cohomologies.  Now, imagine an orbifold or an orbifold eigenset that is just as I have here mentioned, except, that the so-eluded-to orbifold or orbifold eigenset is of an annharmonic based nature.  Then, the ghost-based indices would be similar in cohomological index, yet, these ghosts would would bear a different delineatory-based index of distribution.  I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.

The Third Part of the Fifth Session of Course 17 About the Ricci Scalar

The Noether current is not always of a harmonic format among both all of the superstrings and/or all of the orbifolds that work to comprise any given arbitrary orbifold eigenset.  For instance, let us here consider a given arbitrary orbifold, that is of the just eluded-to general basis of format that I have described in the directly previous sentence.  Let us say, arbitrarily, that the orbifold eigenset in question is comprised of ten orbifolds -- that each are comprised of ten-thousand superstrings of discrete energy permittivity.  Let us say that the topological sway of each of the superstrings of each orbifold that works to comprise the said respective given arbitrary orbifold eigenset in question is of a non-congruent directoral pull.  For instance, each superstring that works to comprise the so-stated orbifolds -- that work to comprise the whole so-eluded-to orbifold eigenset -- is delineated by one Planck-Length and/or one Planck-Radii at a different directional-based wave-tug/wave-pull, than all of the other superstrings that also work to comprise the orbifolds -- that work to comprise the said orbifold eigenset, that is here in question.  Also, in such a scenario, the topological-based swaying of each of the orbifolds -- as a whole -- will, in this given arbitrary case, be pulled in a different genus of wave-tug/wave-pull, over the course of the group metric in which such an orbifold eigenset is functionally operating as a Hamiltonian operator, over time.  This general condition that I have just described is a general condition of an orbifold eigenset, that would here not bear a harmonic format -- among both those superstrings and those orbifolds that would here work to comprise the so-stated given arbitrary orbifold eigenset, that is here in question.  Yet also, orbfolds and other topological settings often have  Real-based singularities that exist in-between each of the other orbifolds and superstrings, that work to comprise a given arbitrary orbifold eigenset, that may happen in either a harmonic or in an annharmonic manner.  I will continue with the suspense later!  To be continued!  Sincerely, Sam Roach.

Part Two of the Fifth Session of Course 17 About the Ricci Scalar

Each time that an orbifold eigenset iterates, it kinematically differentiates either radially and/or transversally.  If the just mentioned respective given arbitrary orbifold eigenset is moving in a Noether manner,then, the said given arbitrary orbifold will consist of superstrings that will each move either one Planck-Length and/or one Planck-Radii per iteration of group instanton that is here involved.  Yet, if an orbifold eigenset is, instead, of a tachyonic-based flow of superstrings -- then,  these superstrings, of which work to comprise the so-eluded-to given arbitrary directly corresponding orbifold, this of which works to comprise a directly corresponding given arbitrary orbifold eigenset -- then, the superstrings that work to comprise the said orbifold eigenset will be delineated at a distribution that bears a scalar amplitude of more than one Planck-Lengths and/or more then one Planck-Radii -- per the respective correlative iterations of group instanton, that would here directly correspond to that group metric in which such a so-stated orbifold eigenset is moving kinematically in a tachyonic-based manner.  As long as the Noether-based current is applicable to any given arbitrary world-sheet -- that would here work to bear a mappable tracing of a so-eluded to correlative superstring of discrete energy permittivity, and, if the so-stated superstring that I have just mentioned, in this given arbitrary case, is of a Real Reimmanian-based nature that bears no Chern-Simmons spurs in both its Lagrangian-based path and in its metrical-based delineation, then, the said world-sheet -- during the directly corresponding iterations of group instanton -- is said to bear a hermitian format of topology.  So, as long as the superstrings of discrete energy permittivity -- that work to comprise any given arbitrary orbifold -- is being applicable to a Noether-based current over time -- and, if the said orbifold is of a Real Reimmanian-based nature that bears no Chern-Simmons spurs in both is Lagrangian-based paths and in its metrical-based delineation, then, the so-eluded-to orbifold, during the directly corresponding iterations of group istanton, is said to bear a hermitian format of topology.  This is true, in both of the cases of the respective hermitian-based world-sheets, and also of the respective hermitian-based orbifolds, -- whether the correlative light-cone-gauge topology is of an abelian or Kaluza-Klein light-cone-gauge topology, or, if the correlative light-cone-gauge topology is instead of a a non-abelian or Yang-Mills light-cone-gauge topology.  This does not, however, work to describe all of the superstrings that work to comprise the so-eluded-to orbifolds and/or the so-eluded-to orbifold eigensets that I have just mentioned.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of the Fifth Session of Course 17 About the Ricci Scalar

Superstrings and world-sheets kinematically differentiate both radially and/or transversally per iteration of group instanton.  So, each time that a superstring of discrete energy permittivity iterates per instanton, the so-stated superstring differentiates either radially and/or transversally -- depending upon both the format as to whether or not the given arbitrary superstring is undergoing a certain genus of conformal invariance, and/or if the said superstring is going through a condition of viable perturbation that is not conformally invariant in genus (but still of a Noether-based flow), or, if the so-eluded-to superstring is undergoing some type of format of a tachyonic-based flow.  Each time that a world-sheet iterates -- if the directly corresponding superstring that worked to form the said world-sheet is of a Noether-based flow, over the course of the extrapolatable mappable tracing of those given arbitrary ghost-based indices, that indicate both the existence and the activity of the so-stated given arbitrary world-sheet -- the mentioned world-sheet will be translated one Planck-Length and/or one Planck-Radii from the initially based eluded-to general condition of delineation to the next eluded-to general condition of delineation.  Yet, if a superstring of discrete energy permittivity is of a tachyonic-based manner, then, the distribution of the scalar magnitude as to the delineatory index of how far any given arbitrary superstring is delineated -- from one specific spot to the next -- will then here involve a kinematic-based extrapolation of more than one Planck-Length and/or more than one Planck-Radii per each respective succeeding iteration of instanton that would then be involved here.  This would then mean that the resultant directly corresponding world-sheets -- of which are the projection of the trajectory of the so-stated given arbitrary superstrings -- will be delineated in such a manner in so that each succeeding iteration of instanton will then here involve a distribution of scalar magnitude that would involve a translation of more than one Planck-Length and/or more than one Planck-Radii per each of such so-stated iterations.  Gravity is altered or perturbed to a certain extent, whenever there is tachyonic activity.  This is because tachyonic activity effects the Ricci Scalar -- via the effect that this has upon the respective given arbitrary Rarita Structure eigenstates.  I will continue with the suspense later!  To be Continued!
Sam Roach.