Heuristic Gravitational Force / Anti Gravitational Force -- Restraint Of Inferred Tendencies

 Heuristic Gravitational Force, tends to impel the general restraint, upon the kinematic distributional delineation of a given arbitrary Noether-Based mass-bearing Hamiltonian Operator, in so as to incur the general physical tendency, of working to help allow for a proximal local condition of conformal invariance. Whereas; Anti Gravitational Force, as imparted upon a given arbitrary Noether-Based mass-bearing Hamiltonian Operator, tends to impart the general physical condition of restraint, upon the initially incurred  physical condition of conformal invariance, that is here to have initially been occurring, in so as to tend to work to help allow, for the spontaneously ensuing potential kinematic distributional delineation, of the topological manifold, that is here to be of the holonomic substrate of the earlier stated given arbitrary respective Noether-Based mass-bearing Hamiltonian Operator, of which is here to be theoretically described in a general manner, in this particular genus of a case scenario. SAM ROACH. 

Superstrings -- Super-Conformal Invariance At An Internal Reference-Frame -- Abelian Light-Cone-Gauge Topology

 Superstrings of discrete energy permittivity, that are here to work to bear a tense of super-conformal invariance, at an internal reference-frame, (to where, such superstrings are here to be exhibiting the display, of a correlative tense of a Majorana-Weyl-Invariant-Mode), are to tend to work to bear an abelian light-cone-gauge topology. It follows, then, that; Superstrings of discrete energy permittivity, that are here to Not be working to bear a tense of super-conformal invariance, at an internal reference-frame, (to where, such superstrings are Not be be exhibiting the display, of a correlative tense of a Majorana-Weyl-Invariant-Mode), are to tend to work to bear a non abelian light-cone-gauge topology. Sincerely, Samuel.

Toroidal-Shaped Cohomology-Related World-Sheets -- Gliosis-Sherk-Olive Ghosts

 Mass-Bearing superstrings of discrete energy permittivity, tend to work to form toroidal-shaped cohomology-related world-sheets. World-Sheets are the projection of the trajectory of discrete energy phenomenology (superstrings). Cohomology may be perceived of, as being of the eminent topological substrate, of the core-field-density of discrete energy quanta. What I worked to describe of, during some earlier times in my blog, as being "ghosts," -- were actually what I meant to describe of, as being "cohomology-related eigenstates." I referred to such said "eigenstates," as being of a ghost-like nature, since the actual specific phenomenology that I was here to be referring to, is of a constantly indistinguishably different nature. (To where, although these "appear" to be consistently spontaneous latched upon eigenstates, that are stable in super conformal invariance at a covariant locus, in time and space, the specific phenomenology that is here to be latching, at the inferred covariant respective loci, are to constantly be of different actual "stuff.") Those ghost-like phenomenology, that are here to be directly appertaining, to the multiplicity of the toroidal-shaped topological manifolds, that are here to be directly associated with those  respective cohomology-related world-sheets, that are here to be formed by the resultant projected trajectory, of mass-bearing superstrings of discrete energy permittivity, may be described of here, as being of the general nature, of acting as, "Gliosis-Sherk-Olive" ghosts. (1989). SAMUEL DAVID ROACH.

A Basic Example Of Ward-Polarization

Here is a basic general example, of what may be termed of as a phenomenon -- in which there is to be the Ward-Cauchy-based condition of Ward-Polarization:

Let us initially say that one is to have an orbifold eigenset, that is to be undergoing a tense of conformal invariance at its internal reference-frame, that is here to work to bear a tense of what would here be at least the equivalence -- of a tense of angular momentum, that is subtended in what would here be the relative forward-holomorphic direction.  Let's next say, that over the translation of a relatively small distance, as taken in the earlier mentioned forward-holomorphic direction, from where the initially stated orbifold eigenset is to be bearing its so-eluded-to tightly-knit location of vibrational oscillation,  -- there is to be the bearings of a tense of a quantum of electromagnetic energy to be present.  However, there is here, in this general case, an orbifold eigenset, that is placed in-between the direction of the angular momentum that is of the initially stated orbifold eigenset and the so-stated quantum of electromagnetic energy -- that is here to be placed in such a manner, to where the relative holomorphic direction of the orbifold eigenset that is here to get in the way, is to be orthogonal to the holomorphic direction of the initially stated orbifold eigenset.  Such a substringular condition of such a case, may then work to partially, if not completely, block any otherwise eminent Yukawa Coupling to then to be able to be achieved, between the initially said orbifold eigenset and the so-eluded-to electromagnetic energy-based orbifold eigenset.  This general genus of a Ward-Cauchy-related condition,  is one of basically countless types of situations -- in which there is to be the phenomenon, of what may be termed of as Ward-Polarization.  Samuel David Roach.

Annharmonically Scattered Orbifold Eigenset

Let us initially consider an orbifold eigenset, that is undergoing a Majorana-Weyl-Invariant-Mode.  It is thus, at the moment here, under the Ward-Cauchy constraints of a tense of conformal invariance, or, in this case, of a tense of superconformal invariance -- at an internal reference-frame, that is Poincare to the topological stratum of the said orbifold eigenset. Such a superconformally invariant orbifold eigenset, is here to tend to be exhibiting a De Rham cohomology.  It is then to be scattered, via a Rayleigh scattering, of which is of an annharmonic scattering.  This will then tend to mean, that the orbifold eigenset that is of such a case -- will tend to be perturbated out of its initially stated De Rham cohomology, into a Doubolt cohomology, at least initially -- in the process of being scattered  out of such a tense of a Majorana-Weyl-Invariant-Mode.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Partials As To Lorentz-Four-Contractions

Let us initially consider an orbifold eigenset, as I had described yesterday -- of which is a set of superstrings that operate in so as to perform one specific function, that goes from being of a superconformal invariant nature, to then scattering briefly into a looser mode of Majorana-Weyl-Invariance, to then scattering back into a tighter tense of conformal invariance, and back again, and so on.  Let us next say -- that as this is happening, the field of the said orbifold eigenset as a whole, is to be otherwise tending to be traveling in the relative holomorphic direction at a constant rate.  In this manner -- there are to here to be two different general partials of the correlative Lorentz-Four-Contraction, that are to be Yukawa to the so-eluded-to Fourier differentiation, that is of the said orbifold eigenset, in this just mentioned process.  There is to be that Lorentz-Four-Contraction partial, that is due to the directly pertinent tense of the scalar amplitude of the extent of the directly corresponding Majorana-Weyl-Invariant-Mode, that is to be differential in its Yukawa influence upon the so-stated orbifold eigenset, -- and, there is also to be that Lorentz-Four-Contraction partial, that is due to the directly pertinent tense of the scalar amplitude of what would otherwise be the tendency of a motion that is in the relatively metrical smooth holomorphic motion of the said orbifold eigenset, as it is here to be translated as a whole, across what may be termed of here as an approximate discrete unitary Lagrangian path, that is to bear both a codifferentiable and a codeterminable cohomological wave-tug -- across the space-time stratum of both that Hamiltonian operand that is in the direction of the region of its perturbative Majorana-Weyl-Invariant-Mode, as well as that Hamiltonian operand that is of the tendency of moving in the relatively holomorphic direction of the region of the mappable-tracing of the just mentioned discrete unitary Lagrangian path.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Calabi-Yau Manifolds And Yau-Exact Strings

Mass-Bearing superstrings of discrete energy permittivity, have a tendency of behaving in a Yau-Exact manner, when such superstrings are to be set into a tense of superconformal invariance -- when this is taken at the Poincare level to a directly corresponding internal reference frame, in which any given arbitrary orbifold eigenset that is to be comprised of such respective superstrings -- is to be differentiating in a Fourier-based manner, that works here to display a Rham-based cohomology.  This is in terms, again, of the interactions of a Calabi-Yau manifold, that is of a relatively maintained Ward-Cauchy-based pulsation -- in which both the transversal-based eigenindices and the torsional-based eigenindices, that are of the correlative mass-bearing superstrings of discrete energy permittivity, are to both behave as such in a hermitian-based manner, -- in so long as the directly corresponding orbifold eigenset is to remain as behaving in a superconformally invariant manner, in which it is to here to be translated via a Fourier Transformation, that is here to be working to form a Rham-related cohomology over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Gaussian Transformations And The Kahler-Metric, In General

Let us initially consider one given arbitrary orbifold eigenset, -- that is here to be eminently Yukawa to the Kahler-Metric.  Here is a brief synapsis, in both a curt and in a general manner, as to what is to happen here.:  At the onset of such a Ward-Caucy group-related metric --the so-eluded-to set of superstrings, that are to here be operating to perform one specific function, are to first here, bear an eminent Yukawa-based relationship that is not of a Gliosis-based nature, with the Kahler-Metric -- for the initial 95 iterations of group-related instanton -- in which this is happening.  For the ensuing 191 iterations of the said tense of instanton, the correlative orbifold eigenset is to be Gliosis to the so-eluded-to eigenstate of the Kahler-Metric.  For the next 95 iterations of the said tense of instanton, the correlative orbifold eigenset is to bear an eminent Yakawa-based relationship with the Kahler-Metric, yet not in a Gliosis-based manner.  For the next three iterations of group-related instanton -- the said orbifold eigenset is only mildly Yukawa in an eminent manner,  to the so-eluded-to Kahler-Metric eigenstate, -- while the directly corresponding Higgs Boson eigenstate along with the correlative holonomic substrate of the directly corresponding Klein Bottle eigenstate, are to work to re-position themselves, -- in so as to work to prepare for the activity of a slightly different proximal local Fourier-related operation, that is to involve the eminent Yukawa-based bearings of the Kahler-Metric.
I will explain this in much more detail in Course 24 -- as to conformal invariance and superconformal invariance.  I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Operators And Group-Attractors, Part Six

Thus, conformally invariant sets of substringular phenomenology, like Majorana-Weyl-Invariant-Mode related masses -- tend to have more of a convergent set of relations.  Yet, covariant sets of substringular phenomenology -- that tend to diverge,  tend to be relatively more inexact and nonlinear in the expansion of their directly corresponding anti-chiral-based eigenindices, than covariant sets of substringular phenomenology that converge (to where the adjacent of such eigenindices will here be, instead, of an even-based chirality), as such said eigenindices are to tend to then be drawn into different respective substringular groupings.  However, first-ordered point particles, and waves that are delineated as norm-state-projections via the Fourier-based activity, that is here to be of the nature of certain given arbitrary differential geometries that are of such said first-ordered point particles, when such of these "building blocks" -- that are of the rudiments that work to form the composition of both superstrings and norm-state-projections -- when directed with the right angular momentum at the substringular level -- may often act as a fractal of an inductor of the conformal invariance for a set of one or more superstrings, and may often then act as a metrical-gauge-based Hamiltonian operator, that would work here to physically exist as an "integrating factor"-based holonomic substrate, or, in other words, as a catalyst, -- for the correlative Yukawa-based interaction of the directly corresponding group-attractors, to then act upon the topological surface of the directly corresponding specific given arbitrary discrete quanta of energy of such a respective case, in so as to bring this said discrete energy into a tense or a state of Majorana-Weyl-Invariance, at the Poincare level, that is to here be proximal localized at the Ward-Neumman/Ward-Caucy stratum that is to here be Gliossi in this case, to the holonomic substrate that is directly affiliated with the correlative discrete energy, that is being brought into a tense of conformal invariance.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Operators And Group Attractors, Part 3

As I was eluding to before, this "disappearing act" works to help form the basis, of what may here be considered as an association with both the minimum distance and the minimum time that a superstringular entity may travel, to where the discrete values that are to here be relative to a direct correlation -- with either the Planck Length and/or the Planck Radius  -- may then be established, based upon a directly correlative extrapolation of such a so-eluded-to scenario.  Now, you may wonder -- how does the homeostasis of the bearings of a superstring of discrete energy permittivity, actually work together, -- when this is taken in our initial consideration of relativity, to where this will consequently work-out in the real world, in so as to come into play with any given arbitrary set, that is of that general sequential substringular iterations of group-related instanton, that come together in so as to work to help to form the Fourier-based translation of energy, that is being conveyed over time?  The following may help to start to explain this generic type of question:  Certain first-ordered point particles will end-up at about roughly the same spot over a sequential series of instantons, on account of such a directly related set of superstrings -- that are here to be comprised of such so-stated first-ordered point particles, that are to here be in the process of what may here be called a tense of superconformal invariance.  When a set of superstrings of discrete energy permittivity, are to here be undergoing a tense of superconformal invariance -- at what is to here be at the Poincare level to the proximal localized tense of static equilibrium, that is to here be involved with such a tense of a relatively stable framework that may be then considered to be of a relatively non-kinematic tense, over time, to where then, such a said set of superstrings that are to be conformally invariant in such a so-stated manner, are to here be undergoing a relatively tightly-knit tense of a Majorana-Weyl-Invariant-Mode.  Thus, the directly associated sequential series of group-related instantons of such a tightly-knit tense of conformal invariance, are then said to converge upon the directly corresponding Hamiltonian operand -- by which these are to be in a steady-state with, -- over the directly associated time by which such a static-based framework is to not be kinematically perturbated from the said proximal localized locus of field operators.  Such a tense of a framework, that is to here be in a relatively tightly-knit tense of conformal invariance, is to then, during such a relative tense of invariance, to tend to be in the process of being kept from perturbating as a divergent metrical-gauge-based Hamiltonian operator, by the Fourier-based influence of a set of one or more group-attractors -- that will as well, tend to act in so as to help to keep the said convergent covariant set of operators in tact, as a relatively static Hamiltoniain operation, by the Fourier-based activity that is translated by the activity of the self-same entities that I have just described of as being a directly influential tense of group-attractors, that are to then be Yukawa to the eigenstates of the field generators of the so-eluded-to convergent eigenindices -- that are here to be in the said tense of superconformal invariance.  Now if the so-eluded-to tendency of the so-stated activity of the directly associated group-attractors is to susequently diverge from being Yukawa to the topological substrate of the so-eluded-to superconformally invariant field -- this will often work to cause the initially stated static-based field, to go into the process of a Rayleigh-based scatttering of its correlative eigeninidces, -- which will consequetly tend to work to form an annharmonic wave-tug upon the homotopic residue of the initially static set of superstrings.  This will then tend to form an odd chirality among the adjacent superstrings that were intially of an even chirality -- which will consequently work to disorient any immediately ensuing extrapolation of the point particles that will have here worked to initially help to form the so-eluded-to superstrings of discrete energy permititivty that we were initially discussing.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Noether Currents, In General

When a tense of a given arbitrary Ward-Caucy state of a set of conditions, that may work here to describe a sense of Majorana-Weyl-Covariance,  that may here act in so as to be extrapolated in such a manner, in so as to work to describe an orbifold eigenset that is in a state of superconformal invariance, which will then work to describe a proximally local tense of Majorana-Weyl-Invariance -- then, it's locally proximal framework is not in and of itself exhibiting a strong pull into a Fourier-based alteration in its delineation from that so-stated locally proximal framework -- even if the so-eluded-to internal-based framework that is to here be in a tense of superconformal invariance, is to exist in a set of one or more externally-based frameworks that are to instead exhibit a strong pull into a Fourier-based alteration in its delineation from the Ward-Caucy bounds that are Poincare to the exterior of the so-eluded-to more external frameworks, of such a respective given arbitrary case scenario.  Yet, if any given arbitrary locally proximal substringular framwork, that may here work to describe the Fourier-based motion of an orbifold eigenset, is to be in a state of kinetic motion -- to where the said orbifold eigenset is to not be in a state of superconformal invariance, then, the set of discrete energy quanta that would here work to come together as a group -- will behave in such a manner in so as to describe a Hamiltonian operator, that is to be kinematic in its sequential series of delineations, to where this will be of a kinematic substringular framework -- that will be moving from one definitive substringular region to another, over the completion of a set of group-related instantons.  When one is to basically have an orbifold eigenset, that acts as a Ward-Caucy-based Hamiltonian operator -- that is to here be differentiating in a Fourier-based manner -- but at a rate that is slower than the propagation of light -- then, the directly corresponding tense of the Noether-based current, that is to here be exhibited by the so-stated orbifold eigenset, will work to bear at least some sort of cohomological-based inhibition, over the correlative set of motion in which the said respective orbifold eigenset is to be delineated from one substringular locus to another, over time.  Such a so-eluded-to orbifold eigenset, will then bear a tense of Majorana-Weyl-Covariance -- to where, the tighter-knit that the tense of the said Majorana-Weyl-Covariance is -- the lower that the tense of the correlative Noether Current tends to be.  Likewise, the looser-knit that the tense of the said Majorana-Weyl-Covariance is -- the higher that the tense of the correlative Noether Current tends to be.  The lower that the Noether Current is, the slower that the directly corresponding velocity of the correlative orbifold eigenset tends to be.  The higher that the Noether Current is, the faster that the directly corresponding velocity of the correlative orbifold eigenset tends to be.
Lots from there.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Ending Part Of Session 13 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

When one is to have the substringular condition of a relatively small orbifold eigenset, that is to here undergo the Kahler-Metric in a spontaneous-based manner -- then, the scalar amplitude of the tense of the directly corresponding Majorana-Weyl-Invariant-Mode -- will then tend to be affiliated with that correlative motion of the directly corresponding Klein Bottle eigenstate, that will here work to bear a relatively tightly-knit tense of conformal invariance, when this is to here be taken from within the proximal localized reference-frame, that is Poincare to the direct association of the so-stated orbifold eigenset with its directly corresponding Klein Bottle eigenstate.  Likewise -- when one is to instead have a relatively large orbifold eigenset, that is to here undergo the Kahler-Metric in a spontaneous-based manner -- the scalar amplitude of the tense of the directly corresponding Majorana-Weyl-Invariant-Mode -- will then tend to be affiliated with the correlative motion of the directly corresponding Klein Bottle eigenstate, that will here work to bear the condition of having a relatively less tightly-knit tense of conformal invariance, than that which would be afflilated with the earlier mentioned relatively smaller orbifold eigenset, when this is to here be taken from within the proximal localized reference-frame -- that is Poincare to the direct association of the so-stated orbifold eigenset, with its directly corresponding Klein Bottle eigenstate.

Tenses Of Relative Stability

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

An Elaboration As To My Last Post

Let us here, first consider the physical situation of which I ended-up mentioning in my last post.  One will here have a diamond-like shape, that is situated right above an arbitrary horizonal axis -- this just mentioned axis of which is here to be considered arbitrarily as the x axis.  Let us now say that this said diamond-like shape were to have, as well, a trivially isomorphic diamond-like shape -- that is to be situated just below the first so-stated diamond-like shape, on the negative quadrant of what may be termed here as an arbitrary y axis.  Now, let us say -- that one were to bear a Laplacian-based shift of the two said entities that have been mentioned here, as bearing a diamond-like shape -- to where the so-stated relative top diamond-like configuration that is situated in the positive y quadrants, will bear an integration of indices, that are pulled both around and "into the page" from its initial flat-space-like initial configuration, -- while there will, simultaneously, from the vantage-point of the center of the so-eluded-to coniaxion, be the condition of the so-stated relative bottom diamond-like configuration -- that is situated in the negative y quadrants, working to bear an integration of indices, that are pulled both around and "out of the page" from its initial flat-space-like initial configuration.    The annulus that I am about to mention will act as the so-eluded-to "washer." As I have here eluded-to -- the volume-based region that goes Into the page may be considered here as the region for a relative positive z-based region, while, the volume-based region that goes Out of the page may be considered here as the region for a relative negative z-based axial region.  Besides both the x axis, the y axis, and the z axis -- three other spatially-based coniaxial directorals (l hat, m hat, and n hat, arbitrarily) are to be integrated into the coming together of the Laplacian-based picture of this respective given arbitrary situation.  The last two of such so-eluded-to spatially-based coniaxial directorals (directly associated here arbitrarily to m hat and n hat, in this given arbitrary case), are of a curled-up nature.  Consider this spatial integration of indices -- that are integrated as I have suggested -- to work at forming a toroidal-based entity.  The annulus of the toroid may be considered here, to be bearing in a relative holomorphic-based manner -- as is going from just outside of the relatively antiholomorphic end of the very center of the said toroid, on the i hat directoral positioning -- that would here tend to be centered as is going right from a spot proximal to the x axis -- while then going, in a holomorphic and a relatively left-moving manner, until it works to exit the Ward-Neumman bounds of the holonomic substrate of the entity of the so-stated toroidal-based shape, that is of this said given arbitrary Laplacian-based example.  Since this particular example works to include the conical-based edges of the so-stated diamond-like shapes, that I have here mentioned -- the so-stated toroidal-based  structure that I have just mentioned as forming, will be as a theoretical genus of a toroidal-based cohomology, that works to bear certain conical cyclic permutations -- that may be extrapolated in a Laplacian-based manner.  This would be similar but different to the GSO type of a ghost anomaly -- that may be formed by the physical memory of a superstring of a mass-bearing eigenmember, that is from the Ward-Caucy bounds of an electron -- that would be probable as existing in a condition of a respective given arbitrary tense of a Majorana-Weyl-Invariance-Mode -- over a directly corresponding Fourier-Transformation, in which such a superstring that is differentiating in a kinematic manner, over time, is undergoing the general process of conformal invariance.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

Part One of Session 16 of Course 18 -- The Ricci Scalar and Kaeler Differentiation

The Schotky Construction is composed of the manner in which the Klein Bottle is put together.  In other words, the composition of any given arbitrary Klein Bottle eigenstate is based upon the make-up of the Schotky Construction.  The Schotky Construction bears a make-up that is based upon the consideration of those respective orientifolds, of this given arbitrary consideration -- that are physically held together by the correlative Wilson-based Ward-Caucy delineations, that work to comprise the manner in which the so-stated relative lengthwise and thickness-wise ends of the said Schotky Construction are put together, in so as to form the substringular-based attributes as to the way that any respective given arbitrary Klein Bottle eigenstate is put together.  I will describe the nature of such a construction later.  This so-mentioned Schotky Construction's general physical composition in the substringular, is always how any actual unfrayed Klein Bottle eigenstate is put together -- whenever such a said eigenstate of this so-stated genus of substringular format is of the capability of being able to act as the "key player" of what is utilized in so as to move any respective given arbitrary Higgs Boson eigenstate, that is of a correlative nature, into the general core-field-density of the activity of the directly affiliated multiplicit Kaeler-Metric eigencondition of group metrical eigenbase.  The physical tense of any given arbitrary Klein Bottle eigenstate tends to act, as much as feasible, in so as to exist in a state of optimum conformal invariance.  Often, what may work to appear as what acts, in a kinematic manner, as specific Klein Bottle eigenstates, are phenomena that are being utilized in  a tense of indistinguishable difference -- particularly, if the correlative superstrings that are here being directly involved in such a case, are of a tachyonic-based nature.  Yet, due to the manner of the activity of the multiplicit Klein Bottle eigenstate -- on account of both the manner of its Schotky Construction, and also, the general "apparatus" of the Kaeler-Metric-based eigenmatrix-based inter-relationshipts -- the motion of the said Klein Bottle, in general, is relatively situated in a tense of a Majorana-Weyl Invariant Mode.  I will continue with the suspense later!  To Be Continued!  Sam Roach.

The Next Part of Session 15 of Course 18 -- The Ricci Scalar and Kaeler Differentiation

Let us go back to the case in point that I had left off at during my last post.  What we have here is a collective set of orbifold eigensets that are both covariant, codifferentiable, and codeterminable -- in a condition-based state of Noether Flow -- in which both the respective individual said orbifold eigensets, as well as the resultant of the interaction of such so-stated orbifold eigensets, are all moving under the means of a Noether-based flow, over a sequential series of group-related instantons.  This would here mean that the initial condition of the kinematic-based differential flow of the initial interaction of the said set of orbifold eigensets, of this particular case in point, is not of a tachyonic-based nature.  After a respective given arbitrary relatively transient group metric of iterative instantons, the initial Noether-based flow of the interactive set of orbifold eigensets of this case are perturbated -- into an ensuing tense of what is here to become a tachyonic-based flow of cohomological-based indices, when given the physical memory of the mappable tracing, as to both the plotting of both the existence and the activity of those superstrings of discrete energy permittivity, that have here undergone the performance of a set of unique interactive operations -- that have here acted in so as to do a  specific set of functions in the substringular.  The respective given arbitrary interaction of a covariant codifferentiable, and codeterminable set of orbifold eigensets, that work to perform one set of operational-based functions -- may either maintain a static-based substringular state of kinematic-based activities, work to perform a state of conformal invariance ( of which may be either of a superconformal-based or of a conformal-based nature), or, the so-eluded-to operational-based pretense of the genus of such a substringlular set of interactive functions may work to perform a divergent pretense of kinematic-based activity in the substringular.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

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

So, as eluded-to before, Chern-Simmons singularities may often be traceable in cohomological-based stratum, as well as in conformally invariant orbifold-based fields.  If one is to extrapolate the tracing of a cohomology that is otherwise smooth in mappable topology -- due to the dual existing conditions of having both jointal-based and smooth-curved-based aberrations, along the contour of the mappable trace of its ghost-based physical path over time -- those permutations, that are directly the result of the lack of smoothness in the here eluded-to mappable tracing of the physical memory of the path of the correlative cohomological holnomic stratum, will here work to form a tense of unique Chern-Simmons singularities, of which will here work to form a Chern-Simmons format of a cohomological-based pattern.  Such a substringular tense of a Chern-Simmons ghost-based field will then here directly involve either superstrings, and/or orbifolds, and/or a tense of a perturbative orbifold-based field, that will have altered -- over a transient group metric of a relatively limited sequential series of instantons -- from an initial tense of conformal invariance, into a relatively new local tense of conformal invariance.  What is here happening, is that an initial relatively limited number of superstrings is initially iterating in a tense of a relative condition of Majorana-Weyl-Invariance.  The resultant cohomological-based pattern is initially at least partially hermitian in composure, over a relatively brief duration of time.  Either a Lagrangian-based spike and/or a metrical-based spike will then happen spontaneously and abruptly, to the correlative given arbitrary set of directly pertinent superstrings -- working to form a Chern-Simmons-based field, that will here work to cause a relative lack of topological smoothness in the Laplacian-based mappable tracing of the ghost-based extrapolation, the latter of which works to indicate the immediate what, how, where, and when of the here so-stated directly pertinent set of superstrings that have undergone the just eluded-to altered stated of the correlative Chern-Simmons-based delineations, has thus been happening.  Any perturbative tensors that are interactive upon a substringular holonomic stratum will here work to form a perturbation in the directly corresponding Majorana-Weyl-Invariant modulus.  This will then work to form a relative condition of group covariance.  This just eluded-to alteration in the relative local field index will then move in the direction of most stability, ensuing the correlative delineation of either a spike-like and/or a spurious-based singularity that is then pulled-out of the here mentioned general locus of substringular cohomological-based topological stratum.
I will continue with the next part later!  Sam.

Part Two of the Test Solutions to the Last Test of Course 16

1)  The Chan-Patton rules of superstrings are principles that work to govern the condition of a mass having a Kaluza-Klein light-cone-gauge topology as always traveling at under the speed of light.  If a mass is translated into a tachyonic flow -- via the conversion of its light-cone-gauge from a Kaluza-Klein topology to a Yang-Mills topology temporarily ---, then, it can likewise temporarily display the general effect of the so-stated Chan-Patton rules during the said course of a tachyonic propulsion.  After the just-eluded-to tachyonic-flow, the mass that was translated is brought back into a condition of Kaluza-Klein light-cone-gauge topology, at which point the said mass goes back into obeying Chan-Patton rules.

2)  World-Sheets that appertain to the mappable tracing of tachyonic-based superstrings are an abberation from Chan-Patton rules.  Otherwise, the mappable tracing of Noether-based superstrings is the holonomic substrate of the extrapolation of world-sheets that obey Chan-Patton rules.

3) As superstrings are made unorientable by the formation of a heteromorphic field that exists for a given arbitrary so-stated superstring and its directly corresponding counterpart -- during a directly correlative duration of BRST, the said superstring is then pulled into a tachyonic-based flow, on account of the just-eluded-to perturbation -- during the ensuing eluded-to group metric.

4)  A Yang-Mills light-cone-gauge topology is of a non-abelian nature, while, a Kaluza-Klein light-cone-gauge topology is of an abelian nature.  A non-abelian topology bears relatively less of a direct wave-push/wave-pull at its topological edge than an abelian topology does.  A relatively less abelian format of a light-cone-gauge topological eigenstate is more capable of propagating in the manner of electromagnetic energy, since this allows for a harmonic wave modulus at light-speed that would be sinusoidal and not flush, which thereby does not here cause any threat of aiming to bear an infinite fractal modulae.

5)  The Kaeler-Metric is the group metric in which a superstring is brought into the kinematic activity, to where it is capable of re-attaining the discrete fractals of energy permittivity, to where energy may spontaneously exist aned persist-- as the directly appertaining eluded-to given arbitrary Fadeev-Popov-Trace eigenstate -- that is correlative to the so-stated superstring -- is brought into the kinematic activity to where it is capable of re-attaining the discrete fractals of energy impedance to where energy may spontaneously exist and persist.  When a superstring bears a cohomology that reverses in terms of directoral holomorphicity, this works to initiate the activity of a Kaeler-Metric.

6)  A Calabi-Metric is a Kaeler-Metric that directly involves the scattering of electromagnetic energy.  When discrete entropic photons are formed, this is an indication of a Calabi-Metric.

7)  When light scattering happens in Earth's atmosphere, then this scattering of electromagnetic energy here involves a Calabi-Metric that is essential for the formation of the existence of heat in our planet's biosphere.

8)  The Noether Current is the general flow of substringular motion that is not over light speed.  All non-tachyonic superstrings move the Planck-Length and/or the Planck-Radius per increment of group instanton.  Yet, electromagnetic energy, which, is when a group of one or more superstrings -- here, photons -- travel as a group through a discrete and unitized Lagrangian through enough of a scalar amplitude -- as a group propagation -- until it interacts with infrared-based photons.  This happens in so that the so-eluded-to photons -- if in a vacuum -- will propagate here one Planck Length per directly appertaining group iteration of instanton.

9)  Depending upon the degree of the conformal invariance of any given arbitrary tense of Noether-Flow, the less conformally invariant the so-stated tense is, the faster that the just-eluded-to superstring moves, relative to their environment.  The faster that the so-stated superstrings move, the closer that these superstrings are to "light-speed."  The closer that  a Noether-based flow appertaining to a mass is to light-speed, the greater that the Lorentz-Four-Contraction is.  The greater the Lorentz-Four-Contraction is upon any given arbitrary superstring of mass, the smaller that its relative length and time are, and, the greater is its relative mass is.  Overcoming Noether Flow, in so as to allow for a mass to be translated to light-speed or greater -- without bearing all of the mass in the universe -- may be done by the conversion of the directly associated light-cone-gauge topology from a Kaluza-Klein topology to a Yang-Mills topology -- during what would here be a temporary translation.

10  A Noether Current is constant for any given arbitrary phenomena that bear both a Kaluza-Klein light-cone-gauge topology and Yau-Exact singularities.  By converting the relative light-cone-gauge of the just-eluded-to mass into a Yang-Mills light-cone-gauge topology temporarily, one may overcome the so-stated Noether Flow into a brief condition of tachyonic propulsion.

I will continue with the start of Course 17 Soon!  Sam.

Group Activity Involving Lorentz-Four-Contractions

When an orifold and/or an orbifold eigenset moves -- as a discrete unit -- in a relatively straight and transversel manner, based upon Snell's Law, through a discrete Lagrangian, for more than 384 instantons, then, the said orbifold and/or orbifold eigenset is said to behave as a holonomic substrate of physical space that is one form or another of electromagnetic energy.  When an orbifold and/or an orbifold eigenset is a quantum unit of electromagnetic energy, then, the distance between the central inter-connectivity of where the given arbitrary first-ordered light-cone-gauge eigenstates of all of the superstrings that work to form the said orbifold and/or orbifold eigenset bind with the directly corresponding Fadeev-Popov-Traces that work to form the directly correlating units of discrete energy impedance -- up to the central inter-connectivity as to where the eluded to light-cone-gauge eigenstates bind with the here corresponding superstrings that I have mentioned, is equal to pi times the Planck Length. Also, under the same conditions, the distance between the eluded to superstrings that work to comprise the said orbifold and/or orbifold eigenstate with the directly corresponding counterparts of the said superstrings will also be equal to pi times the Planck Length.  When a superstring is fully uncontracted -- due to the said superstring existing in a tense of static equilibrium as a state of superconformal invariance, then, the previous mentioned lengths of substringular field-based inter-connectivity will be shortened by one Planck Length each.  So, multiply whatever a given arbitrary Lorentz-Four-Contraction is times 10^(-43) meters, while then adding this distance to the two given respective lengths of substringular inter-connectivitiy that I had recently eluded to in this post ( onto the eluded to lengths of such field bindings that would apply for a fully uncontracted superstring), and this will work to indicate the respective lengths of the so-stated scalars of substringular inter-connectivity that work to bind both a Fadeev-Popov-Trace to its directly corresponding superstring & the distance of relativistic lengths of the directlty corresponding superstrings with their immediate counterparts.  So, when a given arbitrary orbifold and/or a given arbitrary orbifold eigenset is Lorentz-Four-Contracted by a discrete amount, each superstring that works to comprise the eluded to orbifold and/or orbifold eigenset behaves as is according to the math that I have just eluded to.  This is possible, because the condition of homotopy works to allow for mini-string segments to be ebbed into and out of the various substringular settings over time.  The reason for me stating "over 384 instantons" is because a discrete gauge-metric of any given arbitrary eigenmetric of Kaeler-Metric happens in 384 instantons -- as I will discuss more in course 24 about Conformal and Superconformal Invariance.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Test Questions to The First Test Of Course 13

1)  In simple terms, how may a swiveled one-dimensional superstring convert into a basically straight one-dimensional superstring?

2)  How are one-dimensional superstrings generally shaped during an iteration of group instanton?

3)  How may a one-dimensional superstring be conformally invariant with other one-dimensional superstrings two-dimensional superstrings?

4)  Explain conformal invariance in terms of indistinguishable differences.

5)  What is an abelian geometry?

6)  What is a nonabelian geometry?

7)  When are inertia and momentum of superstrings quantified?

8)  Whan are inertia and momentum of superstrings not quantified?

9)  When are inertia and momentumjerked?

10)  Explain when a superstring is partially explainable by an abelian geometry.

11)  Explain what happens when inertia and momentum of a set of superstrings are invariant upon the said superstrings.