Chan-Patton Rules

If something is Yau-Exact, then, it is as according to Chan-Patton rules.  Yet, not all superstrings that obey Chan-Patton rules are Yau-Exact.  A superstring works to obey Chan-Patton rules if its mapped-out path does not have any Lagrangian-based singularities. Yet, some superstrings have a lack of Lagrangian-based singularities, yet, still have metrical-based singularities -- such as plain kinetic energy.  The latter eluded to format is a case of a phenomenon that is Chan-Patton, yet, it is not Yau-Exact.  To Be Continued.
Samuel David Roach.

Some More of a Preperation For The Next Session of Course 16

Certain laws of physics work to govern the general tendency and ability of superstrings of discrete energy permittivity to vibrate  in the manner of which these happen to vibrate in.  The vibration of a superstring, when at the metrical indices in which these iterate at group instanton, is controlled by the condition of bearing either an annharmonic or a harmonic oscillation -- for one-dimensional superstrings and for two-dimensional superstrings, respectively.  All superstrings of discrete energy permittivity, at the eluded to indices of iteration of group instanton, bear at least some sort of tendency of torsion -- as is according to certain respective eigenbases -- for either one-dimensional superstrings in one general manner, and, for two-dimensional superstrings in another general manner.  Depending upon the various spatial conditions that work to govern the said respective superstrings of discrete energy permittivity, there is a certain amount of variety as to what the correlative eigenbases may be.  This would thus work to correspond to a general tendency for harmonic eigenstates for two-dimensional superstrings, and, this would thus work to correspond to a general tendency for annharmonic eigenstates for one-dimensional superstrings.  Such bases would work to correlate the eigenspace that directly corresponds to the activity of each superstring, over the course of each succeeding iteration of group instanton in which these kinematically differentiate in per correlative iteration.  The changes in Ward-Caucy denotations that work to describe the activity of the directly associated superstrings works to describe the both the harmonic oscillation of two-dimensional superstrings over the course of the eluded to iterations, and, the annharmoanic oscillation of one-dimensional superstrings over the course of the eluded to iterations. This denotation works to describe the various degrees of both the torsioning of the superstrings and the format as to how and to what degree that the here directly corresponding superstrings, bear their respective geni of having a basis of swivel-shape, along the topological contour of the said superstrings.  These various conditions that work to both form and to also describe the harmonics and the annharmonics of the respective two and one-dimensional superstrings -- at the multiplicit iterations of group instanton -- is either hermtian, when the motion of the directly corresponding superstring moves smoothly through space, or, it is Chern-Simmons, when the motion of the directly corresponding superstring bears spurs in its Lagrangian-based path -- over a sequential series of iterations.  Yet, even if the eluded to Lagrangian-based path is hermitian, if there is any annharmonics in the metric of the redelnieation of any given arbitrary superstring -- as it is being redistributed over time, then, there will be at least some Chern-Simmons singularities, when in terms of the mapping of the motion of the said superstring over the eluded to duration of time.  The directly prior condition is true, whether the superstring is two-dimensional or one-dimensional -- even though two-dimensional superstrings at iteration vibrate harmonically and one-dimensional superstrings vibrate annharmonically, during the very course of the multiplicit iterations of group instanton, taken per individual iteration of group instanton, in and of itself.  When a superstring, over a sequential series of instantons, is Yau-Exact, when in terms of both it Lagrnagian-based path being hermitian and its metical based Hamiltonian operation being hermitian, then, it is said to have obeyed Chan-Patton rules.  A superstring will always tend to be of a Noether-based flow if it is obeying Chan-Patton rules, yet, not all Noether-based superstrings obey Chan-Patton rules.  So, when a superstring becomes tachyonic, it will then digress from Chan-Patton rules.
To be continued!  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Lorentz-Four-Contractions and Orbifolds

If a given arbitrary physical phenomenon moves through either a binary or a tritiary-based Lagrangian, in the process of traveling at such a velocity to where the said physical phenomena bears a Lorentz-Four-Contraction of two for either the two spatial dimensions that are appertaining to that eluded to motion that is going through a binary Lagrangian, or, for those three spatial dimensions that are appertaining to that eluded to motion that is going through a tritiary Lagrangian, then, these two or three respective given arbitrary spatial dimensions will be the ones, of the said physical phenomenon that has here been eluded to as moving as such, that will be contracted to the scalar amplitude of two in both respective given arbitrary cases.  This is given the conditions of this bilateral given arbitrary set of cases, in which the eluded to formats of physical scenario involve one or more additional spatial dimensions than those that are here moving, in each respective case, in such a manner in so that all of those spatial dimensions that are here directly involved with the directoral pull of each individual case of the kinematic flow of the two so-stated Lagrangian spatial delineations over time will thence be contracted to the same degree of scalar amplitude.  This is because the velocity of each of the spatial dimensions that are directly associated with each of the eluded to kinematic flow geni in both respective cases are moving at the same eluded to velocity -- to where the Lorentz-Four-Contractions of each of the just eluded to parametric-based spatial dimensions that are contracted are thus contracted to a scalar factor of two.  Such a general format of motion would then here involve a typically hermitian-based format of spatial curvature -- over that duration that would here involve the Hamiltonian operation of the eluded to physical phenomenon that is moving through either a binary or in a tritiary-based basis of Lagrangian-based space, in which the said genus of both individual respective Hamiltonian operands that are crossed during the process of the transversal motion of the said physical phenomenon over time is moving in a curvature that changes in either the same number of spatial derivatives or less than the number of dimensions that it is moving in in an operand-based tense over a sequential series of instanton, to where the then here present existence of Chern-Simmons singularities is minimal -- these just mentioned geni of singularities would only exist here if there is a metrical spur in the kinematic-based harmonics of the motion of the eluded to general format of physical phenomena.  To Be Continued!  Sam Roach.

More About Orbifolds and Lorentz-Four-Contractions

Let us take into consideration a given arbitrary case of a set of orbifolds that move in one general direction, at such a velocity in which their directly associated Lorentz-Four-Contraction is of a scalar amplitude of two.  Let us say that the physical phenomenon that is here -- under this given arbitrary case scenario -- bearing a spatial range of 10 spatial dimensions plus time, over the course of that motion at which the said directly corresponding physical phenomenon works to bear a Lorentz-Four-Contraction of two.  Those superstrings that work to comprise the spatial dimension that is in the here direction of the unitary basis  in which the so eluded to physical phenomenon that is traveling here is going in, will be the superstrings that will contract to the scalar amplitude of two -- over the course of that kinematic activity that works to cause the said Lorentz-Four-Contraction that I stated in this case to be 2.  The other 9 spatial dimensions that were here eluded to -- that work to comprise that physical entity that is here to be traveling in so as to bear the so-stated Lorentz-Four-Contraction -- will only be contracted as according to the extent at which their directly affiliated physical parametric-based spatial dimensionality is moving st as a velocity, that is, in conisderation of the condition as to the velocity of each of the other spatial dimensions, when taking at a unitary basis for each of such eluded to respective dimensions taken individually.  So, the Lorentz-Four-Contraction of the so eluded to spatial dimension that is being contracted is contracted as such in this case, at both the level that is Poincaire to the so-stated superstrings, as well as at the level that is Poincaire to the so-stated orbifolds.  I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

Lorentz-Four-Contractions And Orbifolds

Let us here consider a given arbitrary orbifold -- a given arbitrary set of superstrings that operate in so as to perform a specific function.  The orbifold will here be Lorentz-Four-Contracted to a scalar amplitude of 2, in this given arbitrary example.  Each of the superstrings that would here work to comprise the so-stated orbifold will then be de-compactified to the degree of being completely not Lorentz-Four-Contracted by a factor of 1.5*10^8, in this specifid given arbitrary example.  Each of the superstrings that would then here work to comprise the said orbifold -- over the course of the eluded to de-compactification -- will be "stretched-out" during the directly corresponding Polyakov Action eigenstate, that is here directly affiliated with that iteration of group instanton that is directly associated with the so-stated Lorentz-Four-Contraction that happens to the scalar factor of two, by a factor of 1.5*10^8.  As the so eluded to Polyakov Action eigenstate is operating in so as to perform its function in this case, each superstring that works to comprise the said orbifold will be de-compactified in so as to maintain both its general Lagrangian-based proportionality, and, its directly affiliated core-field proportionality, as it had right before the so stated activity of the so eluded to Polyakov Action eigenstate that is correlative in this case.  So, depending upon the spatial arrangement of those superstrings that are delineated as these are -- from within the said given arbitrary orbifold upon the onset of the directly associated iteration of group instanton, the perturbation of the shape of the orbifold that is due to the so eluded to Lorentz-Four-Contraction will vary.  This will also vary, depending upon whether the superstrings involved here are one-dimensional or two-dimensional.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

An Aside About The Lorentz-Four Contraction Behavior of Superstrings

As any given arbitrary superstring that bears a given arbitrary degree of both a partitional-based and a swivel-based genus of perturbation during the course of any specific given arbitrary conditionality of a Lorentz-Four-Contraction -- that is worked upon the just eluded to format of superstring -- is undergoing both its Polyakov Action eigenstate and its Bette Action eigenstate simultaneously through a central conipoint over the course of a specific directly associated iteration of group instanton that directly relates to this, the directly associated de-compactification that acts as the inverse operation of what is to be deemed of as what here is to directly correspond to the directly affiliated Lorentz-Four-Contraction, that is then here happening to the so-stated directly corresponding superstring, will be formated as a Clifford Expansion that is applied to the said superstring -- between the first-ordered point particles that work to form the so-stated superstring of discrete energy permittivity -- in such a manner in so that the eluded to de-compactification that is to the inverse scalar amplitude to the said Lorentz-Four-Contraction, that acts in so as to apply the so-stated "contraction", will "stretch" the correlative superstring in such a manner in so that the whole general shape of the given superstring will be maintained in both its Lagrangian-based mappable proportionality, and, in so that the format of the mappable tracing of the "partitions" that work to comprise the here given arbitrary superstring will have a maintained proportionality -- when in terms of the general format of the shape that the said superstring would have, even if it were not de-compactifiied.  This is in terms of the given arbitrary dimensionality of what the eluded to superstring were to bear.  So, if the given arbitrary superstring was one-dimensional, then, as it is de-compactified in so as to bear its eluded to Lorentz-Four-Contraction, both its swivel-shape-based basis and both its general dimensional format and its core-based field dimensionality, including its directly based field genus, will be maintained in proportionality during its directly corresponding Polyakov-Action eigenstate.  So, as a given arbitrary two-dimensional superstring that is undergoing the same general format of de-compactification will be directed,  this will happen in so as to maintain both its Lagrangian-based proportionality and its core-field-based proportionaity, over the course of its directly associated Polyakov-Action eigenstate.  So, what we view of as a "contraction" is actually an extrapolation of what is here a de-compactification that is generally at a minimum for photons in a vacuum.  So, when there is a relative minimum Lorentz-Four-Contraction, the eluded to de-compactification is at more of a maximum.  To Be Continued. Sam Roach.

A Little Tid Bit About Course 16

Both one and two-dimensional superstrings of discrete energy permittivity are vibrating thread-like phenomena that oscillate in one general manner in so as to operate as one given arbitrary genus of a Hamiltonian-based function, and these oscillate in another general manner in so as to operate as another given arbitrary genus of a Hamiltonian-based function, etc... .  So, this is true of both vibrating strands of discrete energy, and, also for vibrating hoops of discrete energy.  As I have so stated before, superstrings generally move kinematically in a tendancy of Noether-based flow over time.  The closer that a superstring is to moving in the direction of and/or becoming of a tachyonic-based nature -- in which such a directly associated superstring will then act in less of a manner that would otherwise be more similar to a Noether-based flow -- then, the scalar amplitude of the degree of the perturbation of the topological homotopic substrate that works to act as that disturbance that acts as the just eluded to general condition of superstring, will be of a more swivel-based fluctuation -- along the variation of the parameters that would here appertain to the here intrinsic spatial delineation of the topological sway of the so-stated superstring that would here be of a more perturbative topological-based vibrational oscillation.  This is since the condition of a tachyonic superstring is a significant perturbative-based tense that devolves from the general condition of a Noether-based flow.  This would then mean that, as any given arbitrary superstring is altered in so as to work to become of a tachyonic-based flow, then, the relative degree of the then inherent perturbation in the condition of the directly associated superstring, as being a relatively place-wise disturbance in space -- that is re-delineated per the sequential series of the iterations of group instanton, that integrate in so as to form the flow of multiplicit motion that works to form the general entity of energy -- will be of a hightened scalar amplitude.  Logically speaking on the otherhand, as an initially tachyonic superstring works to become of a more Noether-based flow over time, the relative degree of the scalar amplitude of the perturbation of the vibrational oscillation of the relative disturbance that works to form the just eluded to superstring will be lowered to a more conformally invariant manner, over the just eluded to duration of group metric that directly relates to the said general manner of activity.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Second Aside as a Prelude to the Ensuing Session of Course 16

Both one and two-dimensional superstrings of discrete energy permittivity exist as basically respective vibrating strands and vibrating hoops -- as a general concept.  One dimensional superstrings are tiny vibrating strands of energy quanta, and, two-dimensional superstrings are tiny vibrating hoops of energy quanta.  Superstrings are generally phenomena of discrete energy that act as closed-loops.  Superstrings that are generally thought of as closed-loops are generally either heterotic superstrings, or, these are often two-dimensional superstrings of discrete energy permittivity (the latter as an ansantz).  With the way things actually happen in the substringular, one-dimensional superstrings are generally vibrating annharmonically during the course of their iterating at each index of the sequential series of group instanton.  Such a genus of vibrational format works to distinguish such oscillating open strands -- that may be thought of generally as one-dimensional superstrings -- as a perturbative linear-based curve that is unsettled along its topological surface -- at the Poincaire level, when one works to map-out the homotopic substrate of such a discrete physical phenomenon at a closed region that is Gliossi to the Hamiltonian operation of the disturbance of the kinematic-based space, that works to function as the just mentioned open-strand, or one-dimensional superstring of discrete energy permittivity.  Also, closed-loops that work to act as two-dimensional superstrings of discrete energy permittivity tend to vibrate in an oscillatory manner that is generally of a harmonic manner over each idex of the sequential series of discrete moments that act as the metrical duration of the genus of group metrics that are known of as the iterations of group instanton.  Such a basis of an oscillatory-based format of a vibrational genus is a disturbance of a kinematic-based space, that may be mapped-out as a perturbation of the multiplicit set of closed-space regions where two-dimensional superstrings are delineated per said iteration, which acts as a topological trace that is homotopic at each eluded to directly associated topological increment of Hamiltonian operation, of such vibrating hoop-like phenomena -- at the respective multiplicit Poincaire-based level.  This eluded to tracing is along the general regional-basis that is Gliossi to the eluded to mapping-out of such superstrings.  The directly prior condition happens in such a manner in so that this works to distinguish such a discrete phenomena of vibration as being of a perturbative hoop-like phenomena that operates in so as to vary in their spatial parameters over the course of the eluded to general basis of a harmonic genus of oscillatory vibration.

The Second Part of the Aside To Course 16 From Earlier

Harmonic oscillation of a Yau-Exact genus of a Real-based cohomology in world-sheets varies in hermitian eigenstates, per both substringular metric and per iteration.  Such a format of a harmonic oscillation works to obey the conditions of a Chan-Patton basis of factors, that correlate to the operational genus of those given arbitrary superstrings -- that operate in both a Lagrangian and in a metrical manner that is Yau-Exact in function.  This is the case, whether the directly associated world-sheets that work to form the eluded to ghost anomalies in question are created by a one-dimensional superstring of discrete energy permttivity, or, if the eluded to ghost anomalies in question are created by a two-dimensinonal sueprstring of discrete energy permittivity.  So, any given arbitrary Yau-Exact genus of a Real-based cohomology is going to differentiate both in a Lagrangian manner and in a metrical manner that is purely hermitian -- when in terms of the its directly corresponding harmonic oscillation -- if the eluded to cohomology -- that the eluded to mapping-out of the directly associated ghost anomalies, is of a Rham-based nature.  Yet, if a cohomological tense of a ghost anomaly-based distribution is configured, instead, in a Doubolt-based nature, then, the just eluded to tense of a ghost anomaly-based distribution will tend to at least bear some format and/or genus of a Chern-Simmons-based ghost anomaly-based pattern, that is therefore not Yau-Exact in nature over its delineation-based index over time.  This is always true if the cohomology  that I am here describing is kept as a Real-based cohomology, yet, if one is instead discussing a cohomology that is veered from being an initially considered Real-based cohomology into a Njenhuis-based cohomology -- that would here then bear no given arbitrary Chern-Simmons-based singulaties -- over that metrical and/or Lagrangian set of conditions that work to describe the delineatory indices of an attributed given arbitrary superstring or set of superstrings that are pulled off of the here relatively Real Reimmanian plane, over a sequential series of iterations of group instantaon that may be used to describe the correlative alteration in the directoral pull of the just eluded to motion of the directly associated general substringular format of kinematic flow, then, what may here be being described may here be a cohomological pattern that is kept Yau-Exact, yet, will here convert from being a Real-based cohomology into being a Njenhuis-based cohomology  (that is then of a Doubolt nature instead of a Rham nature). The genus of what I just described as the exception to the just prior mentioned general format, is what the case often is when one has an antiholomorphic Kaeler Metric that is inculcated from within the general spatial premises of a regional substringular locus.  The genus of the operation of the hermitian differential flow that would then here exist -- in the just eluded to general locus -- is a cohomological set of topological-based sways that works to obey a Li Algebra-based Yau-Exact harmonic oscillation, that is pulled off of the relative Real Reimmanian plane with both no Lagrangian-based nor metrical-based spikes or spurs of delineatory singularities -- at the here relevant Poincaire level.  Such a genus of a Yau-Exact-based kinematic motion of superstrings will tend to bear at least some sort of linear format of delineatory perturbation of sway from one locus of consideration where a given arbitrary substrigular flow is existent at at one iteration of group instanton, to the next locus of consideration as to where the said given arbitrary substringular flow is existent at at the next iteration of group instanton.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

The First Part of an Aside to Course 16

When a superstring reiterates through a trajectory, the given superstring that was just mentioned works to form a ghost anomaly -- that acts as the physical memory of the just eluded to world-sheet.  (A world-sheet is a discrete trajectory of a superstring.)  When either a one-dimensional superstring of discrete energy permittivity, or, when a two-dimensional superstring of discrete energy permittivity, forms a world-sheet -- there is often an annulus formed from within the Ward-Neumman bounds of the ghost anomaly that acts as the physical memory of the just eluded to world-sheet.  At the substringular level, the just mentioned genus of annulus is here an oriface or "hole" where there are no first-ordered point particles present -- at any given arbitrary iteration of group instanton, that works to directly correspond to the said condition of there being an annulus -- from within the Ward-Neumman bounds of the Hamiltonian operand of the projection of the trajectory of any given arbitrary superstring of discrete energy permittivity -- that would work to form such a said annulus over the course of the kinematic activity of such a given arbitrary superstring.  An annulus here is an empty projection that works to bear no first-ordered point particles that would otherwise contain such eluded to first-ordered point particles.  World-Sheet projection that bears both a Lagrangian-based smoothness and a metrical-based smoothness over time is said to bear a Yau-Exact genus of Real cohomology.  A Yau-Exact genus of Real cohomology does not in and of itself bear any directly corresponding Chern-Simmons singularities, when considering this from within the premises of its Ward-Neumman bounds, from within either the Lagrangian-based and/or from within the metrical-based kinematic orientation that works to directly affiliate with any given arbitrary ghost anomaly, of which corresponds to the trajectory of the motion of the corresponding superstrings of discrete energy permittivity that may be considered here as forming the eluded to projection over time.  A Yau-Exact genus of a Real cohomology tends to kinematically differentiate within the Ward-Caucy bounds, over time, in such a manner that bears a harmonic oscillation during the directly corresponding sequential series of iterations of group instanton -- in which the correlative superstrings of discrete energy permittivity that I have here eluded to are differentially associating as having the said Yau-Exact condition of a Real-based cohomology.  The directly associated Fadeev-Popov-Trace eigenstates that would here thus correlate to the said superstrings of discrete energy permittivity -- of which act as the corresponding discrete units of energy impedance -- would thus act accordingly as physical phenomena that bear a Yau-Exact genus of Real cohomology.  The difference in operational function that exists between a discrete unit of energy permittivity and a discrete unit of energy impedance is that the respective superstrings work to pull the discrete energy in the general manner of the relative holomorphic directoral topological-based sway, while the respective Fadeev-Popov-Trace eigenstates work to hold the discrete energy, in a homotopic manner,  back enough to keep the said energy from resonating.   Superstrings act as discrete units ofenergy permittivity, while, Fadeev-Popov-Trace eigenstates act as discrete units of energy impedance.  I will continue with the suspense later! Sam Roach.

Part Three of the Ninth Session of Course 16

Let us say that a specific superstring or a specific set of superstrings is undergoing tachyonic propulsion over a given arbitrary group metric.  Let us say that the said superstring or the said set of superstrings that is here not undergoing Noether Flow under this given arbitrary instant under consideration is going through a Kaeler Metric.  Each succeeding step that would here be directly associated with the individual group instantons in which the said superstring or set of superstrings is progressing over the course of a Kaeler Metric eigenstate happens to where this will then be held at a different specific cite of Gaussian-based Metric -- while yet each of such succeeding steps will involve the same level or genus of added fractal of discrete energy permttivity for the given superstring or set of superstring to work to re-attain there substringular "drive", in so as to progress at being replenished of having the needed added of such a fractal of discrete energy permttivity -- when in terms of what the directly associated superstrings need to gain back in the physical "effort" to remain as discrete units of energy permittiity.  In the meanwhile, the directly correlative Fadeev-Popov-Trace eigenstates that are immediately eigen to the so eluded to superstrings will consequently, over the same general group metric, work to re-attain the corresponding fractals of discrete energy impedance that these need in order to work at being reastablished as being discrete units of energy impedance.  For every superstring or set of superstrings that are tachyonic over the course of a directly corresponding multiplicit Kaeler Metric eigenstate, there is another superstring or another set of superstrings that are also tachyonic over the course of another eigenstate of Kaeler Metric, that is happening simultaneously through the vantage point of a central conipoint.  So, there always tends to be an even number of discrete substringular phenomena that are undergoing tachyonic propulsion over the eluded to added conditionality of going through a multiplicit eigenstate of Kaeler Metric.  This works to form a broader general region in which an eluded to multiplicit Kaeler Metric eigenstate is underway for tachyonic superstrings, that are going through such a progression of Gaussian Transformation. Such a general region is often not configured to a set establishment of a relatively limited region -- depending upon the degree of perturbation in the said tachyonic propulsion.  So, any given arbitrary superstring or set of superstrings always tends to be encoded to be able to proceed through the needed steps of Kaeler Metric eigenstate -- in so as to receive a logical ordering of re-attaining the right sequential series of discrete fractal increments of energy permittivity, so that the eluded to substringular phenomena may evenly be replenished -- in terms of being reinstated as fully "fueled" discrete energy permttivity. Likewise, the directly associated Fadeev-Popov-Trace eigenstates move along with their correlative superstrings in a similar kinematic basis of encodement, so that these will evenly be able to progress as well at re-attaining the right fractals of discrete energy impedance, in so as to be replenished as being discrete units of energy impedance.  I will continue with the suspense later!
Sincerely, Sam Roach.

The Second Part of the Ninth Session of Course 16

If a given arbitrary superstring, or, if a given arbitrary set of superstrings, goes through tachyonic propulsion, the directly corresponding Gaussian conditions of the so-stated superstrings or set of superstrings is temporarily altered.  This said temporary alteration works to form a perturbation in the norm-conditions that would here be directly corresponding to the kinematic differential geometry of the so-stated superstrings, or, set of superstrings, that is here relevant to this specific general case scenario.  The just mentioned format of perturbation will then happen between the just eluded to superstring or set of superstrings and the directly correlative orbifold eigenset that the given substringular members that I had initially implied as existing in this case are involved with, in a Gliossi manner at the Poincaire level. The relative instance that such a genus of perturbation is happening in may be termed of as a spurious moment of group-associated metrical activity. All substringular perturbations may be thought of as bearing a condition of a spurious-based tensoric basis, in one manner or another -- when relative to the immediate surroundings of any given arbitrary kinematic-based differentiating orbifold or orbifold eigenset that is Gliossi to the spatial environment that any given arbitrary superstring or set of superstrings is acting upon.  As such a given arbitrary superstring or set of superstrings works to reach any given arbitrary destination that is Real Reimmanian when relative to the Poincaire level of the directly corresponding orbifold or orbifold eigenset, that bears a specific functional operation -- in terms of what the given arbitrary Hamiltonian operation is here prone to act as in this given arbitrary eluded to case, the Gaussian conditions that would here directly correspond to the affiliated given arbitrary change in local norm-based conditions of the so-eluded to superstring or set of superstrings will tend to conform to what may be described of as the most at rest kinematic differential-based geometric case scenario.  What this entails is that, if the orbifold or orbifold eigenset that has here altered in its Ward-Caucy conditions in so as to conform to what was here an eluded to Gaussian Transformation that was needed in order for their to be a fluency in the spatial re-delineation of the given arbitrary spatial Hamiltonian operand, that is Gliossi to the local metrical activity of the directly associated superstring or superstrings, then, the genus of the kinetic differential geometry of the said orbifold or orbifold eigenstate will be brought into a metrical condition that works to involve less stress upon the topological framework of the affiliated group of substringular phenomena.  This general format of activity tends to bring any given arbitrary condition of tachyonic propulsion back into a tense of Noether Flow, after what would here be a relatively transient duration.  This is due to the condition that tachyonic flow tends to bear more of a stress-based modulus upon any given arbitrary set of one or more superstrings that is at the Poincaire level to the so-eluded to tachyonic-based activity. The prior stated tense of tachyonic propulsion works to involve more of an annharmonic vibration of the directly affiliated group of superstrings, which would then form at least some sort of perturbation in the basis of the directly affiliated amplitude of the wave-tug of the here respective light-cone-gauge eigenstates.  I will continue with the suspense later!  Sincerely, Sam Roach.

Part One of the Ninth Session of Course 16

Strings and world-sheets tend to vibrate with some form or another of either a harmonic or an annharmonic oscillation.  Superstrings and world-sheets tend to obey the Ward-Caucy conditions that appertain to the basis of what are known of as Chan-Patton factors.  What I more specifically mean by "world-sheets" are the ghost anomalies that form as the physical memory of superstrings, as enacted by the mapping-out of the trajectory of the projection of the directly corresponding superstrings.  There are certain conditions that work to cause certain superstrings -- along with the physical mappings of their world-sheets -- to occasionally "disobey" the directly affiliated Ward-Caucy conditions of the corresponding Chan Patton factors.  For one thing, let's consider a condition that may occasionally happen in the substringular -- of which is the condition of tachyonic flow or tachyonic propulsion.  The ability of superstrings to be able to move out of a state of Noether Flow is an exception to the general tendency of the conditionality of Chan Patton factors.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

The Fourth Part of the Eighth Session of Course 16

When substringular phenomena work to rebound -- from a relatively forward-holomorphic directoral topological sway of a group of one or more respective given arbitrary superstrings, into a relatively reverse-holomorphic directoral topological sway of a group of one or more respective given arbitrary superstrings -- these superstrings are then undergoing an antiholomorphic Kaeler Condition that may then here be considered to directly afterward cause the activation of a Wick Action eigenstate, that is utilized to form the activity of a directly ensuing Gaussian Transformation.  The activity of that group metrical-based activity of a Gaussian Metric that directly involves the motion of a group of one or more superstrings that are shook in a Klein Bottle eigenstate, over a series of 191 consecutive general metrics of such an eluded to activity of substringular shaking, in so as to allow for the said directly associated superstrings to re-attain that fractal of discrete energy that these need, in order for the just eluded to substringular phenomena to continue to exist as quanta of discrete energy.  So, in a very real tense, the substringular activity of the rebounding of superstrings tends to indicate the relatively ensuing activity of a Kaeler Metric eigenstate.  Calabi Metric eigenstates are specific cases of Kaeler Metric eigenstates, in which the directly corresponding superstrings that are Gliossi in a metrical manner to the needed reactivation of their discrete energy, happens in such a manner in which the directly corresponding photons are scattered in so as to form the needed quanta of discrete entropy, so that the needed entropic photons may exist, in order for their to be the ability of changes in physical state to occur.  So, Calabi Metric eigenstates are more involved with the scattering of those ghost anomalies that are directly associated with those cohomologies that are appertaining to the interaction of electromagnetic energy with any given arbitrary set phenomena that any given arbitrary set quanta of discrete electromagnetic energy may be directly striking, in a Gliossi manner at the Poincaire level of the just eluded to substringular level.  In any case, the "bouncing" and the rebounding of superstrings that occurs in any given arbitrary case is associated -- in one form or another -- to one form or another of a Kaeler Metric eigenstate.  Such "bouncing" or rebounding of superstrings that directly involves such a format of an antiholomorphic Kaeler condition that involves discrete units of electromagnetic energy (photons) is a specific case of the Kaeler Metric that is known of as a Calabi Metric eigenstate.  Calabi Metric eigenstates bear their chief importance, when in terms of that scattering of ghost-based anomalies that is needed in order to both replenish room for superstrings to have an arena of kinematic activity, as well as in order for there to be a tense of physical residue that is needed in order for those dilatons and dilatinos to be able to be formed so that both gravitons and gravitinos may be formed (so that gravity may have a kinematic-based substrate to be enacted so that gravity may continue to exist). Again, gravity is needed in order for physical phenomena to be able to bear some adjaent amplitude, so that superstrings may bear the general condition of bearing some significant effect upon each other.  Such a revamping of the substringular environment, that is needed in order for superstrings to continue to kinematically codifferentiate -- is the general source of the prevention of black-holes.  The motion of neutrinos is often a key to allowing for an efficient production of entropy that is not obtrusive, in so that the directly affiliated photons may form entropy that is condusive to a bearing less of a potential for the fraying of superstrings.  I will continue with the ninth session later!  Sincerely, Sam Roach.

Part Three of the Eighth Session that is of Course 16

I will here first elaborate upon the operational activity of the Kaeler Metric.  World-Sheets are the trajectory of superstrings.  The kinematic differenatiation of superstrings forms a physical memory as to both the existence and the motion of the directly corresponding superstrings in the form of ghost anomalies.  Ghost anomalies work to inter-connect in so as to form cohomologies.  Cohomologies are the Gliossi import as to the interaction of that multiplicit physical memory of superstrings that works to form the covariant-based codifferentiation of the core field-density of superstrings -- in so as to help at inter-facing the Hamiltonian operational functions of the here directly corresponding given arbitrary superstrings that act in so as to form a basis of the energy that forms the multiverse.  When any given arbitrary physical phenomenon bounces or rebounds -- at a Poincaire-based framework that is equal to or greater than the interactivity of superstrings of discrete energy -- superstrings go from proceeding in one given arbitrary directoral wave-tug/wave-pull topological sway import to going toward a different given arbitrary directoral wave-tug/wave-pull topological sway import.  This just mentioned condition of varied directoral import of topological sway is a condition of the perturbation of the given arbitrary format of the holomorphicity of the directly corresponding superstrings -- that are involved with any of such varied alterations in the topological-based directoral Hamiltonian operation of such a physically-based scenario, that is to happen in the substringular.  As any given arbitrary physical phenomena that are of a substringular nature are initially traveling as a steady-state through a discrete Lagrangian in a given format of directoral import, the so-eluded to phenomena are then said to be traveling in what may be termed of as an arbitrary framework of a given arbitrary holomorophic direction.  The so-stated phenomena that are here to be considered as going in a given arbitrary holomorphic direction are considered to be a holonome that is acting through a physical substrate.  What this means, is that the so-stated physical phenomena -- that here act as a group that consist of a multiplicit quantized  phenomenon -- are a physical state that acts as a Hamiltonian operator that is, at least in part, acting upon the then eluded to Hamiltonian operand, as a functional group attractor that works upon the immediate environment that is in the Lagrangian-based path of the motion of the so-stated multiplicit phenomenon.  When the so-stated multiplicit phenomenon that I have just here mentioned rebounds or bounces upon the substrate that it is acting upon, there is, at least in part, a certain degree of what may be termed of as an antiholomorphic directoral wave-tug/wave-pull that is enacted upon the general region that is Gliossi to the environment that is at the Poincaire level of the motion of the so-stated multiplicit substringular phenomenon that had just "bounced" or rebounded as I have said.  The condition of the bouncing or rebounding of photons upon whatever these scatter upon eludes to the very transient Kaluza-Klein tense of these so-stated photons -- for only the first 384 instantons that occur immediately upon these photons striking anything that these hit.  This is an elaboration of a genus of the Kaeler Metric that is known of as the Calabi Metric.  I will continue with the suspense later!  Again, as an ansantz, photons are always of a Yang-Mills light-cone-gauge topology in a vacuum.  To Be Continued!  Sincerely, Sam Roach.

Part Two of the Eighth Session of Course 16

I will now discuss two of the formats of metric-based duration that are common in the substringular.  These two general geni of metric-based duration are Real Reimmanian-based metrics that are very important metrics that happen over their respective sequential series of iterations of group instanton.  The two individual formats of the respective group metrics that I am about to discuss are the Kaeler Metric and the Calabi Metric.  Every Calabi Metric is an example of a Kaeler Metric, yet, not every Calabi Metric is an example of a Kaeler Metric.  A Kaeler Metric is a group metric that involves the motion of the Klein Bottle -- as it is moving through a relatively unitary-based Lagrangian-based Real Reimmanian Plane, in which the main activity of the here directly corresponding Gaussian Metric is occurring.  During this so-stated Kaeler Metric, the composition of the eluded to Schotky Construction is moving along a Mikowski surface -- in which the so eluded to Klein Bottle eigenstate is in such a position to where the directly correlative superstrings that here need to gain a set quantum fractal of discrete energy permittivity are shook in the said Klein Bottle eigenstate, in such a manner in so that such superstrings of discrete energy permittivity may then remain as such.  Simultaneously -- through a central conipoint -- the directly corresponding Fadeev-Popov-Trace eigenstates that are directly attached to the so-eluded to superstrings of discrete energy are shook as well, in so that the so-stated Fadeev-Popov-Trace eigenstates may re-attain their set quantum of fractal of discrete energy impedance, so that the said Fadeev-Popov-Trace eigenstates may remain as discrete units of energy impedance.  This so mentioned Kaeler Metric happens over a metrical duration of 191 iterations of group instanton (of the 384 of its directly corresponding Gaussian Metric (not 382, because of the needed spatial re-adjustment)), as I will describe more in course 24 -- which is about conformal and superconformal invariance.  Each time that a dual unit of discrete energy permittivity that is inextricably bound to discrete energy impedance is shook back-and-forth eight times in the directly corresponding Klein Bottle eigenstate per iteration of group instanton, the directly corresponding discrete energy re-attains one of the 191 quantum units of fractal of discrete energy permittivity and one of the 191 quantum units of fractal of discrete energy impedance that are needed, in the process of re-attaining the need of both superstrings to gradually re-attain the 191 discrete fractal units of both the respective energy permittivity and the respective energy impedance that are needed in order for both superstrings to respectively bear full energy permittivity, and, in order for their directly corresponding Fadeev-Popov-Trace eigenstates to bear full energy impedance.  After the 191 iterations of group instanton that are involved in one eigenstate of any given arbitrary activity of Kaeler Metric that is Gliossi to the "reactivation" of both superstrings and their directly corresponding Fadeev-Popov-Trace eigenstates, then, the so-stated superstrings will then bear full energy permittivity, and, the so-stated Fadeev-Popov-Trace eigenstates will then bear full energy impedance.  The so-stated shaking activity of the Klein Bottle happens, per each segment of an eigenstate of Kaeler Metirc, at the end of each respective iteration of group instanton, after an individual metric of BRST while yet near the starting duration of the ensuing generally unnoticed portion of Ultimon Flow.  So, if a superstring and its directly corresponding Fadeev-Popov-Trace eigenstate is to undergo a Kaeler Metric, right after the correlative iteration of BRST -- while yet right before the correlative Regge Action eigenstate, the said superstring and its directly corresponding Fadeev-Popov-Trace eigenstate are pulled into their correlative Klein Bottle eigenstate and shook back-and-forth eight times (16 overall eluded to topological-based sways) in the eluded to composition of Schotky Construction, in order to bring the eluded to substringular phenomena that are to re-attain set quantum fractal of discrete energy into such a condition.  So, after the eluded to 191 iterations of group instanton that are of any given arbitrary Kaeler Metric eigenstate, the directly correpsonding superstring and its correlatvie Fadeev-Popov-Trace eigenstate are re-conditioned to be of full capability as discrete energy.  A Calabi Metric is a Kaeler Metric that is appertaining to superstrings that are photons that were just scattered by any given arbitrary phenomena that these have just struck.   So, Calabi Metrics are Kaeler Metrics that directly involve the production of entropy.  I will get more into what Calabi Metrics are in course 20.  I will continue with the suspense later!
Sincerely,
Samuel David Roach.

Part One of the Eighth Session of Course 16

There are different types of periods within time that are essential for the existence of space and time.  What this means is that there are countless gauge-metrics -- both individual motions of eignestates of holonomic substrate of metric-gauge, as well as group metrics that integrate duration-wise, in so as to act within a discrete unit of time -- that occur within any given arbitrary individual duration of group instanton.  The course of group instanton -- which is mainly comprised of eigenstates of BRST -- is the general format of a discrete unit of time.  This is because we are only able to directly detect any given arbitrary motion in equal to or more than one integer-based multiple of group instanton.  Group instanton is the multiplicit-based integration of the condition of instanton, that is applicable to the reiterative basis of the delineatory and redelineation of substringular phenomena -- as this so-stated phenomena is fretted from one established framework of covariant, codiffereniable, and codeterminable distribution eigenbasis, that goes from one spot and one cohesive differentation -- toward the ensuing sequential series of distribution eigenbasis.  This is an eigenbasis that here appertains to the kinematic format of motion of the directly corresponding substringular discrete phenomena.  Such phenomena are thence pulled into those kinematic inter-relations that work to form the condition of both perpetual and sustainable energy in the multiverse.  It is the motion of the inter-relationship of the mutivarious and multiplicit substringular phenomena -- that occurs during the generally unnoticed iterations of Ultimon Flow -- that are not bound in a static-based framework, that works to help determine the directly corresponding covariance of the multiplicit delineatory bases of superstrings as a whole.  Such bases operate as an integrative set of Hodge-based Hamiltonian tensoric eigenstate of kinematic Gaussian spaces, that more directly work to control the perturbation of the general index of the Majorana-Weyl-Covariance of space-time-fabric -- in so as to allow for the existent flow of the general pattern of kinematic change, that works to allow for the continued multiplicit motion that is essential in order for energy to continue to exist.

The Last Part of the Seventh Session of Course 16

Both Yang-Mills light-cone-gauge topology and Kaluza-Klein light-cone-gauge topology work to involve mini-string segments -- or, in other words, substringular field-density eigenstates -- that work to connect and reconnect superstrings and other substringular phenomena that are homotopic in nature, to one another, per each successive series of the iterations of group instanton.  Such a general basis of activity also works to both connect and reconnect the multivarious and the multiplicit homotopic cohomological indices, in the form of the homotopic recycling of ghost-based indices, over the same general successive series of iterations of group instanton.  An exception to the just eluded to conditionality of Cassimer Invariance is the fraying of substringular phenomena, that involves both the existence and the kinematic differetiation of black-holes.  The just stated existence and kinematic differentiation of black-holes is not necessarily permanent -- such fraying-based activity may often be temporary.  I will continue with the next session later! Sincerely, Sam Roach.