Order Out Of Chaos

Just as an instanton is 10^(-43)rd of a second, the fraction of instanton in which a superstring of discrete energy permittivity is ordered -- right before the Polyakov Action -- is 1/10^(-43)rd of instanton.
The fraction of instanton in which the Polyakov Action does its initial task of working to stretch the perceived length of a superstring of discrete energy permittivity to the inverse of the degree of its Lorentz-Four-Contraction is ~6.005846973*10^(-8)th of any given arbitrary instanton.
Here's where I came up with the directly prior indicated fraction of instanton.:
Take 1/150,000th of instanton (150,000 is the number of layers of reality that are potentially unfrayed in each respective universe) minus the inverse of the number of overall layers of reality that are in each respective universe (1/159,000), initially.
Now, multiply this fraction by 1/2pi.  (The fraction of Planck Time that is  Planck Bar Time.)
This is the fraction of instanton that it takes for superstrings to stretch to the inverse of their apparent contraction.

For the remainder of the BRST portion of instanton, the Polyakov Action eigenstates cause the first-ordered point particles that work to comprise the directly related superstrings to vibrate in a manner that is more ordered than outside of BRST, yet, less ordered than the condition that the said superstrings are in at the initial 10^(-43)rd of instanton that happens right before the Polyakov Action takes a hold of the directly related superstrings.

The Polyakov Action takes a hold of superstrings at the points in gauge-metric when the fractal modulus that relates to the interaction that exists between a superstring and its couterstring begins the kinematic portion of what I terms of as the Imaginary Exchange of Real Residue.

I am calling them as I see them.  I may not be perfect, (perfection is a fallacy), yet, I am describing things in a manner that has to be at least close.  I am not trying to pull a fast one on anyone.

Sincerely,
Sam Roach

Substringular Pressurized Vacuum

During the metric in which the space-hole happens -- which is during the metric in which the Bases of Light is going on -- mini-string that exists in-between superstrings and their counterstrings begins to unfray, due to the fractal stress that happens between the mini-Popov-traces that majorize in the eluded to Bases of Light and the setting of the superstrings that exist near their counterparts, in the manner that this happens right before the instanton-quaternionic-field-impulse-mode.  Just as such unfraying begins to happen, the surrounding stress -- that may be accounted for by a residual fractal of pressurized vacuum applying its wave-tug/wave-pull -- works upon the said superstringular-like phenomena and their corresponding counterstrings.  This stress -- that is due to the ultimate fractal of pressurized vacuum that is applied to the here present "attempt" of unfraying -- works to snap superstrings back into an array with their corresponding counterstrings, in so that substringular phenomena will not actually be frayed. Right after the directly prior condition, the instanton-quaternionic-field-impulse-mode works to re-relate the mini-Popov-traces with their corresponding superstrings and counterstrings -- which also works to encode where and how the just mentioned substringular phenomena is to be redelineated at and how over the course of the next iteration of group instanton.  To be continued!  Sincerely, Sam Roach.

A Basic Example of a Clifford Expansion

Often, a kinematic-based Clifford Expansion happens in a euler manner -- such as is the basic situation with the topology of light-cone-gauge eigenstates that are fed mini-string segments at the general topological cite of a superstring during a Polyakov Action eigenmetric, over the general course of BRST. This is when a superstring expands its basic Ward Caucy bounds to the inverse of its manner and degree of Lorentz-Four-Contraction. Please read some of my other writings as to the topic of Fock Space, Gravity, and the Light-Cone-Gauge. This may work to answer many of your questions as to some of the correspondences that inter-relate a general format of euler expansion to the relative covariance of certain topological cites. Sam Roach.

Smaller Than The Planck-Length

In order for superstrings to exist, these are comprised of first-ordered point particles that approximate a hoop or a strand -- for two and one-dimensional superstrings, respectively. In order for first-ordered point particles to exist, these particles must be comprised of mini-string that weaves into a "ball" of substringular "yarn." First-Ordered point particles also work to comprise the basis of norm-states and point commutators. The fields that work to inter-bind superstrings are comprised of mini-string segments. In order for mini-string segments to exist, these must be comprised of beads of second-ordered point particles. Second-Ordered point particles only exist where there is mini-string. In order for there to be second-ordered point particles, there must be third-ordered point particles that work to comprise the said second-ordered point particles. In order for third-ordered point particles to exist, there must be sub-mini-string that not only works to comprise the said third-ordered point particles, yet, the said sub-mini-string also works to link the second-ordered point particles in such a manner in so that the just mentioned particles may array into the said "bead-like" phenomena that I mentioned as mini-string. Sub-Mini-String -- that works to indirectly form the mini-string, of which is basically beaded second-ordered point particles -- is the ultimate fractal of pressurized vacuum. So, just as mini-string is two levels of the substringular lower in general size than superstrings, the said sub-mini-string is two levels of the substringular lower in general size than second-ordered point particles. So, beaded second-ordered point particles form substringular fields, and, sub-mini-string inter-binds the said "beads" while yet also working to comprise the mentioned third-ordered point particles that happen to work to comprise the said second-ordered point particles. Since the sub-mini-string is what links the "beads" that work to form substringular fields, the said sub-mini-string is that completed fractal of pressurized vacuum that acts as the smallest level of physical phenomenon that acts as more than a placeholder. I will continue with the suspense later! Sincerely, Sam Roach.

When Superstrings Are Basically Flush, Ideally

Superstrings of discrete energy permittivity are in the earlier mentioned relatively flush condition -- besides the partitions that I had discussed -- at the very beginning of BRST, right after the instanton-quaternioinic-field-impulse-mode.  Just after the said superstrings of discrete energy permittivity in space-time-fabric have completed the directly prior said mode that works to delineate these to the positioning of their next iteration of group instanton, the mentinioned superstrings very transiently organize in a relatively flush manner, when not including their discrepencies that I word of as partitions.  Immediately ensuing such an organization, the superstriings of discrete energy permttitivty that I here have eluded to undergo the Polyakov Action -- that also happens during the Bette Acton.  At this point in metrical duration, superstrings as I have discussed will then expand to the inverse degree and manner that these appear to have contracted.  Also, as the said superstrings are then undergoing a relative variance from what was directly before a relatively flush pattern of being a vibrating hoop or a vibrating strand, respectively for two and one dimensional superstrings, these superstrings then "attempt" to become orientable.  As the first-ordered point particles that work to comprise the make-up of the direclty corresponding superstrings begin to "wiggle" from the directly prior relatively flush condition, these orientate in a manner that is either smoothly kinematic in homeomorphic relation to their directly corresponding counterstrings when these are to be Noether in their next iteration during group instanton, or, heteromorphic in terms of the anharmonic multiplicit Grassman condition that these bear if the directly related superstrings are to be tachyonic in their next iteration during group instanton.  This goes for both two and one-dimensional superstrigs.  Even though the "wiggle" of one-dimensional superstrings is anharmonic in a timeless manner during the general flow of BRST, the inter-relation of the net Grassman Constant that exists between a one-dimensional superstring and its counterpart is kinetically homeomorphic if it is to be Noether in its ensuing iteration of group instanton. -- Its just that the kinetically homeomorphic Grassman Condition that exists for one-dimensional superstrings during the core part of BRST is not as smooth curved as the kinematic homeomorphic Grassman Condition that exists for two-dimensional superstrings.  What is meant by "Constant" by mentioning the Grassman Constant is what is to be a consistent shape in the direct field that binds a superstring of discrete energy permittivity with its counterpart.  If such an "attempted" consistency is not maintained over the duration of the Bette Action during BRST, and, if the directly related superstring is not made orientable during the ensuing Regge Action, then, the given arbitrary superstring will not be orientable, and thus, the said superstring will become tachyonic.  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Session 12 of Course 13, Part one

There are differences between a superstring and a counterstring.  Here, we will compare the differences between a superstring of discrete energy -- that exists in one set of world-tubes -- and its counterstring.  A one-dimensional superstring is ideally a basically straight strand of first-ordered point particles, with the exception from straightness being one or more partitions that exist interior to the ends of the said superstring's opposite Neumman bounds.  The said one or more partitions are first-ordered point particles that may be mapped over to the side of the general line of the given arbitrary stream of point particles by a static-based distance of the diameter of one first-ordered point particle.  Such point particles that I am referring to have the diameter of 10^(-86) meters in the substringular -- even though these may be extrapolated as having a diameter of 3*10^(-78) meters in the globally distinguishable, due to certain effects that happens to these particles during the Polyakov Action.  A one-dimensional superstring that is relatively ideal has a counterstring that has one or more partitions on the relatively opposite side of the string when relative to the given superstring.  The Grassman Constant of such a superstring/counterstring inter-relation is here the angle of difference that exists between the partitions of the said given one-dimensional superstring and the corresponding partitions of the one-dimensional counterstring.  A two-dimensional superstring is ideally a basic hoop of first-ordered point particles, with the exception from "perfect" roundness being partitions that work to allow for discrete permittivity -- just as with one-d superstrings.  Part two later!

Hamiltonians -- A Tid Bit About These

When one is referring to the operational-based Hamiltonian, one is here talking about the momentum of a superstring.  Such a Hamiltonian operation here specifically refers to the permittivity of a given arbitrary superstring.  The discrete impedance of a substringular unit is physically localized at the directly corresponding Fadeev-Popov-Trace that corelates to the said given superstring that may be arbitrarily conisdered in an individual case.  Substringular permittivity may be viewed of as being "into the board" in the general direction of the Lagrangian-based directoral-basis that is being considered here in any individual arbitrary case that may be extrapolated by a format relating to a Sterling approximation.  However, the substringular impedance may be viewed of as being "out of the board" in the general direction that is in the reverse of the Lagrangian-based directoral-basis that is being considered here in any individual arbitrary case that may be extrapolated by a format relating to a Sterling approximation.  So, if a superstring is moving through a unitary Lagrangian over a metrical-based time-wise format, then, the permittivity of the superstring -- that here acts as the Hamiltonian operation of the said given arbitrary superstring -- is directorally in the path of the motion of the said superstring when taken through the trajectory of the projection of the directly corresponding said unitary Lagrangian.  So, the inverse of the directly related Hamiltonian operation -- the equal and opposite response of the corelative Hamiltonian operation -- is the impedance of the given arbitrary superstring.  Such impedance acts in the opposite directoral path of the direclty corresponding permittivity, and thus, discrete substringular impedance may be mapped in the opposite holomorphicity of the path of the direclty correponding substringular permittivity.

Solutions to The Second Test Of Course 13

1)  An operator-based Hamiltonian is the inertia of a superstringular phenomenon.

2)  An operational-based Hamiltonian is the momentum of a superstringular phenomenon.

3)  An operand of a Hamiltonian is the space that a superstring is operating through.

4)  Imaginary exchange is a substringular exchange of substringular indices that are delineated as such off of the relative Real Reimmanian plane.

5) The Imaginary exchange of Real Residue involves the relative wobbling of a discrete substringular Hamiltonian operator as it functions during BRST.

6)  As a superstring of discrete energy permittivity closes, this action acts as a Hamiltonian operation that happens via the Fujikawa Coupling as according to the Green Function in the relative forward holomorphic direction.

7)  As a superstring opens, this action acts as a Hamiltonian operation that happens via the inverse of the Fujikawa Coupling as according to the Green Function in the relative reverse holomorphic direction.

8)  When a superstring both begins to open while yet also moves radially one Planck radian during an inverse of the the Fujikawa Coupling, the Hamiltonian operation then performs two Noether-based tasks at once -- making the directly related Hamiltonian format to be multifunctional in the relative reverse holomorphic direction.

9)  As a superstring begins to close as it simultaneously moves radially one Planck radian via the Fujikawa Coupling, the directly related Hamiltonian is here multifunctional in the relative forward holomorphic direction.

10)  As a superstring both begins to open -- while yet also moves transversally one Planck-length during the duration that works to bind two group instantons, such a multifunctional Hamiltonian is still Noether-based in the relative reverse holomorphic direction , yet, it will then have more of a chance here at being less conformally invariant -- and thus the said superstring will have more of a potential at becoming tachyonic.

11)  When a superstring both begins to close while yet also moves transversally by on Planck-length, this multifunctional Hamiltonian operation is still Noether-based, yet, this said superstring will then have more of a chance at being less conformally invariant -- and thus this said superstring will have more of a chance at becoming tachyonic.

Course 13, Session 11, Second Test -- Questions

1)  What is an operator-based Hamiltonian?

2)  What is an operational-based Hamiltonian?

3)  What is the operand of a Hamiltonian?

4) Describe Imaginary Exchange.

5)  How does Imaginary Exchange relate to an operator-based Hamiltonian?

6)  Describe the Hamiltonian of a closing superstring.

7)  Describe the Hamiltonian of an opening superstring.

8)  Describe the multifunctional Hamiltonian of an opening string that moves radially by one Planck radian.

9)  Describe the multifunctional Hamiltonian of a closing string that moves radially by one Plank radian.

10)  Describe the multifunctional Hamiltonian of an opening string that moves transversally by one Planck length.

11)  Describe the multifunctional Hamiltonian of a closing string that moves transversally by one Planck length.

Nous Somme Ici

Worm-Holes are phenomena that inter-bind completely different spots in space by contorting space-time-fabric in such a manner in so that one may be able to go light years of distance into space in a relatively short period of time. It takes a dark matter source in order to temporarily form such a phenomenon. Many worm-holes simply exist at certain spots in the multiverse. Yet, many worm-holes may be temporarily created by a dark matter source in so that relatively instantaneous travel may occur. This is different from black-holes. Black-Holes are phenomena that are created by a collapsed matter source that ends up acting like an apex with a funneling phenomenon-based activity that torsions in so as to bring its surroundings into it in a manner that works to fray the space-time-fabric that enters it. These are two totally different formats of phenomena. Yet, both black-holes and worm-holes existence depends upon different distinctive geni of dark phenomena. The funneling phenomenon-based activity of a black-hole that works to bring its surroundings into it is a form of dark phenomena. Dark phenomena is phenomena that is Ward polarized from electromagnetic energy that moves into its general premesis. Worm-Holes as these are are an advantage if utilized appropriately, while black-holes as these are are a disadvantage to phenomena. There is a solution that is able to alter the condition of the seeming need for black-holes in the centers of our galaxies. We want space-time-fabric unfrayed for a continued existence of our world. Sam Roach.                                          

Dimensionality and Gravitational Pull

When a phenomenon is traveling with more spatial dimensions that are directly associated with the immediate field of the said phenomenon, when compared to the condition of the same phenomenon when it is traveling in fewer spatial dimensions, the degree of the relative scalar amplitude of gravity in general that is applied to the initially mentioned phenomenon is dependent upon whether or not the said immediate field -- that the said phenomenon that is traveling in additional spatial dimensions is traveling through per time -- has more of an abelian geometry applied to it, or, whether it has more of a non-abelian geometry applied to it. So, when a phenomenon is traveling in more dimensions than it usually is traveling through over an analogous timeframe -- these timeframes of which act through the same duration and through the same general format of terrestrial-based path -- if the initially mentioned phenomenon has more of an abelian-based differentially geometric field applied to it, then, the gravitational force that will act upon it will be greater than if it traveled in fewer spatial dimensions over the given arbitrary duration in the given arbitrary general format of projection. Yet, if the initially mentioned phenomenon has more of a non-abelian-based differentially geometric field applied to it, then, the gravitational force that will act upon it will be less than if it had traveled in fewer spatial dimensions over the given arbitrary duration in the given arbitrary general format of projection. This is because extraneous wave-tug and/or wave-pull that is abrasive upon a phenomenon under such an eluded to substringular scenario will add extraneous impedance upon the Rarita Structure-based eigenindices that are applied to a given phenomenon over a respective common duration in a respective common format of projection, while, a lowering of wave-tug and/or wave-pull that would otherwise be abrasive upon a phenomenon under such an eluded to substringular scenario will work to decrease the extraneous impedance upon the Rarita Structure-based eigenindices that are applied to a given phenomenon over a respective common duration in a respective common format of projection.  Less extraneous impedance acting upon a phenomenon means a both an added potential for permittivity and propagation of the immediate field of a given arbitrary phenomenon, and, such an added potential for permittivity and propagation is shown when there is less of a gravitational limitation that is imposed upon the same  stated given arbitrary phenomenon.  Sincerely, Samuel David Roach.                                          

Session 10 of Course 13

When a superstring opens or when a superstring closes, this involves both momentum and inertia.  So, when a string opens, or, when a string closes, this involves a Hamiltonian.  A Hamiltonian expression describes a quantum of momentum.  The permittivity of momentum is inertia itself.  So, the permittivity of what is described by a Hamiltonian expression is inertia.  Such inertia is just a quantum of inertia.  Strings tend to spatially differentiate from their immediate field per iteration of instanton.  The kinematics of superstrings allows for kinematic change in the globally distinguishable, when this kinematic effect happens at instanton.  Strings that close often differentiate kinematically in an alterior manner after the iterations of instanton that happen around the time that these strings close as I had just eluded to.  Strings that open often differentiate kinematically in an alterior manner after the iterations of instanton that happen around the time that these strings open as I had just eluded to.  Such kimematic action happens both during those metrics of the generally unnoticed portion of Ultimon Flow, and also per iteration of instanton.  Each of such general metrical activities of which works to integrate into the globally distinguishable basis of activity.  These kinematic actions always involve both momentum and inertia.  The cross between the phenomena of the said superstrings and the action of the same said superstrings per instanton happens in such a manner in so as to produce the momentum of the mentioned superstrings. The permittivity of this momentum is the inertia of these strings.  This is true of superstrings that close in order to form bosons.  The alterior kinematic differentiation of a string that happens at the same time and upon the same superstring when this superstring opens, or, the alterior kinematic differentiation of a string that happens at the same time and upon the same superstring when this said string closes instead, has a multifunctional  momentum that may be described of as a multiplicitly functional unitary Hamiltonian that acts upon one state, taken respectively.  So, when a one-dimensional string closes while yet also differentiates one Planck-radian kinematically in a spin-orbital manner in the gauge-metrical duration of one transient set of instantons, this will then work to allow the said superstring to undergo a multifunctional Hamiltonian.  This multifunctional Hamiltonian is both one radial operator-based Hamiltonian that functions in a spin-orbital manner along with a Fujikawa Coupling at the same locus and also during the same transient set of instantons.  So, when a two-dimensional string opens in so that it differentiates one Planck-radian in the said spin-orbital tense after an instanton, the said string will have had just undergone a multiplicitly functional unitary Hamiltonian.  This multifunctional Hamiltonian is here one transversal operator-based Hamiltonian when in terms of closing, while yet at the same time being one radial operator-based Hamiltonian in terms of the directly associated spin-orbital motion that happens over the same transient duration of instantons.  If these closing and opening strings kinematically differentiate alterially by more than one Planck-length transversally per iteration of instanton, then, the said superstrings will have here undergone more than one Hamiltonian of transversal-based momentum during the same given instanton that it closed or opened.  Having more than one transversal operator-based Hamiltonian per instanton involve at least some sort of tachyonic propulsion.

Session 9 of Course 13

When a one-dimensional superstring closes to form a two-dimensional superstring, or, when a two-dimensional string opens to form a one-dimensional string, radial and transversal momentum is used to allow the Green Function to transpire in order for these given strings to close or open, respectively.  The net momentum used to completely close an open string, or, the net momentum used to completely open a closed string is one quantum's worth of transversal stringular momentum.  This said momentum may be described by one Hamiltonian expression of transversal operator-based momentum.  The action of this momentum may be described by one Hamiltonian expression of transversal operationally-based momentum.  Correlative operator-based and operationally-based momenta are equal in scalar magnitude.  The net momentum used to completely open a completely closed string is one quantum's worth of transversal stringular momentum.  This momentum may be described by one Hamiltonian expression of transveral operator-based momentum.  The action of this momentum may be described by one Hamiltonian expression of transversal operationally-based momentum.  As always, correlative operator-based and operationally-based momenta are equal in scalar magnitude  -- when in terms of an analogous but different genus of scalar magnitude format.  Before a completely open one-dimensional string is shut, it iterates during the directly corresponding group instanton via an imaginary exchange with its counterpart as I described this during the last lesson.  After the said iteration of group instanton, a given arbitrary superstring and its counterpart cycle the Ultimon.  During the beginning of the generally unnoticed portion of Ultimon Flow, the directly affiliated first-ordered point particles that had comprised any individual given arbitrary superstring, that is here to begin the process of closing -- in so that it may become bosonic -- has just iterated over the course of the directly prior instanton.  This is when the said first-ordered point particles begin to separate to a certain restrained extent, and the encoding that is here to allow for the beginning of the Green Function is in the process of starting.  After a very limited number of a sequential series of group instantons, the here codeterminable activity of the said eigenmetric of the Green Function is then completed, and the Hamiltonian that directly corresponds to the eluded to Fujikawa Coupling that involves the said Green Function is then completely exerted.  At an ensuing iteration of group instanton, the two-dimensional superstring that is now formed by the hermitian bending of a one-dimensional superstring, and, the counterpart of the same said string, has -- at this point --  developed different fields of force than those of a one-dimensional superstring.  The imaginary exchange of Real residue that happens over the corresponding iterations of BRST that behave as these should for two-dimensional strings will now happen in a similar way as before the given arbitrary superstring became bosonic, except that the string is now involving both a different genus of topology and a different genus of light-cone-gauge eigenstate -- when in consideration of the format of the mode in which the corresponding discrete energy "wobbles" in so that it is then able to spring from instanton into the generally unnoticed portion of Ultimon Flow.  The same idea, yet is reverse, happens when two-dimensional strings form one-dimensional strings via the inverse of the Fujikawa Coupling via the inverse operation of the Green Function.

Session 8 of Course 13

When superstrings reiterate, these may close -- if these begin as one-dimensional.  Or, when superstrings begin as two-dimensional -- these may open when these said superstrings reiterate.  We only notice iteration time when in terms of the reiteration of the group instanton portion of Ultimon Flow.  Besides the iterations of group instanton, there is the generally unnoticed portion of Ultimon Flow.  Ultimion time that is generally unnoticed is mainly needed for both group association, group reconnectivity, and also for the essential exchanges of imaginary residue that work toward the recycling of sub-mini-string in the form of the ultimate fractal of pressurized vacuum -- this exchange of which works to recycle the delineatory conditions of norm and ground states.  Norm-States have more to do with the conditions of curved transition through space both in terms of Laplacian and Fourier-based settings.  Ground-States have more to do with the conditions of jointal transition through space both is terms of Laplacian and Fourier-based settings.  Residue that happens outside of the metrics that are directly associated with the iterations of group instanton is imaginary residue.  Imaginary residue works to allow for the majority of the exchange that exists between superstrings.  Imaginary residue may be commuted with either an imaginary exchange or a real exchange -- depending upon the situation.  Stringular residue has an imaginary exchange when the top or the bottom of the directly related first-ordered point particles of one string exchange with the bottom or the top of the directly corresponding first-ordered point particles of another string.  For instance, in the imaginary exchange of the real residue of a superstring when in direct relation to its corresponding counterstring, the bottom fabric of the point commutators of the said string initially commute to the top of the point commutators of the counterstring, in such a manner in so that this activity lifts the said counterstring in a way that brings the counterstring closer to the initially mentioned superstring.  This causes the bottom of the fabric of the counterstring to exchange mini-stringular residue to the top of the mentioned superstring, this of which works to push the said superstring into the prior field of directly corresponding light-cone-gauge eigenstate.  This triggors the mechanism of strings to be able to undergo the ensuing generally unnoticed portion of Ultimon Flow.  This eluded to springing acitivity also works to simultaneously impel the directly related Planck-related phenomena and the mini-strings connectivity that forms as the basis of the light-cone-gauge to travel around the Ultimon.  The exchange here between strings and counterstrings is thus imaginary because it is exchanged off of the Real Reimmanian plane. Real stringular exchange happens, as a general tendency, on the Real Reimmanian plane.

Session 7 of Course 13

The quantum amount of momentum for the substringular is denoted by the Hamiltonian expression.  No momentum exists as momentum below the Hamiltonian level of the smallest sorts.  There are many forms of quantum momentum.  This means that there are many forms of Hamiltonian expressions.  The smallest quantum of momentum for superstrings is the radial operator-based quantum of momentum.  The smallest value for a Hamiltonian expression is thus the radial operator-based value of the just mentioned  quantum of momentum.  The radial operator-based quantum of momentum equals the transversal operator-based quantum of momentum divided by two pi. Other forms of Hamiltonian values that equal the radial operator-based quantum of momentum and the transversal operator-based quantum of momentum are the radial operational quantum of momentum and the transversal operational quantum of momentum, respectively.  The difference between these is that the operator-based momentum acts as the actor of the "motion" while the operational momentum acts as the action of the momentum.  Both operator-wise and operational momentum may be used to describe the situation of one quantum of momentum -- both as a momentum of being and also as a momentum of action.  The operand-based quantum of momentum-based impedance is the holomorphism of the operator-based quantum of momentum that provides a place for momentum to occur.

Orientations Between Orbifolds and Orbifold eigensets

An orbifold is a set of one or more superstrings that work together in such a manner in so as to operate as a specific function.  An orbifold eigenset is a set of one or more orbifolds that work together in such a manner in so as to operate as a specific function.  Each orbifold of an orbifold eigenset that is comprised of more than one orbifold has a slightly different part to play in the overall operation of the here stated given arbitrary orbifold eigenset.  Let us here consider two different orbifold eigensets that would represent two different spaces that functioned in so as to perform two different operations.  The first of such orbifold eigensets in this given arbitrary case will here consist of one orbifold only.  The second of such orbifold eigensets in the same said case scenario will here consist of many orbifold eigensets.  Both of the mentioned orbifold eigensets is formatted in such a manner in so as to be Real Reimmanian in terms of their Gaussian characteristics.  So, both of the said two orbifold eigensets can then be solved into a Gaussian format that is not complex in terms of their determinant genus.  The first respective orbifold eigenset will here contain fewer superstrings than the second mentioned respective orbifold eigenset.  So, the translation of the differential geometry of the spatial inter-relation of the first said orbifold eigenset would tend to here be easier to format into Gaussian form than the translation of the differential geometry of the spatial inter-relation of the second said orbifold eigenset.  In order to compare the Hamiltonian operations of the two mentioned given arbitrary orbifold eigensets, one must take a Jacobian eigenbasis that will here translate the patterning of the first mentioned orbifold eigenset to the second mentioned orbifold eigenset.  Now, take the two orbifolds over time.  Both of the said orbifold eigensets here will be moved through a Lagrangian that will here involve a majorization of codifferentiable, codeterminable, and covariant special re-delineation through time as the two mentioned different physically-based spaces kinematically move through a binary Hilbert-based spatial operand that is here fixed when one is considering the hermitian and non-spurious nature of the trajectory of the projection of the two correlatively moving physically moving spaces that move at a steady-state-based Hamiltonian-based pulse that is Yau-Exact -- while yet constant in terms of the genus of the directoral-based flow of the said kinematic flow of the two eluded to orbifold eigensets.  Let us now say, in this case, that the two spaces form two binary paths that move away from each other over time in a hyperbolic manner that is smooth in trajectoral path per iteration of group instanton.  Then, the longer that the motion of the two said eigensets continues to be performed over time, the less direct influence that these two orbifolds have upon each other.  Such a non-Chern-Simmons-based flow that is constant in acceleration over time is an example of a Dirac operational index that bears a certain degree of Clifford Expansion that is maintained until it is perturbated by an outside force.
I will continue with the suspense later!  Sincerely, Samuel David Roach.

About The Ghost Anomalies Of Certain Heterotic Superstrings

The ghost anomalies of E(6)XE(6) superstrings in forward-time-moving-associated space are the residue of redelineated positive-norm-states that are redelineated by the motion of the said type of hetorotic strings per iteration of group instanton.  As positive-norm-states are "bumped", the just mentioned physical memory of the motion and existence of the said E(6)XE(6) strings is formed. This redelineation of the said format of norm-states works to form ghost anomalies that work to show the directly related pattern of both the motion and the condition of the said heterotic strings as these move through their respective Lagrangians over a given arbitrary duration of Real-based time.  Over a transient period of time after the said ghost anomalies of the said heterotic strings is formed, there are negative-norm-states that scatter the ghost anomalies just discussed in so that the arrangement of the distribution of the directly related positive-norm-states is scrambled into a real-based residue per iteration of group instanton.  Such scattered ghost anomaly-based indices that are here scattered will then tend to be pulled toward the relative interior of the directly related orbifold and/or the directly related orbifold eigenset that is arbitrarily being considered here.  The ghost anomalies of E(8)XE(8) superstrings tend to be "shuffled" toward the relative exterior of its directly associated orbifold and/or orbifold eigenset, or, sometimes toward the immediate exterial field that works here to be adjacent to the directly related orbifold and/or orbifold eigenset.  Just as with E(6)XE(6) superstrings, the directly related ghost anomalies that the said E(8)XE(8) superstrings form is created by the said Yakawa-based interaction of forward-moving norm-states with the said E(8)XE(8) superstrings right before the directly associated iterations of group BRST.  Again it is the eluded to backward-moving norm-states that work to scatter the eluded to ghost anomalies that are then formed here.  The scattered ghosts of E(8)XE(8) superstrings that are not directly impending to fray and the scattered ghosts of E(6)XE(6) superstrings that are not impending to fray always tend to bear no Gliossi-based Yakawa interaction with the ghosts of superstrings of discrete energy permittivity UNLESS there is a definitive cohomoligical index that is here used to pull these into their direct ghost-based field by the holonomic substrate of a directly related group attractor.  Again, with forward-moving-time-based substringular activity, it is the positive-norm-states that form ghost anomalies and it is the negative-norm-states that scatter ghost anomalies.  With backward-moving-time-based substringular activity, it is then the negative-norm-states that form ghost anomalies and it is the positive-norm-states that scatter ghost anomalies.  I will continue with the suspense later!  Sincerely, Sam Roach.

Universe-Based Translation

If one were to utilize a certain given arbitrary Hamiltoian Operator as a physically functionable Jacobian-group attractor, one may be able to translate an orbifold or an orbifold eigenset that may here act as a given arbitrary physical space into an orbifold or an orbifold eigenset that belongs to a specific other given arbitrary universe.  So, one may here consider one orbifold or orbifold eigenset that may here belong to our universe.  Now, consider a different orbifold or orbifold eigenset that in this given case belongs to a completely different universe.  Consider what Jacobian eigenbasis would be able to translate the initial said orbifold or orbifold eigenset from belonging to the initially mentioned universe into belonging to the universe that the second said orbifold or orbifold eigenset belongs to.  Here, the given said physical holonomic substrate that works upon the initially mentioned physically-based space is then the directly associated Hamiltonian Operator.  The process of the translation of one physically denoted space into belonging to a different universe -- so that both of the mentioned eluded to spaces will here be of the same universe -- is here the directly associated Hamiltoian Operation.  The space in which the said translation of a physical entity translating from one universe to another is here the given arbitrary Hamiltonian Operand.  This is a rather unique cased of Hamiltonian-basesd Jacobian eigenbases.  Hamiltonian-based Jacobian eigenbases normally instead work to relate physically oriented spaces that are of the same universe.  This is a little bit of food for thought.  I will continue with the suspense later!  Sincerely, Samuel Roach.

A Little Tad Bit More As To Certain Ghost Anomalies

Ghosts formed by gauge-bosons and other substringular heterotic strings (not including what I term of as the Main Heterotic String Fabric) scatter elsewhere back into the directly corresponding relative Real Reimmanian Plane.  So, a given substringulr heterotic superstring "bumps" upon certain relatively forward-based norm-states.  This forms a physical memory in the form of ghost anomaly.  As relatively backward-based norm-states scatter upon the said ghost anomaly, the directly corresponding scattered norm-indices redistribute and redelineate back into what is here the given arbitrary relative Real Reimmanian Plane.  This simply forms a re-delineation of the directly related first-ordered point particles as these may be mapped and extrapolated per iteration of group instanton.  Certain superfolous substringular phenomena also occasionally works to form certain ghost anomalies that  scatter the said ghosts simply to an alterior distribution or an alterior delineatory positioning that will here exist in what is a Real-based Reimmanian Plane -- when in terms of a certain other superstringular field.  The reason as to why and how the formation of ghost anomalies and their corresponding scattering happens per iteration of group instanton is analogous to the concept of a "zipper."  During the beginning of a given arbitrary instanton-quaternionic-field-impulse-mode, the encodements as to what and where ghost anomalies were during the course of the directly prior iteration of group BRST works to settle the ghosts and the scattered condition of certain ghost anomalies into the delineations that these had at the end of the said directly prior duration of BRST -- like an alagorical  "zipper" is stabilized at a given relative position.  This is due to the encodement that appertains to the activities of both the space-hole and the instanton-quaternionic-field-impulse.  Just as BRST is about to happen, the eluded to substringular phenomena "bumps" into certain norm-states  -- as well as certain norm-states "bump" into reverse-holomorphically-based norm-states.  This causes the condition of BRST to form both a state of respective ghost anomaly formation and ghost anomaly scattering.

A Little Bit More As To The Past Discussio of Ghosts

The ghosts of counterstrings and the ghosts of Fadeev-Popov ghosts also interchange residue with Neislon-Kollosh ghosts.  So, to be more specific, it is when the flow of the overall ghost-based composits that appertain to the combined ghost-based residue that corresponds to those norm-states that are scattered by both superstrings, their counterstrings, and their directly corresponding Fadeev-Popov-Trace-based ghosts that forms a flow with the recycled residue of norm-states that exist in a scattered mode in so as to form Neilson-Kollosh ghosts -- that forms a format of sequential harmonic mode until such a flow is perturbated.  It is the general condition of the temporary clogging of a general locus -- when in terms of a specific general locus where ghosts are being exchanged via the recycling of their residues -- that works to indirectly, via the motion of Schwinger Indices along a relatively Njenhuis sector of a directly associated Rarita Structure eigenstate, to form a Wick Action eigenstate in so as to allow for a direct change in holomorphicity.  Such a perturbation works to then soon allow for the activity of a Gaussian Transformation that happens via the Kaeler-Metric.

Part Two As To The Discussion About Ghosts

To get back to the last post's case scenario:  Once dilatons and dilatinos are formed, these move off of the relative Real Reimmenian Plane in so as to become gravitational particles known of respectively as gravitons and gravitinos.  The said gravitons and gravitinos move per iteration of group instanton to scatter the directly corresponding forward-holomoriphic-based norm-states in so as to scatter these in so as to form physical memories known of as Neilson-Kollosh ghosts (this type of general category of ghost anomaly).  As the given arbitrary respective regions where Neison-Kollosh ghosts are formed begin to clutter on account of the condition of beginning to work at forming a lack of room in the said given arbitrary respective region that is here off of the initially mentioned Real Reimmanian Plane, the said Neilson-Kollosh ghosts are then undergoing the process of scattering into certain residue that then flows back into the Real Reimmanian Plane in the form of positive and negative-norm-projections and positive and negative -norm-states that even-out back into the initially mentioned said Real plane in so as to work to re-establish the general format of the condition of Fock Space both on and off of the again eluded to Real and Njenhuis Planes.  The flow of the exchange of Gliossi-Shirk-Olive ghosts into Neilson-Kollosh ghosts works to form a kinematic metrical harmonics that is smooth in terms of a general lack of spurious sub-metrics -- the initial said flow tends to begin in a relatively hermitian manner that is low in terms of Chern-Simmons metrical singularites.  As soon as the just mentioned mode of harmonics -- in terms of the initial kinematic flow of the exchange of Gliossi-Shirk-Olive ghosts with Neilson-Kollosh ghosts -- changes in terms of its directly related sequential pattern of recycling mode (when the pattern of the harmonics as to the sequence in which the flow of the exchange of such ghost-based residue's recycling is altered), then, this is when such a mentioned flow is altered or perturbated.  I will continue with the suspense later!
Sincerely, Sam Roach.

About The Flow Of Certain Ghost Anomalies, part one

Gliossi-Shirk-Olive ghosts are the physical evidence of the trajectory of specific superstrings that act as discrete units of energy permittivity.  Such evidence is literally the pattern-based distribution of scattered positive-norm-states (for forward-moving time-based superstrings) that are redelineated by the motion of superstrings that have moved into their general substringular neighborhoods after a sequential series of instantons in which the said superstrings of energy permittivity have been redelineated over time.  Such a redelineation of positive-norm-states is only formatted over the course of successive iterations of group instanton, since, both the positive-norm-states and the negative-norm-states resituate themselves during the instanton-quaternionic-field-impulse-mode into what their delineation was directly before the directly prior generally unnoticed portion of Ultimon Flow.  So, at the end of a given arbitrary instanton-quaternionic-field-impulse-mode, as the superstrings of discrete energy permittivity are re-delineated to their ensuing position at which these are to reiterate at over the course of the ensuing duration of group BRST, the said superstrings of discrete energy permittivity "bump into" norm-states that are moving in the same general directoral basis of holomorphicity as the said superstrings are about to iterate over the directly corresponding duration of group instanton.  As the said superstrings do the mentioned "bumping into" the said norm-states, the eluded to interaction works to displace the said directly related norm-states.  This redistribution works to form a delineation that forms a pattern that may be used as an extrapolation as to where certain superstrings of discrete energy permittivity were at relatively recent iterations of group instanton.  As Gliossi-Shirk-Olive ghosts are increased in quantity and in substringular-based Ward-volume, these are scattered by norm-states that move in the opposite holomorphic-based directoral flow in such a manner that these form both dilatons and dilatinos.  The just written about dilatons and dilatinos -- once formed -- then move off of the Real Reimmanian Plane.  I will continue with the suspense later!  Sincerely, Sam Roach.

A Little Bit More As To The Wick Action

Whenever a set of one or more superstrings changes in its general holomoriphic-based directoral trajectory, its alteration in holomorphicity is caused by the occurance of a Wick Action eigenstate.  The existence of the motion of a Wick Action eigenstate is indicative of the soon occurance of a Gaussian Transformation.  A Gaussian Transformation is that general format of group metric that works to allow for those changes in norm conditions that are necessary in order that kinematic motion may be both spontaneous and persistent.  Gaussian Transformations also simultaneously work to allow for both superstrings to re-attain discrete permittivity and for their corresponding Fadeev-Popov-Traces to re-attain discrete impedance.  This way, the directly related given arbitrary superstrings may be able to remain as discrete units of energy permittivity, and also, so that the directly related given arbitrary Fadeev-Popov-Traces may be able to remain as discrete units of energy impedance.  Gaussian Transformations that work to allow for the perpetual existence of entropy are known of as gauge-transformations.  Gauge-Transformations are those Gaussian Transformations that involve Calabi-based interations.  Calabi-Interations are interactions in which photons scatter upon a holonomic substrate.  So, whenever a group of one or more superstrings are perturbated holomorphically, this change in the general tendency of the said group of one more superstrings that here act to perform a given arbitrary function is caused by the start of the activity of a Wick Action eigenstate.  Here is how a Wick Action eigenstate is formed in so that immediate alterations in holomorphicity that occur to a group of one or more superstrings may happen in order to allow for what will here soon allow for the activity of a Kaeler-Metric in which a Gaussian Transformation may occur.:  A set of one or more superstrings vibrates along what is here a given specific trajectoral projection over a certain given period of time.  The said set of superstrings will here bear a vibrational pulse that is correlative to the local genus and format of the directly corresponding Schwinger-Indices.  The said Schwinger-Indices act upon the Rarita Structure eigenstates that are local to the general eluded to path of the said group of superstrings.  The mentioned Schwinger-Index eigenstates will here be influenced by both their relativity to locally-based electromagnetic energy and the pull of the locally-based gravitational forces -- the latter of which happens via the Ricci Scalar.  As soon as their is a significant Yakawa-based torsion that will here occur between the eluded to directly related electromotive force and the gravitational force, under the indirect control of the topological swaying that is influenced by the local indices that appertain to the strong force, their is then a given arbitrary alteration in the genus of the directly related local Chern-Simmons eigenstates -- when in terms of both the parity and/or the chirality of the directly related group of superstrings that have here moved in one format of holomorphicity over a certain period of time.  What I mean by a significant Yakawa-based torsioning is a binding of wave-tug and/or a binding of wave-pull that acts in so as to perturbate the flow of the directly related Gliossi-Shirk-Olive ghosts with the directly related Neilson-Kollosh ghosts.  Such a change in the conditions of the local Chern-Simmons eigenstates' genus will then here form a condition of spuriousness in the said given arbitrary group of superstrings that are moving along the originally mentioned trajectoral-based path.  This eluded to torsion will here form a certain format of a Hausendorf Projection that is caused as an equal and opposite reaction to the strain that would here be caused by the said torsioning of E.M. upon gravity that are local here.  The initial activity that happens upon the formation of the eluded to Wick Action eigenstate will here  be a change in the directoral-holomrophic-based format of trajectory of the said given arbitrary group of superstrings that are moving along the prior stated path.  The said change in holomorphicity will then act in so as to indirectly cause what will soon be here at the general local substringular cite -- a Gaussian Transformation.  This flow of kinematic activity will then not only allow for those changes in positioning via the directly related changes in norm conditions that allow for there to be enough organization of room at the general local cite to allow for the continued motion of the said related superstrings, yet, it will also -- via the directly related Kaeler-Metric eigenmetric -- work to allow for the re-attainment of the respective permittivity and impedance that allows for the said superstrings to move as discrete units of energy permittivity and for the said Fadeev-Popov-Traces to move as discrete units of energy impedance.  I will continue with the suspense later!  Sam Roach.

Formats For Different Types Of Kunneth-Based Formulations

There are 32 spatial dimensions in one set of parallel universes.  This means that there are 16 general genus-formats of Njenhuity in one set of parallel universes.  So, even though there are 9.1*10^(82) universes in one set of parallel universe, these universes that work to comprise this set consist of a total of the said 16 general genus-formats of Njenhuity from within the said set of parallel universes.  This means that even though one could theoretically compare one orbifold that exists in correlation with one other orbifold from a total of the eluded to 9.1*10^(82) different respective universes from within our set of universes, and, such a correspondence -- when in terms of the covariance between these said orbifolds, would involve a Kunneth Formulation in order to work to determine a specific Li-Algebra-based Gaussian spatial relationship between each individual respective orbifold that is being considered here with each other at once -- over a given arbitrary Laplacian Transformation, one may often more specifically compare 16 orbifolds that exist as individual orbifolds that exist in different universes that each bear a different genus of Njenhuity.  Such a correspondence may be used in order to work to compare the covariant Laplacian and the covariant Fourier codeterminable and codifferentible eigenbases that show an actual spatial inter-relationship between universes from the same set that are not only different, yet, also each bear a different tense of complex spatial genus.  I will continue with the suspense later!  Sincerely, Sam Roach.

The Next Heads-Up As To Course 19

Let us say that one arbitrarily considered four orbifolds that each belonged to four different respective universes of the same set of parallel universes.  Let us now say that one arbitrarily chose one of these four orbifolds to be of a Real Reimmanian condition that is here of our universe.  Let us now also consider an arbitrary given condition of each of the other three orbifolds each bears three different respective genus-based formats of Njenhuity -- as such a condition is considered over a Laplacian-based format in which each of the four said orbifolds that here belong to different universes each display four different general formats of complex-number-based geni, on consideration of the here given arbitrary condition of these each being completely Njenhuis to one another as according to a basic Li Algebra-based covariant, codifferentiable, and codeterminable manner. So, as one, in a given case scenario, takes the Hodge Index as to the number of overall superstrings that work to comprise the arbitrarily Real Reimmanian-based orbifold that is of our universe, one merely does a pattern-based extrapolation that talleys the number of overall superstrings that make up the said orbifold.  Yet, when one takes the Hodge Index as to the number of overall superstrings of the other three respective orbifolds, one talleys an Imaginary-Number-based extrapolation as to the pattern-based counting of the number of superstrings that are within each of the three other said orbifolds that belong to three different respective universes that are each completely Njenhuis toward one another.  At this point, one may compare the Li-Algebra-based Gaussian formats of the four orbifolds that are covariant -- although completely not of the same Real Reimmanian basis.  Such an inter-relationship is known of as a Kunneth Formulaton.  Now, if one is to take a certain given arbitrary complex-based Jacobian that may be utilized to be multiplied by one of the universes, one may be able to derive an alteration of the Gaussian basis that may work to compare one of the said orbifolds to one of the other ones via the eluded to Imaginary Li-Algebra mathematical basis.  One may then do such a general activity in so as to compare the Laplacian-based covariance of all four given arbitrary orbifolds as spaces in so as to relate these via specific Jacobians that here work to find a set of common complex mathematical bases that work to here correspond the said four different spaces that each are from four different respective parallel universes.

A Heads-Up To Course 19

According to the Heisnburg Principle, one can not detect exactly where an electron is and what it is doing at the exact same time.  One may only be able to approximate -- with a certain degree of expectation value, exactly where any given electron is at and what it is doing at the exact same time.  Superstrings are even more difficult to be able to determine exactly where these are at and what these are doing at the same time.  Therefore, it takes an even more touchy extrapolation as to the expectation value as to where these are at and what these are doing simultaneously.  An expectation value is a probability as to the existence of a condition that is determined anywhere from 0 to 1.  An expectation value of 0 means that there is no way of something being a certain way.  An expectation value of 1 means that there is complete certainty as to something being a given arbitrarily determined way.  A Sterling Approximation has to do with an extrapolatory approximation as to exactly where a superstring is and what it is doing at the exact same time.  Again, with a Sterling Approximation, the expectation value will always be between 0 and 1.  When one works to determine exactly where a smaller phenomenon than a superstring is and what it is doing at the exact same time, one may take fractals of what I have just described of as the basis of a Sterling Approximation.  So, by making the mentioned Sterling Approximations and their fractals into consideration as an integrative unit of determination, and then, by putting these together in a methodical manner, one may work to determine with at least some rigor where certain superstrings and/or groups of superstrings are at and what these are doing at relatively the same time.  The said general format of approximations involves a higher degree of certainty for groups of superstrings that act together as a unit than for individually operating superstrings.  This is why it is easier to determine the trajectorial projection of an orbifold than the trajectorial projection of an individual superstring.  Such extrapolations may be determined with optimum certainty to work at finding out relatively well what is going on in the substringular, and, at what locus or region such activity is happening at over a given arbitrary metrical locus in which such activity is occurring.  I will continue with the next heads-up as to course 19 later!  Sincerely, 
Samuel David Roach.

The Last Test Solution To The First Test Of Course 13

1)  When both inerita and momentum are invariant upon a superstring, this means that over the observable extrapolation in which the said superstring is traced through its trajectorial projection, the pulse of the said superstrings Hamiltonian operation, as well as  the pulse of its Hamilonian operator,  is maintained as these are per eigenmetric in which the said superstring is differentiatin in  kinmatically over time.  For instance, if a given arbitrary superstring works to bear a given arbitrary Hamiltonian operation per a consistently observably transient-based extrapoloation -- along with the Hamiltonian operator of which works to function as having the said Hamiltonian operator that I have here eluded to, then, after every of such discrete set of eluded to instantons in which the said superstring is observably extrapolated, in such a manner in so that the conisdered Hamiltonian operator that is here directly pertainent and the considered Hamiltonian operation that is here directly pertainent as well are maintanined as such per each of the said conistent metrical pulses in which the said superstrings may here be considered as existing in as is according to the given case scenario.  This means that not only would the given operator of the directly related substringular momentum be either identically the same or else indistinguishably replaced over the eluded to extrapolatory-based metric in which such a superstring is here considered, yet, the function of such a substringular momentum would here remain the same over the same given arbitrary directly associated metric (duration that is here under specific consideration).  This not only conisders that the integrable vaible scalar amplitude of the said substrigular momentum is here maintained over the said kinematically-based said duration, yet, it also considers the overall directoral push and/or pull of the both the radial and the transversal tenses of the said superstring over the course of the said whole overall duration that is here under conisderation as being maintained over the eluded to Fourier Transformation.

The Next Part of the Test Solutions To the First Test of Course 13

9)  Inertia and momentum are jerked when the general flow of any given arbitrary respective Hamiltonian operators and Hamiltonian operations are altered or perturbated from the trajectory that these had initially undergone.  So, as a superstring's inertial and momentum-wise tendencies over a relatively secure period of time are abruptly changed over a more transient period of time, this abrupt change in both discrete substringular inertia and discrete substringular momentum is a change in the directoral path and/or the specific genus of the Noether Flow of the mentioned substringular locus where the said superstring is moving over a given arbitrary Fourier Transformation -- that is directly involve here.  Such an alteration in the directoral path and/or the specific genus of Noether Flow of a superstring is a change in a fractal of substringular acceleration.  Such a change in "acceleration" is a jerk, or, in other words, this is a jerk of both the Hamiltonian-based inertia and  the Hamiltonian-based momentum of the said superstring.

10)  When a superstring initially bears a direct effectual wave-tug and/or a direct effectual wave-pull upon a given arbitrary substringular holonomic substrate that it acts upon, while then, at an ensuing period of time over a given arbitrary Fourier Transformation, the said superstring at this point lacks a direct effectual wave-tug and/or a direct effectual wave-pull upon the prior mentioned given arbitrary substringular holonomic substrate that was initially mentioned, then, the superstring that I eluded to as varying in its ability to bear a direct effectual wave-tug and/or a direct effectual wave-pull upon some exterialized entity that it is acting upon may be described of as acting via a partially abelian geometry over time.  Or, in a second scenario, if the initial superstring mentioned here instead bears a direct effectual wave-tug and/or a direct effectual wave-pull upon one initial holonomic substrate that may be mentioned here, while, the said superstring that was brought up in the beginning of this sentence -- at the same bearing of metrical locus at the vantage point of a centralized conipoint-- lacks both a direct effectual wave-tug and/or a direct effectual wave-pull upon another holonomic substrate that it is touching in a Yakawa manner that may here be of a Gliossi tangency in this given arbitrary example, then, in this case too, the said superstring initially mentioned in this second case will here too be considered to bear a partially abelian geometry upon its environment.  In this second case, the tendancy of having a partially abelian geometry may be viewed even at a "snapshot" of extrapolation that may here be described over a pertainent Laplacian Transformation -- based upon the derivation of the potential as to how the related push and pull of the directorals of the said superstring bear upon the directly related surrounding Poincaire-based eigenstates that may work to influence the impending interactions that work upon the whole overall holonomic substrate that the said superstring is acting upon.
I will answer the last question later!  Sincerely, Sam Roach.

Part Three Of The Test Solutions To The First Test Of Course 13

8)  Inertia and momentum are not quantified for substringular activities that "try" to act either as only part of one discrete substringular Hamiltonian operation or as only part of one discrete substringular Hamilonian operation, respectively.  A discrete Hamiltonian operator in context with an entity that acts as a source that forms the physical momentum of a superstring acts in discrete units when in reference to the Hamiltonian operation as the momentum of a given arbitrary superstring.  A discrete Hamiltonian operator in context with an entity that acts as a source that forms the physical momentum of a first-ordered point particle acts in discrete units when in reference to the Hamiltonian operation as the momentum of a given arbitrary first-ordered point particle.  A discrete Hamiltonian operator in context with an entity that acts as a source that forms the physical momentum of a second-ordered point particle acts in discrete units when in reference to the Hamiltonian operation as the momentum of a given arbitrary second-ordered point particle.  This is the general idea here.  Again, a given arbitrary Hamiltonian operator is what acts as the basis of substringular inertia, while, a given arbitrary Hamiltonian operation is what acts as the basis of substringular momentum.  I will continue with the suspense later!  Sincerely, Samuel David Roach.
P.S.  Another way of looking at it is to consider the discrete manner of initially considering what is a to be here thought of as discrete Hamiltonian operators and discrete Hamiltonian operations as the smallest units of respective inertia and the smallest units of respective momentum that appertain to the direct activity of superstrings.  The smaller-based formats that acts as extrapolatory means of considering lower levels of Hamiltonian operators and Hamiltonian operations may be considered as discrete fractals of the initially said purveyed discrete Hamiltonian operators and the discrete Hamiltonian operations that would here appertain to the pulse of superstrings as these move through space over time.

Part Two of the Little Bit Of a Heads-Up about Courses 16 and 26

I left-off last time writing about the mapping-out of the trajectorial projection of a superstring that bears some sort of eluded to Chern-Simmons tendancies, as the superstring given in this scenario moves through space over time.  Even though the given arbitrary superstring that I had left-off writing about in my last post moved in a hermitian manner as an entity that may be mapped-out as a general trace of ghost anomalies -- that work to indicate the directly prior motion of the said superstring that is being discussed here -- the said directly related perturbation of the said superstring's time-oriented pulse that is here anharmonic -- due to the transient change in the acceleration of the said string's oscillation, at the simultaneous gauge-metric in which the third derivative that directly relates to the change in the general motion of the superstrings over time is happening (at the vantage point of the conipoint of the general locus of the overall activity of the given arbitrary activity that is being discussed in this scenario), the said alteration of the harmonics of the flow of the motion of the said superstring, as it is projected along the path of its trajectory over time, works to form a residue of physically-related singularity that actually does bear a Chern-Simmons-based mode -- since this said condition forms an aberration of stability in the harmonics of the said kinematic projection of the said superstring.  This would make this current case example of a path of a superstring that is considered over the time in which the superstring is forming such a path a partially Chern-Simmons field field trajectory.  Any field trajectory that bears any genus of Chern-Simmons singularity-founded-basis -- whether such a genus of perturbation bears an integrative basis of singularity that is not discrete OR even if there is only a partial condition of a singularity that is thus not discrete, even though such a singularity may be offset by a countering bases that may here work to unitize the Jacobian eigencondition of the otherwise considered Chern-Simmons genus, is  here considered a given arbitrary example of a Cevita Interaction.

A Little Heads Up To Courses 16 and 26, Part One

Let us say that a superstring is to move thru a path in such a manner in so that it changes in four derivatives, in which that said superstring performs such a change in a three-dimensional-based Minkowski plane in such a manner that it jerks kinematically in what was initially a harmonic rhythm that is made anharmonically elongated in a Fourier-based pulse of metric at the same locus that the said superstring is here said to undergo the said change in four derivatives -- this said elongation of kinematically-based operation of pulse of which is conimetrically and coniaxial-based formatted at the conicenter of the just mentioned spot, to where the Ward-Caucy-based tensoric concavity that here alters in its topological curvature is here temporarily jerked out of what started as a harmonically flowing superstring that then becomes temporarily anharmonic -- at the said relatively discrete said locus of perturbation that is arbitrarily given as such in this case.  The genus of Chern-Simmons-based singularity could then be described by infinity times infinity, or, in other words, by infinity squared.  If, at a position of the trajectory of the Lagrangian-based path of the said superstring that tis further down the path of the said superstring that is further down the Fourier-based mapping of the projection of that stated superstring -- at an ensuing metrically bracketed time locus, the said superstring changes in three derivatives while it simultaneously, thru the mentioined conipoint's vantage point, jerks at this locus in an anharmonically-metrical manner in such a way that the pulse of the just mentioned superstring is sped-up at the conicenter of the coniaxial at where the said superstring was at when it here changed in three derivatives as a plane of a one-dimensional superstring that moves as a two-dimensional field that moves thru a unitary exterialized Lagrangian, then, the genus of its Chern-Simmons singularity format may be described of as being discrete relative to 1/infinity, or, in other words, the directly related singularity here would equal 0+.  The curvature of the said one-dimensional superstring here would be hermitian when in terms of the overall Laplacian-based mapping of the trajectory of its path -- as may be denoted by the extrapolation of the field import of its Gliossi-Shirk-Olive ghost-based field indices, these indices of which here are comprised of as positive-norm-state indices that work to trace the said mapping of the mentioned path as a timeless-oriented differentiation.  I will continue with conveying the basis of this concept later!  Sincerely, Samuel David Roach.

Part Two of the Solutions To The First Test Of Course 13

5)  An abelian geometry is the Laplacian-based differential framework of substringular phenomena that bears a wave-tug and/or a wave-pull that has a Hamiltonian operational-basis that is directly effectual when in terms of the Yakawa-based flow of mapped-out delineation of one local tense of partial differential framework relative to another local tense of partial differential framework.  The sequenial series of such a basis may often be applicable to a kinematic fluidity of motion that may be described by a Fourier Transformation.  In other situations, the kinematic fluidity of motion of what was initially a Laplacian-based mapping-out of a covariant, codifferentiable, and codeterminable condition of an abelian-based geometric scenario may be applicable to a duration that happens either within the overall metric of a given arbitrary group instanton, or, in other cases, one may consider at times the abelian-geometric conditions of either a snapshot as to what happens in-between individual durations of instanton, or, at times, instead, one may consider the abelian-geometric conditions of a kinematic flow of topological-based substringular substrate that occurs during the generally unnoticed portion of Ultimon Flow.

6)  A non-abelian geometry is a geomtric condition that differs from an abelian geometry on account of the wave-tug and/or the wave-pull that is here pertainant having here a Hamiltonian operational-basis that is directly non-effectual in terms of one substringular substrate towards another -- when under the conditions of the Yakawa-based flow of the mapped-out delineation of one local tense of partial differential framework relative to another local tense of partial differential framework.

7)  Both momentum and inertia are quantified by the basis of discrete Hamiltonian-based operations, discrete Hamiltonian-based operators, thru given arbitrary Lagrangians that here exists as discrete Hamiltonian-based operands.  A given arbitrary  discrete quantum of momentum specifically is quantified by the basis of a discrete Hamiltonian operation, while a given arbitrary discrete quantum  of inertia specifically is quantified by the basis of a discrete Hamiltonian operator.  The given arbitrary region in which the said Hamiltonian operation of momentum is pulled or tugged into -- as a holonomic substrate that exists as an entity that acts as a Hamiltonian operation of inertia -- is what I have termed of as the said discrete Hamiltonian-based operand

Part One Of The Test Solutions To The First Test Of Course 13

1)  If a swivel-shaped one-dimensional superstring is brought into a conditional tense of relative conformal invariance -- that, in the process, works to help the directly associated Bette Action eigenmetrics to have an even-functional Grassman Constant, then, the said one-dimensional superstring is more likely to remain in motion as according to Noether Flow, and, thereby, have more of a tendency to become basically straightened as a physical entity that acts as a holomomic substrate in its codifferentiable, codeterminable general locus.

2)  Generally, one-dimensional superstrings are relatively straight vibrating strands of physical phenomena -- except for the relatively few abberations that are due to these superstrings having anywhere from one to 3*10^8 partitions. This is at iteration.

3)  If a given arbitrary one-dimensional superstring differentiates kinematically within a relatively tightly-knit locus with a relatively low scalar amplitude that is directly associated with the Lagrangian of its physical trajectory over time, and, if certain other one and two-dimensional superstrings that are relatively adjacent here obey the same just mentioned Chan-Patton conditions, then, their codifferentiation will tend to be conformally invariant.

4)  Let us say that a given arbitrary set of a countable number of superstrings differentiate kinematically in a relatively tightly-knit locus over a relatively brief amount of time, the directly related mini-string segments that work to comprise the topology of the said superstrings has other segments that will here interplay at the said locus in this scenario -- in such a manner in so that a casual pervayance would not be able to detect the said eluded to replacement, due to the condition that the given need for the recycling of topological holomomic substrate that one may be able to extrapolate when in terms of the literally actual "stuff" that had been there has been redistributed in a manner that allows for the whole given cite to remain appearing as unchanged.  This is both in terms of the same format as to what was there being the same throughout the said alteration -- as well as the manner as to the behavior as to what was there also being the same throughout the said alteration.  Such an indistinguishable, yet actual change in venue, is a given arbitrary example of what is known of as indistinguishable difference.