Part Five of the Eleventh Session of Course 16

In the real world, superstrings that are bosonic  -- over one individual course of their substringular history, in which such discrete phenomena are closed loops -- are constantly vibrating as oscillating hoops, particularly over the course of instanton.  Likewise, in the real world, superstrings that are fermionic -- over one individual course of their substringular history, in which such discrete phenomena are open segments that are composed of first-ordered point particles that integrate as one relatively linear-based phenomena -- are constantly vibrating as oscillating strands, particularly over the course of instanton.  Certain laws work to govern the tendency and ability of superstrings of discrete energy permittivity to vibrate in the manner in which these do vibrate.  The vibration of any given arbitrary superstring -- over the course of an iteration of instanton -- is controlled by the condition of a directly corresponding harmonic-based oscillation.  All superstrings over the course of an individual iteration of instanton, are varied in the sway of their topological structure -- in both a stand-still consideration, and, also, in-between the multivarious gauge-metrics in which such superstrings act, in so as to behave as the discrete phenomena that these are, in order to be fundamental units of energy permttivity.  Such a topological sway always acts in so as to conform to an eigenbasis, for either any directly corresponding one-dimensional superstrings and for any directly corresponding two-dimensional superstrings.  Such an eigenbasis may be of either of an annharmonic nature -- when in terms of the delineation of its eigenvalues -- when in terms of one-dimensional superstrings, over the course of the correlative iteration of instanton, or, such an eigenbasis may be of a harmonic nature -- when in terms of the delineation of its eigenvalues -- when in terms of two-dimensional superstrings, again, over the course of the correlative iteration of instanton. The just eluded-to eigenvalues, in this case, work to describe the individual indices of the alteration of the directly corresponding Ward-Caucy derivatives, that works to describe the flow of the eluded-to Ward-Caucy-Plane -- in either a non-metrical and/or in a metrical-based manner.  The changes in Ward-Caucy denotations in the said superstrings work to describe harmonic oscillation eigenvalues, while, the different curved contours of any given arbitrary substringular space work to describe harmonic oscillation eigenspaces.  The different conditions that work to allow for superstrings to harmonically oscillate over a sequential series of group instanton  -- in a relatively hermitian manner -- are the gist of Chan-Patton factors.  This is why perturbations in the flow of a set of superstrings by a tachyonic flow, over time, is a key relation that works to temporarily break Chan-Patton factors. I will continue with the suspense later!
To Be Continued!  Sincerely, Samuel Roach.

Gell-Mann-Najshima-Relations

Those sets of boundary-based conditions of multiplicitly acting quarks -- when one discerns the covariance of their so-eluded-to parity-based interactions -- that work to establish the kinematic interplay of their Ward-Caucy-bounds, as taken over the multiplicit Sterlilng-based approximations of their sequential series of iterations of directly assoicated group instantons, that work to form that energy that such quarks function in, in so as to operate as such a partial of any directly related subatomic source of physical entity over time, is what works to define the existence of Gell-Mann-Najshima-Relations.

Sub-Light-Cone-Gauge-Topology

When one considers the topology of either a superstring at the Gliossi-based Ward-Neumman-bounds of its directly corresponding core-field-density at the Poincaire level, the correlative counterpart of the so-stated superstring at the Gliossi-based Ward-Neumman-bounds of its directly corresponding core-field-density at the Poincaire level, or the correlative Fadeev-Popov-Trace eigenstate at the Gliossi-based Ward-Neumman-bounds of its directly corresponding core-field-density at the Poincaire level, the mini-string segments that work to form the eluded-to topological formats bear different abelian-based tendencies that work to form the physical nature of the corresponding genus of the counterpart of the so-stated discrete energy permittivity, as with the corresponding discrete energy impedance, respectively.  A superstring of discrete energy permittivity bears a relatively abelian composition of the integration of the partition-based segments at the timeless moment of its iteration of the bascially stand-still Hamiltonian-mode that it imparts, over the course of such a succeeding display of group instanton that it acts as being of one discrete partial of -- over the sequential series of such iterations, of which works to form the mobility of discrete energy "thrust" over time.  This is at a level that is more succinct than the light-cone-gauge-based-level -- since this is at the Ward-Neumman-based mappable tracing of its topology, at the corresponding Gliossi-based core-field-density that it works to designate as at the Poincaire level, as I have already mentioned.  This here relative abelian nature is a consideration of its comparative kinematic-based differential geometry, that is more of an integration of supplemental-based partials. Through the relatively non-abelian-based nature of its directly corresponding Fadeev-Popov-Trace eigenstate -- that works to form that discrete energy impedance that would here interact with the eluded-to discrete energy permittivity, that is of the so-stated general condition of its correlative superstring.  Again, this is at the Gliossi-based topology that is at the Poincaire level of the respective superstring -- when this is related to the Gliossi-based topology that is taken at the Poincaire level of the respective Fadeev-Popov-Trace eigenstate.  As eluded-to before, this is due to the less supplemental-based and timeless based delineation of the mini-string segments that work to comprise the said given arbitrary Fadeev-Popov-Trace eigenstate.  Counterstrings bear a relatively abelian-based topology at the Gliossi-based core-field-density of their respective topological-based eigenstate, as taken at the Poincaire level -- such as is the differential oscillation-based nature of their correlative directly associated superstrings.

The Next Part of the 11th Session of Course 16

A superstring becomes unorientable when there is an abundance of alterior mini-string that is fed into the so-stated superstring that is not directly compatible with the interaction that exists between its directly corresponding permittivity that is formed by the activity of the said superstring and the directly corresponding impedance -- the latter of which is produced by the activity of the given arbitrary Fadeev-Popov-Trace eigenstate that is correlative to the said given arbitrary superstring. This alterior mini-string acts as a tumultuous core-field-density that works to cause the correlative given artibitrary superstring that is here being discussed to twist and "shimmer" in an annharmnonic manner that is not condusive to the functional operation of the directly corresponding Bette Action eigenmetric that inherently works to establish a homeomorphic orientation between a given superstring and its directly corresponding substringular counterpart.  When the activity of any given arbitrary Bette Action eigenmetric does not work at actually forming a homeomorphic-based differential geometry between any given arbitrary superstring and its counterpart, then, the Grassman Constant that would otherwise be formed between the so-stated superstring and its counterpart will not be maintained.  This lack in homeomorphicity will then work to cause the ensuing Regge Action eigenmetric to work at forming an orientation between the said superstring and its counterpart -- in so as to be able to work at forming a relatively second chance at forming some sort of a homeomorphic correlation between the Poincaire-based gauge-metrical activity of the so-stated superstring and its directly corresponding counterpart.  The just stated Regge Action eigenmetric works at doing this by acting as a projecting slope that the superstring and its counterpart move through over a relatively very transient Lagrangian -- that works over the course of the eluded-to gauge-metric -- in so as to form an optimum path for the so-stated given arbitrary superstring and its counterpart to be able to then possibly form a homeomorphic-based orientation in the "nick of time."  If that so-eluded-to shimmering of the superstring -- that is caused by the eluded-to alterior added mini-string that is both added to the Poincaire-based field of both the so-stated superstring and its counterpart & is also not condusive to the inter-relationship that is to exist between the fractals of the directly corresponding discrete energy permittivity and the fractals of its directly corresponding discrete energy impedance, which is caused by external pressures that act in a regional-based Gliossi manner upon the said superstring and its counterpart -- to where this makes both the so-stated Bette Action eigenmetric and the so-stated Regge Action eigenmetric unable to form the eluded-to orientation, then, the said superstring will immediately and spontaneously become tachyonic.  This will make the indistinguishably different Regge Action eigenmetrics scatter annharmonically over the course of the ensuing set of the directly corresponding group instantons that are correlative to the interaction of the said tachyonic superstring.

Part Three of the Eleventh Session of Course 16

A Njenhuis Klein-Gordan mechanism is an interaction that happens when transversel, radial, and/or spin-orbital tensors that are off of the Real Reimmanian Plane interact with a given arbitrary superstring of discrete energy permittivity at a tangent of normalcy that is orphoganal to the extra dimensionality of the Imaginary-based subspaces that are directly correlative to any pertainent given arbitrary case scenario.  For instance, let us say that a given arbitrary superstring has just become non-orientable.  The so-stated superstring is not able to be orientable during both the directly corresponding Bette Action eigenstate and the directly corresponding Regge Action eigenstate.  Under the just stated conditions, the said given arbitrary superstring will become tachyonic over the course of the ensuing iteration of group instanton that the so-stated superstring will be flowing into -- for over the course of one or more instantons. Since the superstring is to now become at least temporarily tachyonic in this case scenario, the ensuing one or more eigenmetrics of the Regge Action eigenstates that will be directly involved with the interaction of the said given arbitrary superstring with its envronment over a sequential series of instantons will be initially scattered annharmonically at the initial stage of such a perturbation of the so-stated superstring -- due to the said superstring that is here being discussed going from a Noether-based flow into a tahchyonic-based flow.  Those tensors that act upon the said superstring -- in the form of norm-state projections -- in so as to allow for the superstring to be able to succeed at its needed path at becoming tachyonic, will bear a subtended directoral basis that is Njenhuis in nature.  When the said superstring that is here becoming at least temporarily tachyonic is also undergoing a change in norm conditions -- known of as a Gaussian Transformation -- then, the activity of that substringular scattering that is involved with the eluded-to genus of the added condition of the Kaeler Metric being introduced into the activity of the here tachyonic superstring will be of an annharmonic nature. This annharmonic nature is involved with the here local intrusion of a Klein Bottle eigenstate, along with a geometrical-based need for a perturbation of that indistinguishably different Regge Action eigenstate that will need to "fidget" in order to accomodate the altered genus -- as to the format of how the directly associated superstring will move over the ensuing increment of time that is here correlative.  It is when a tachyonic condition that is directly involved with a superstring that is also entering into an eigenstate of the Kaeler Metric that is when there are both norm-state projections that are Njenhuis that interact upon the correlative superstring, as well as that there will here be a "fidgeting" of the directly corresponding indistinguishably different Regge Action eigenstate that is to take the "brunt" of the motion of the here newly developed tachyonic nature of the so-stated superstring that has just left from being of a Noether-based nature.  Yet, when a superstring remains, instead, of a Noether-based nature, then, when a Kaeler-Metric is introduced to a superstring that is to undergo a Gaussian Transformation, the directly corresponding scattering of the correlative Regge Action eigenstate is instead of a harmonic nature, since, here, the general nature of the flow of the so-stated superstring is, in this case, not perturbated out of this here said condition.  This scattering is directly related to the nature of the flow of the correlative superstring as it is projected through a Regge Slope eigenstate.  If the kinematic projection through such a slope is hermitian, then, it is being harmonically scattered.  Yet, if the kinematic projection through such a slope is Chern-Simmons in its basic nature, then, it is being annharmonically scattered.  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Two of the Eleventh Session of Course 16

The Regge Action is a gauge-metric that happens during the very ending of instanton.  A given arbitrary Regge Action eigenstate is scattered anharmonically in a condition that may be called a relatively perturbative Regge scattering when the directly corresponding superstring that is to go through the trajectory of the correlative Regge Slope is effected, in one manner or another, by one or more relatively Njenhuis-based  Klein-Gordan mechaism eigenstates -- in the form of tensoric norm-based projections that are not spontaneously caused by the general activity of a correlative Kaeler Metric.  Whereas, a harmonic-based Regge scattering is caused by the onset of a Kaeler Metric upon the core-field-density of a superstring that is about to begin to undergo a Gaussian Transformation -- when such an onset generally only involves Real Reimmanian-based tensors that act upon the so-stated superstring, in the form of tensors that have the capacity of being spontaneously caused by the general activity of a correlative Kaeler Metric.  This is on account of the condition that the introduction of the motion of a Klein Bottle upon the regional-based core-field-density that, appertains to the general field that exists in-between any given arbitrary superstring and its locus as to where its correlative Regge Slope is to subsequently happen -- is a perturbation in the so-eluded to regional field at the onset of a directly assoiciated Kaeler Metric (which is that activity of a Schotky Construction that most directly involves the activity that superstrings must go through in order to be able to reattain enough of a fractal of discrete energy permittivity so that the said superstrings may be able to remain as energy.) The consequent spatial rearrangements that happen via such a so-stated metric -- so that norm-conditions in the differentiatl geometry of superstrings may be able to perform their needed changes, so that motion may both persist and exist over time -- may be called a Gaussian Transformation.  Yet, if a Kaeler Metric is directly involved with a superstring that is to be tachyonic, then, its directly corresponding Regge scattering is then of an anharmonic manner.

Session 11 of Course 16, Part One

The bounds of a world-sheet -- as is traced by the mapping of a directly affiliated ghost anomaly -- is defined by where a superstring of discrete energy permittivity starts iterating, while then stops iterating, in a specific region, before it scatters after a set of iterations of group instanton in which the so-stated superstring of discrete energy permittivity is kinematically differentiating in over time.  This is to be considered in increments of the BRST metrical-based durations of group instanton that come before each individual eigenstate of the directly correlative Regge scatterings, that happen after each respective individual iteration of the eluded to eigenstates of BRST.  This is also to be considered, in this case, while the said superstring is moving kinematically in a Noether-based manner -- in so as to be an increment of a group metric that happens prior to any potential tachyonic propulsion that could possibly happen after the said condition of Noether Flow is terminated by the condition of the eluded-to superstring becoming non-orientable over time.  You see, every time that any given arbitrary superstring iterates over the course of every individual local duration of BRST -- the individual increments of BRST of which occupy a majority of each increment of instanton, that would here represent each sequential "fret" of those sequential series of instantons of which integrate in so as to form that flow of motion over time that works to form energy, the energy just eluded-to of which comes in discrete quantums of energy (these quantums of which come in integer amounts that are never fractional), to where the so-stated superstring will afterwords complete each of the eluded-to increments of instanton by undergoing the Regge Action.  This ensuing activity is immediate, if there is here no Kaeler Metric happening to the said given arbitrary superstring.  Yet, if there is a Kaeler Metric that is metrically Gliossi to the activity of the time-wise increments of the iterations of instanton that directly appertain to the kinematic motion of the so-stated superstring, then, immediately after each directly correlative and respective iteration of BRST -- that would thus appertain to the metrical flow of the said string, there is an eigenstate of the said Kaler Metric that is intially affectual, of which is followed by the directly prior eluded-to Regge Action eigenstate.  In cases of the latter-mentioned example, the given arbitrary eigenstate of the so-stated Kaeler Metric is equal in duration to the directly affiliated Regge Action eigenstate -- which means that here, the scalar-based duration of the so-stated Regge Action eigenstate will then be happening in half of what would be its regular duration.  The Regge scattering that I had mentioned earlier is the activity of the perturbation of a superstring, that happens right at the end of an individual local duration of any given arbitrary instanton that may be here considered.  When a superstring is orientable, it will then be formated to ensue in a quality of the nature of Noether Flow.  Yet, when a superstring becomes unorientable, then, it will then be formated to ensue in a quality of tachyonic flow.  Yet, this is only if the eluded-to superstring is both unorienable during the directly corresponding eigenstate of BRST and also unorientable during the directly corresponding eigenstate of the Regge Action.  If the torsioning of a superstring that is not orientable during a given arbitrary local duration of BRST bears certain Njehuis tensors that are not spontaneously normalizable enough to bear a condition of orientable quality -- for the directly corresponding core-field-density that exists in-between the said superstring and its counterstring -- during the correlative Regge Action, then, the genus of scattering that would then happen during the so-stated Regge Action will cause the so-stated superstring to remain at that point in gauge-metric as still unorientable, and thus, the said given arbitrary superstring will be tachyonic immediately afterword.  I will continue with the suspense later!  Sincererly, Sam Roach.

Part Two of the Very Next Addendum

The prior mentioned linear-based segments are subtended from the point to where these so-stated segments are directly connected to the correlative Fadeev-Popov-Trace eigenstate -- to the point to where these so-stated segments are directly connected to the correlative superstring of discrete energy permittivity, in any individual case scenario where there is a light-cone-gauge eigenstate that is of the said Kaluza-Klein topology.  The eluded-to supplemental delineation of the said mini-string segments that work to form the said eluded-to first-ordered light-cone-gauge topology that is of a Kaluza-Klein nature are barely "tractable", when this is considered over the course of any individual iteration of BRST -- where light-cone-gauge topology is metrically functionable.  Yet, such a light-cone-gauge distribution curves as according to the general local curvature of space-time-fabric at the Poincaire level of the delineation of the main core-field-density -- that exists directly in-between the so-stated Fadeev-Popov-Trace eigenstate and its corresponding superstring of discrete energy permttivity (in an individual case), to where such a linear-based delineation of the eluded-to mini-string segments that work to form the physical framework of the holonomic substrate of the Ward-Neumman sub-Hamiltonian operation, that exists here during the so-stated given arbitrary iteration of BRST -- is not positioned or delineated as a Wilson-based linearity, at any fret of what may be taken as a snapshot of such an individual basis of the said core-field-density operators, of which is  over the course of the gauge-metrics that happen during the so-stated duration of BRST.  Yet, the activity that I call the "Imaginary Exchange of Real Residue" works to form a sub-group metrical delineation, that would here work to average a morphological index of distributary delineation -- that works to form a sub-Sterling-based approximaation of a Wilson-based linearity, when among those eluded-to indices of main-core-field-density that are comprised of as the so-eluded to mini-string segments that are "plucked" in so as to refurbish the activity of the Rarita Structure.  I will continue with the suspense later!
Sincerely, Samuel David Roach.

The Very Next Addendum to the Ensuing Course About The Sixteenth Course

A Kaluza-Klein light-cone-gauge topology is that genus of inter-connective topological binding that works to connect any given arbitrary Fadeev-Popov-Trace eigenstate to its directly corresponding superstring of discrete energy permittivity (that is in the relative forward-holomorphic direction) in a supplemental manner, in such a manner in so as to make the eluded-to mini-string segments that operate in so as to form the main-core-field-density indices to bear a "tight" format of fractal modulus that is basically completely unlooped from within the Gliossi-based loci where these eigenstates of linear-based mini-string segments are subtended from where these so-stated segments are directly connected to the corresponding Fadeev-Popov-Trace eigenstate -- to up to where these so-stated segmensts are directly connected to the corresponding superstring of discrete energy permittivity -- in any individual case scenario where there is a light-cone-gauge eigenstate that is of the said Kaluza-Klein topology.  The eluded-to supplemental delineation of the said mini-string segements that works to form the eluded-to first-ordered light-cone-gauge topology that is of a Kaluza-Klein nature are barely "twitchable", when this is considered over the course of any individual iteration of BRST where light-cone-gauge topology is metricaly functionable, yet, such a light-cone-gauge distribution curves as is according to the general local curvature of space-time-fabric at the Poincaire level of the delineation of the main core-field-density that exists directly in-between the so-stated Fadeev-Popov-Trace eigenstate and its corresponding superstring of discrete energy permittivity, to where such a linear-based delineation of the eluded-to mini-string segments that work to form the physical framework of the holonomic substrate of the Ward-Neumman sub-Hamiltonian operation that exists here during the so-stated given arbitrary iterations of BRST is not positioned or delineaeted as a Wilson-based linearity.  To be Continued!
Sincerely, Sam Roach.

Part Two of the Just Started Session of Course 16

At this point, consider the directly associated Regge Slope eigenstate that corresponds to the given arbitrary superstring and its correlative counterpart, as the kinematic activity of the so-stated Regge Slope eigenstate happens during the gauge-metric of the integrand locant-based metric -- that would here be directly associated with the iteration of group instanton that corresponds to the portion of the duration of the said multiplicit instanton, that happens right after the corresponding metric or sub-metric of BRST -- during which the so-eluded to superstring is then here redelineated in such a manner in so as to be able to potentially "grasp" another chance to be able to be orientable.  This is if the case in the given arbitrary scenario, if it is that the given so-stated superstring was unorientable over the directly prior eigenmetric of that Bette Action index, that happened over the eluded to iteration of the simultaneous eigenstate of Polyakov Action -- the two different geni of kinematic activity mentioned here, of which happens at the same general duration when taken through the vantage point of a central conipoint in space.  Now, try to think about the Gaussian conditions of the differentiable subspaces of the said string, as it works to correspond to its directly associated superstring and its counterpart -- over the course of the iteration of the eluded-to eigenmetric of Regge Action.  The trajectoral path of the Regge Action is the Regge Slope.  If the supplemental delineation of those waves of core-field-density that are outwardly extended by the said prior kinematic activity of the directly corresponding Bette Action eigenstate -- as these densely distributed segments of mini-string, that bear a certain degree of torsionability, via the activity of the said eigenstate of the Polyakov Action -- will bear indices that work to orientate the directly affiliated Rarita Structure eigenstates that are most local to the activity that I am describing, on account of the "effort" of the said superstring, to bear a certain degree of renormalization with its counterpart.  If the resulting Gaussian of the just eluded-to inter-relationship works to bear an even function of wave-output --that extends from the general center-state, that may be subtended from in-between the so-stated superstring and its counterpart, over the so-stated Regge Action, then, there will be a genus of homeomorphicity that will then form between the said superstring and its counterpart, as this eluded-to phenomenology is pulled through the said Regge Slope eigenstate, which will make the superstring orientable.  If there is, instead, an odd function of wave output that extends from the so-stated center of substringular interaction, then, the superstring will remain as unorientable, and thus, the superstring will here become tachyonic.

Part one of the Next Session of Course 16 about cohomologies and topologies

The differences that exist between an orientable superstring and an unorientable superstring is based, in part, upon the conditions of normalization.  Take, for instance, a bosonic closed superstring. Consider the format or genus of the Poincaire differentiation of that just mentioned type of superstring, when this is taken along the topology of the Real Reimmanian surface of the eluded to holonomic substrate.  Now, consider the genus of the directly corresponding Polyakov Action eigenstate-based indices, that appertain to the said closed or bosonic superstring -- that is here a two-dimensional superstring of discrete energy permittivity.  At this point, consider the correlative Poincaire differentiation of the given counterpart of the directly corresponding two-dimensional superstring -- when taken along the topological surface of the holonomic substrate that works to define itself as the said substringular counterpart.  Now, consider the activity of the Polyakov Action eigenstate that here bears a Hamiltonian-based operation, in a fractaled tense, upon the so-stated counterpart of the directly associated two-dimensional superstring -- which will always be considered, as eluded to before, as happening during individual discrete iterations of group instanton.  So, when one is to take into consideration the activity of the correlative Bette Action eigenstate that works to directly correspond to the activity of the correlative Polyakov Action eigenstate -- the said Bette Action eigenstate, here, is simultaneous to the said Polyakov Action eigenstate, when taken through the vantage point of a central conipoint in space -- then, the supplemental basis of the Bette Action, in corroberation with the Polyakov Action, will work to determine whether any given arbitrary superstring that is here to be considered is either orientable or unorientable over the course of any given arbitrary iteration of group instanton that is being extrapolated.  I will explain more later, yet, a hint at whether or not a superstring is orientable or not during the Bette Action (any given isolated eigenstate of such, as operating upon any given superstring at its kinematic locus during instanton) is determined in part by both the condition as to whether or not the field that is subtended in-between a given arbitrary superstring and its counterpart that is in question is homeomorphic over the course of the directly corresponding duration of BRST that directly corresponds to the activity of the said superstring at the locus where it iterates during the said discrete implementation of BRST that this appertains to, and, whether or not the supplemental-based field networking that stems from the dual activities of the Bette Action eigenstate and the Polyakov eigenstate -- that are happening at the same gauge-metric through the vantage point of a central conipoint in space, works to form an even number of discrete relatively straight Njenhuis waves that off-shoot from the central locus where a given arbitrary superstring is interacting with its counterpart -- these Njenhuis waves of which work to stimulate the perpetual existence of the Rarita Structure.  Such a supplemental-based field may be simply thought, of, in part, as the result of a linearity that is formed from an interaction that happens in-between two core tangencies.  I will continue with the suspense later!
Sincerely, Sam Roach.