Part Three of Session Five of Course 19 -- The Klein Bottle and Orbifold Differentiation

Orbifolds come together or integrate -- in terms of the correlative Gaussian symmetry-based norm conditions, in so that these may work to form what primarily amounts to either a fractal of a magnetic field, or, a discrete magnetic field -- the initially stated so-eluded-to premise of which would amount to being of a relatively small Hodge-based index of a scalar magnitude of a fractal of quantum-based magnetism.  So, if one were to here consider one set of orbifolds or an orbifold eigenset -- the inter-relations that would here work to involve the Gaussian symmetry-based norm conditions of that so-stated orbifold eigenset, would work to form what primarily amounts to either a fractal of discrete magnetism, or, a relatively small quantum of discrete magnetism itself.  The conditions that would here work to help determine whether or not the said respective given arbitrary orbifold eigenset would here work to amount to either a fractal of discrete magnetism, or, a small quantum "package" of discrete magnetism, would then here be involved with the quantum of both the scalar amplitude of the Hamiltonian operator and the Hamiltonian operation that is in question, and, the Hodge-Index that would here be pertinent to the both the amount of orbifolds that would here be involved & the size of the directly corresponding orbifolds that would here be working to comprise the so-stated respective given arbitrary orbifold eigenset in question.  Such a magnetic-based operation of tendency is particle-wise primarily involved with the integration of the respective given arbitrary Fadeev-Popov-Trace eigenstates -- that are directly corresponding to the said orbifold eigensets in question, and such a magnetic -based operation of tendency is wave-wise primarily involved with the integration of the respective given arbitrary first-ordered light-cone-gauge eigenstates -- that are directly corresponding to the said orbifold eigensets in question.  This is due to the condition that magnetism is primarily involved with the fluctuation of discrete energy impedance.  The superstrings and their correlative counterstrings work to form the respective particle-based discrete energy permittivity and the respective wave-based discrete energy permittivity.  This is due to the condition that the orbifold-based integration of superstrings and their counterstrings work to form both the existence and the activity of the angular momentum of the Hamiltonian operation of an orbifold eigenset, over time.  So, the Fadeev-Popov-Trace eigenstates and their correlative first-ordered light-cone-gauge eigenstates of an orbifold work to form a fractal of a magnetic field, and, the superstrings and their correlative counterstrings work to form a fractal of an electric field.  Voltage is energy per charge, and thus, the fractal of a magnetic field may exist with the consideration of the integration of potentially as few as two consecutive group-related instantons -- whereas, current is charge per time, and thus, a fractal of an electric field needs to then involve a succession of considerabley more consecutive group-related instantons.  To Be Continued!  Sincerely, Sam Roach.

Part Two of Session Five of Course 19 -- The Klein Bottle and Orbifold Differentiation

An eigenstate of a fractal of a magnetic state may be viewed of as a discrete unit of the spin-orbital momentum of the composite of any given arbitrary superstring, its correlative counterstring, its correlative Fadeev-Popov-Trace eigenstate, and its correlative first-ordered light-cone-gauge eigenstate -- as may be extrapolated during one respective given arbitrary iteration of group-related instanton -- in which such so-stated physical states may be considered of as working to bear such a so-eluded-to homotopic relationship. The said superstring and its directly corresponding  counterstring work primarily as the Hamiltonian operators of one respective given arbitrary unit of discrete substringular angular momentum, and thus, the said superstring and its correlative counterstring act primarily as a fundamental fractal of an electric charge.  (Since electric charge is due to the processes of permittivity).  This happens, as such a so-stated superstring and its correlative counterstring are pulled along in the substringular -- over a successive series of group-related instantons.  The said Fadeev-Popov-Trace eigenstate and its directly corresponding first-ordered light-cone-gauge eigenstate, work primarily as the Hamiltonian operators of one respective given arbitrary unit of discrete substringular spin-orital momentum, and thus, the said Fadeev-Popov-Trace eigenstate and its correlative first-ordered light-cone-gauge act primarily -- as a fundamental fractal of discrete magnetic force. (Since magnetic force is due to the processes of impedance.)  -- as such a so-stated Fadeev-Popov-Trace eigenstate and its correlative first-ordered light-cone-gauge eigenstate, are pulled along in the substringular, over a succession of two or more consecutive group-related instantons.
To Be Continued! Sincerely, Sam Roach.

Part One of Session Five of Course 19 -- The Klein Bottle and Orbifold Differentation

An orbifold is a manifold of a group of superstrings, that operate in so as to perform one specific function.  An orbifold eigenset is a group of one or more orbifolds, that operate in so as to perform one specific function.  The  spin-orbital Hamiltonian-based wave-tug/wave-pull of an orbifold, works in so as to act as a quantum fractal of magnetic force -- as such a quantum index of spin-orbital Hamiltonian operation acts in a discrete manner, through a Ward-Caucy-based Lagrangian, over a successive series of group-related instantons.  The quantum tense of the Hamiltonian-based operation, of one of any given arbitrary kinematic-based orbifold eigensets -- that is both codifffereniable, codeterminable, and covariant, upon the holonomic substrate of what acts here as the Hamiltonian-based operand, that the said orbifold eigenset is acting through -- may be expressed as a discrete and integrable set of substringular members, that behave here as a fractal of a tense of a quantum of magnetic-based eigenstates.  These so-stated members, of which may come together in a discrete manner -- in so as to work to form a discrete and viable tense of an actual Real Reimmanian-based magnetism, over time.  It is this magnetic-based interaction, of any respective given arbitrary orbifold eigenset -- of which works to help to cause that needed propagation of the so-eluded-to set of supestrings, that come together in so as to do one needed substringular operation, in so as to work at forming the needed impedance -- via the directly corresponding light-cone-gauge quantization, that is taken in a discrete manner.  This happens, in so as to tend to work to allow for the continued motion of energy.  This, as well, happens, in so as to help in the process of energy to persist as being energy, in and of itself.  The needed angular momentum of the so-stated orbifold eigenset, works in so as to help create the needed fractal of an electrical field -- which is utilized in such a manner, that acts as a discrete operation -- that is above the Poincaire level, of a discrete operation of superstrings that are of discrete energy permittivity, -- while yet acting as a fractal of an electric field,  that is below the Poincaire level of any given arbitrary actual discrete electric charge.  This is due to the condition, that the angular momentum of any respective given arbitrary orbifold eigenset -- works to help form a quantum of a fractal of discrete energy permitttivity.  To Be Continued!  Sincerely, Sam Roach.

An Extra Aside To The Nineteenth Course -- The Klein Bottle And Orbifold Differentiation

Take into consideration any given arbitrary Klein Bottle eigenstate, that is about to go into the general group-metrical Fourier-based translation of the Kaeler-Metric.  Consider the correlative Higgs Boson eigenstate that is then to move the said Klein Bottle eigenstate through the so-stated Kaeler-Metric.  Here is some insight as to what the differential positioning of the so-stated Higgs Boson eigenstate is -- over the course of the said Fourier Transformation of the given arbitrary translation of Kaeler-Metric delineation.  Once the here relatively local Kaeler-Metric is about to commence, the directly corresponding Higgs Boson eigenstate goes from being an isoelliptoabelianoid that bears a dual appexing  that is flush from the relatively reverse-norm-to-holomorphic end to the relatively forward-norm-to-holomorphic end -- to bearing a directoral Laplacian-based theta wave-pull -- that is thence angled radially in the holomorphic or counterclockwise direction -- by a holonomic Ward-Caucy-based delineation of 22.5 degrees, when one considers that the general initial direction of the correlative Klein Bottle eigenstate is to then move in the relative holomorphic, or, in other word, in the general relatively left-bearing direction, over time, during the said Kaeler-Metric.  Here, the relatively phi-based topological wave-tug/wave-pull-based sway will vary, as is according to the metrical-gauge-based Hamiltonian operation -- that is imbued upon the holonomic substrate of the said composite of the correlative Klein Bottle/Higgs Boson bearing eigenstates.  Once the initial 96 iterations of the here relatively local Kaeler-Metric-related instantons have been succeeded, the correlative theta-based directoral-sway of the correlative Higgs Boson eigenstate, that works to move the correlative Klein Bottle eigenstate, will work at being pulled in a holonomic Ward-Caucy-based delineation by 45 degrees, in the relative theta-based directoral parameter.  This happens with the maintenance of a constant Ward-Caucy-based rho, that is in conjunction with the variable topological sway of the correlative Ward-Caucy-based phi directoral delineatoral parameterization -- causing the net perturbation of the theta-based topological sway, that is of the correlative isoelliptoabelianoid-based eigenstate structure -- to then be subtended from the initial Laplacian-based "straight-up-and-down" condition -- by 22.5 degrees of holonomic Ward-Caucy flushness, in the relative antiholomorphic or clockwise-based theta reparameterization -- given that the said correlative Klein Bottle eigenstate is to then move to the ensuing loci that are here to the relative right, over the course of the ensuing 95 iterations of group-related instanton, that are to be directly affiliated with the rest of the local Kaeler-Metric Fourier-based activity that I have been describing here.  To Be Continued!  Sincerely, Sam Roach.

Part Eight of Session Four of Course 19 -- The Klein Bottle and Orbifold Differentiation

Sometimes, when there is a perturbative interaction of a given arbitrary Klein Bottle eigenstate with those superstrings that are to have just entered the said respective given arbitrary Klein Bottle eigenstate in a Gliosis-based manner, over a correlative successive series of group-related instantons -- that would here involve one relatively local Kaeler Metric-based Fourier differentiable substringular activity, such a so-eluded-to Rayleigh scattering that would be to happen here -- in so as to work to initiate the so-eluded-to genus of perturbation that is to form from the so-mentioned hieghtened tense of a spurious substringular condition -- may often work to cause a tense of a tachyonic flow to at least work upon some of the said superstrings, that had here been acted upon by the said respective Klein Bottle eigenstate, in the so-stated perturbative manner.  In such a general manner, the Fourier-based activity of the said Klein Bottle eigenstate may often work to produce some superstrings to temporarily bear a tachyonic flow.  In the manner of as to how any respective given arbitrary Higgs Boson eigenstate may often work to guide the motion of a correlative respective Klein Bottle eigenstate -- in so as to work to help to cause the previously mentioned tachyonic flow, such a so-stated Higgs Boson eigenstate may then often work to help to cause certain tenses of tachyonic-based flow, in certain superstrings that may be extrapolated of as having to have temporarily left their directly previous condition of Noether Flow.
To Be Continued!  Sam Roach.

Part Seven of what is the Fourth Session of Course 19 -- The Klein Bottle and Orbifold Differentiatioin

Although the holonomic substrate of any respective given arbitrary Klein Bottle eigenstate is of the surface area-based region of a parallelepiped-like contour -- that is filled with norm-state-projections, and this holonomic substrate works to bear no orientifold-based construction as a physical "top" to such a "box" at its norm-to-holomorphic end, the Cohomological Mappable Tracing of such a "box" is A Semi-Toroidal Construction That Works To Bear A Respective Virtual Tense Of Mobiaty, at the Poincaire level that is to the so-eluded-to core-field-density -- of the said cohomological mappable tracing of the so-stated respective given arbitrary Klein Bottle eigenstate.
To Be Continued!  Sincerely, Sam Roach.

Part Six of Session Four of Course 19 -- The Klein Bottle And Orbifold Differentiation

The Fourier-based differentiation of the Higgs Action, often tends to help to stimulate superstrings of discrete energy permittivity to enter the Ward-Neumman bounds of the interior of any respective given arbitrary Klein Bottle eigenstate -- by moving any of such said individually taken Klein Bottle eigenstates into the substringular neighborhood of the so-stated given arbitrary superstrings, in a Yakawa-based manner -- in so as to place the said "bottle" in a relatively proximal spot, that is here located to the relative-forward-holomorphic direction of where the so-eluded-to discrete units of energy permittivity of this given case would here be working to bear a high probability of moving into, over the course of the ensuing iteration of BRST.  This here proximal placement of the said respective Klein Bottle eigenstate -- in a directly corresponding covariance to the relatively simultaneous placement of the directly affiliated superstrings of discrete energy permittivity -- that are to then enter the Ward-Neumman bounds of the said Klein Bottle eigenstate, this entry of which would here be enacted in a Gliossi-based contact to the interior of the so-stated Klein Bottle eigenstate, works to form a relatively abelian tendency of the said respective superstrings to then be naturally pulled into the said Klein Bottle -- during the ensuing gauge-metrical activity that is to happen in-between what would here be the immediately following iteration of the local translation of BRST, and the ensuing iteration of the correlative Regge Action.  Superstrings that enter the Ward-Neumman bounds of any respective given arbitrary Klein Bottle, are then spontaneously caused to bear a fractaled tense of a spurious pulsation-based mode -- due to the perturbative vibrational-based oscillations that are worked upon the so-eluded-to topological indices that would here appertain to the correlative holonomic substrate of the correlative substringular composition of the corresponding physical units of discrete units of energy of this given arbitrary case.
To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Five of Session Four of Course 19 -- The Klein Bottle And Orbifold Differentiation

As the holonomic substrate of any given arbitrary Klein Bottle eigenstate is working to bear a Yakawa Coupling-based interaction with its immediate surroundings, in a manner that is directly associated with both a transversel-based topological sway, a radial-based topological sway, and in a spin-orbital-based topological sway -- the so-eluded-to composition of the so-stated holonomic substrate of the respective given arbitrary Klein Bottle eigenstate, is pulled through a Lagrangian in a homotopic-based manner in a respective manner that is here of a Fourier-based translation that is both of a transversel-based directoral wave-tug/wave-pull, a radial-based directoral wave-tug/wave-pull, and in a spin-orbital-based directoral wave-tug/wave-pull, -- in so as to help to work in the formation of the respective given arbitrary template of the physical memory as to both the existence and the activity of the said holonomic substrate of the said Klein Bottle eigenstate of such a given case scenario.  As an ansantz, the physical memory of both the conglomerate existence and the activity of any respective given arbitrary Klein Bottle eigenstate -- is the cohomological format of the said Klein Bottle eigenstate.  The motion of any so-eluded-to given arbitrary Klein Bottle eigenstate, is mainly controlled -- at the Poincaire level that is local to the cite of the substringular neighborhood of the so-eluded-to resultant of the respective Fischler-Suskind-Mechanism -- by the Hamiltonian operation of what is known of as the Higgs Action.  Any respective given arbitrary Higgs Action eigenstate works to help control the drive of both the angular momentum and the spin-orbital momentum of any respective correrlative given arbitrary Klein Bottle eigenstate -- as such a composition of directly corresponding interactive orientifolds is brought both into and through the Fourier-based activity of any directly affiliated Kaeler Metric, over the directly affiliated group-metric, in which the correlative Fischler-Suskind-Mechanism is Gliossi to the functionable operation of a Gaussian Translation of superstrings of discrete energy permittivity, in so as to help to work at both causing the fractals of discrete energy to be locally re-attained at any specific general region, and, in so as to work to allow for the space that energy is to move through, to be less clogged at the directly corresponding correlative proximal Lagrangian-based paths.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

The Fourth Part of Session Four of Course 19 -- The Klein Bottle and Orbifold Differentiation

The norm-state-projections that will then here be trapped inside of the Ward-Neumman bounds of any specific respective given arbitrary Klein Bottle eigenstate -- as well as those superstrings, that act as indices that are placed in the Ward-Neumman bounds of the so-stated Klein Bottle eigenstate in a cyclical-based manner, per each individual group-related instanton, over the course of one relatively local group metrical-based duration of one set Kaeler Metric-based translation -- act as a set of a holonomic substrate of substringular phenomenology, that moves, per each relative transition of group instanton, in both a holomorphic and an antiholmorphic-based manner do to the "shaking" that is here involved, in so as to work to form a fractal of an electromagnetic resonation, that would here tend to be proximal to the said respective given arbitrary Klein Bottle eigenstate of any of such case scenarios.  This is particularly the case, when such a given arbitrary correlative Kaeler Metric is of the general manner of being as an example of a gauge-transformation.  As I will explain later in my writings, whenever there is a Calabi-based interaction that is of the metrical-based mode of being in the process of a Kaeler Metric, the directly corresponding Gaussian Transformation that then is here to follow will always tend to be of a gauge-transformation.  The norm-state-projections that work to comprise the initial interior of any of such so-stated Klein Bottle eigenstates, are harmonically ordered in a spatial manner, as is here in accordance with the Reimman scattering that is here to initially bring an order to the so-eluded-to substringular composition of the said given arbitrary Klein Bottle eigenstate.  The superstrings of discrete energy permittivity that act in so as to enter the interior of such a said composition of such an eigenstate, are here to initially re-contract to a maximum-based contraction, and, after such superstrings of discrete are pulled-out of the interior of such a said Klein Bottle eigenstate -- per each individually taken respective part of each of such iterations of group-related instanton, as is here right before each of such correlative individually taken iterations of the directly corresponding Regge Action eigenstates -- these are pulled out of such a said contractive mode, into their fully uncontracted shape, at each of such individually taken loci in which the Regge Slope is to be Gliossi to the topological substrate of each of such individually taken superstrings of discrete energy permittivity -- that may here be considered in any of such respective given arbitrary case scenarios.  During the metrical endpoint of each directly corresponding iterations of BRST -- that are to here be considered as happening before each individually taken iteration of the mode of one eigenmetric of one specific given arbitrary Kaeler Metric, any superstring of discrete energy that may be considered here, will -- at this point -- be Lorentz-Four-Contracted to the inverse of as to how it is encoded to be expanded in a Clifford-based manner, after the initial instant in which such a directly corresponding mode of BRST is here to be initially commenced.
Superstrings Tend To Always Be Lorentz-Four-Contracted To Their Encoded Degree Of Contraction, At The End Of Each Correlative Iteration Of BRST.
To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Three of Session Four of Course 19 -- The Klein Bottle and Orbifold Differentiation

When any given arbitrary Klein Bottle eiegnstate is being renewed into an indistinguishably different respective given arbitrary Klein Bottle eigenstate, over time, a set of zero-norm-state-projections work to act as a Hamiltonian-based operator -- in so as to help in the initiation of the formation of certain unique and specific ghost-based indices, to be able to exist at the general region of the here re-developing region of the directly corresponding cohomological-based locus.  The correlative Fourier-based activity of such a group-metrical Hamiltonian-based operation -- is to happen at the locus where the said respective given arbitrary Klein Bottle eigenstate is to be gradually recycled into an indistinguishably different Klein Bottle eigenstate -- at the region that is Gliossi to the eigenbase of the here relatively local Majorana-Weyl-Invariant-Mode, that is Yakawa to the tense of the correlative genus of conformal invariance, in which the proximal substringular neighborhood is bearing its here needed "revamping" of cyclic compositional indices.  This happens during the correlative group metric that is contingent to the here correlative Kaeler Metric eigenmetric -- that is to occur in an ensuing manner, right as the said respective given arbitrary Klein Bottle is to bear a recycling mode as to the homotopic condition of the local topological modulae, that is to be re-attained over a correlatively corresponding sequential series of group-related instantons.  The behavior of the so-stated set of zero-norm-state-projections -- that would here act in so as to help in the tendency of the recycling of the norm-state-projections, that are here directly corresponding to the here said respective given arbitrary Klein Bottle eigenstate, works as a group attractor -- that works to bring in a set of relatively forward-holomorphic norm-state-projections, to the cite of the said Klein Bottle eigenstate that is to be indistinguishably replaced.  This happens in so as to work to complete the "second-side, second-edge" of the Mobiaty of the cohomological-based mappable tracing, that is of the so-stated Klein Bottle eigenstate, over a successive series of group-related instantons.  Such positive-norm-state-projections, or, in other words, such relatively forward-holomorphic-norm-state-projections -- tend to work to help the holonomic substrate of the construction of the said given arbitrary Klein Bottle eigenstate -- that is to then bear a recycling of its norm-state quantifiers, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Two of Session Four of Course 19 -- The Klein Bottle and Orbifold Differentiation

The interior of the cohomological-based pattern that is formed by any respective given arbitrary Klein Bottle --is like a limited contorted "toroid" that contains both forward-holomormphic and reverse-holomorphic-based norm-states.  These multivarious norm-states of which tend to differentiate in a Fourier-based manner that is of a relatively harmonic manner, over time.  Yet, when the interaction of the norm-states, that exist from within the Ward-Neumman boundaries of the interior of the holonomic substrate of any respective given arbitrary Klein Bottle eigenstate, act in so as to differentiate kinematically in a relatively rigorous  annharmonic manner over time, the cohomological-based pattern that is formed by both the existence and the activity of the so-stated given arbitrary Klein Bottle eigenstate, eventually is perturbated into a Rayleigh-based scattering of those norm-state indices that had previously existed within the Ward-Caucy bounds of the said Kliein Bottle eigenstate.  This just mentioned general genus of activity of which may often cause the composition of the specific respective given arbitrary Klein Bottle eigenstate to be indistinguishably replaced, via those immediately surrounding eigenindices that may here work to both antiderivate the previous Klein Bottle eigenstate, while yet re-constructing a newly established Klein Bottle-based construction -- in a manner that works to bear a tendency of an indistinguishable difference.  This just-eluded-to recycling-based tendency of a "worn-out" Klein Bottle eigenstate into a newly established so-stated Klein Bottle eigenstate, works to conform to the overall tendency -- that is directly affiliated with the recycling of norm-state-projections, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of Session Four of Course 19 -- the Klein Bottle and Orbifold Differenitiation

The construction of any one particular holonomic substrate of a given arbitrary Klein Bottle eigenstate, is a composition of two orientifolds that are interconnected at the relatively norm-to-reverse-holomorphic end (at the relative bottom of such a construction) by a piecewise fitting rectangular enfoldment, that is brought together in so as to form a parallopiped-like substringular composition.  The relatively norm-to-forward-holomorphic end (the relative top of such a construction) of any respective given arbitrary composition of the holonomic substrate of a said Klein Bottle eigenstate is left open, over the course of any directly corresponding Kaeler Metric group-metrical-related duration, in which such a so-stated Klein Bottle eigenstate-based construction is to be utilized -- in so as to provide the operation of as being a substringular "tool" that is here to work at helping to provide the Fourier-based condition of allowing for those discrete fractals of discrete energy to bear a re-attainment of the state of being discrete energy itself, in so that discrete energy may then be able to exist and persist as the building blocks of energy, period.  The interior of the said holonomic substrate of a so-stated respective given arbitrary Klein Bottle is comprised of by norm-states that are initially (before the so-eluded-to energy that is to work at re-attaining its fractals of discrete energy are to enter its Ward-Neumman bounds) evenly spaced in those physical spatial dimensions, that are most easily explainable at the relative Poincaire level -- to the specific cites of the said norm-states that are based at the so-eluded-to multiplicit region of the said interior of such a respective given arbitrary Klein Bottle eigenstate.  An orientifold is a phenomenon that bears two planes (in this case, rectangular planes) that bear parallel surfaces that are of a Wilson-based linearity (this meaning actually straight, and not curving as space-time-fabric tends to curve).  Such a so-mentioned eigenstate of phenomenology shakes, per iteration of the directly corresponding Kaeler Metric in which discrete energy-based phenomenology is to enter it -- in a Gliossi-based manner.  As such a spin-orbital-based motion is achieved by the Fourier-based activity of the multiplicit Klein Bottle eigenstate, the said eigenstate is also moving transversally back-and-forth through that fitting Lagrangian, that is most fitting to the achievement of a directly corresesponding Gauusian-based Transformation (usually here being a gauge-transformation).  So, as I will explain later in my teachings, as such a phenomenology is being translated as such over time, the cohomological-based mappable tracing of the physical memory of such a Klein Bottle eigenstate will form a set of ghost-based indices, that work to form a morphological-based composition -- that appears to be anything but a parallelopiped-based structure, over time.  Whenever such a directly corresponding Gaussian-based Transformation is here to directly involve the scattering of light in a relatively Gliossi-based manner, then, such a Gaussian Transformation is then said to be a gauge-transformation.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Seven of Session Three of Course 19 -- the Klein Bottle and Orbifold Differentiation

That Fourier-based means, that would here work to involve the stabilization of any respective given arbitrary Klein Bottle eigenstate -- as such a just-mentioned eigenstate is moving through the progression of any directly correlative Kaeler Metric-based activity -- is known as the Fischler-Suskind-Mechanism.  More specificially, the said Fischler-Suskind-Mechanism is that mechanism of a norm-state-projection-based leveraging, that involves the Fourier-based motion of any respective given arbitrary Klein Bottle eigenstate, through those specific iterations of group-related instanton -- in so as to work to pull the so-stated Klein Bottle eigenstate into the various relatively proximal differential geometric positions, in such a successive series of Laplacian-based loci, in so that the covariant positioning of the so-stated Klein Bottle eigenstate when in relation to those superstringular phenomenology that are to enter the correlative Schotky Construction-based composition, is then here made optimum, for the condition of working in this case in so as to bring about the progressively additive re-attainment of those fractals of discrete energy, that are needed in order for discrete energy and thus energy to be able to both exist and persist, over time.  The said Fischler-Suskind-Mechanism, as well, tends to work to help prevent any excessive proximally local tachyonic propulsion, in those specific substringular regions in which such a mechanism of leveraging is being utilized -- in a Yakawa manner.  This tendency of prevention is here due to to the condition that the so-stated Fischler-Suskind-Mechanism works to help the directly corresponding respective given arbitrary Klein Bottle eigenstate, of any specifically related case scenario, to trap fewer superstrings of discrete energy permittivity than what would happen otherwise, if such a condition of leveraging were to happen in any other general manner, during the here pertinent Kaeler Metric eigenmetric.  This just-mentioned tendency -- plus the condition of the metaphorically "limp-shade" manner of any given arbitrary Klein Bottle eigenstate --- works to cause the composition of any respective construction of a correlative Klein Bottle eigenstate to exhibit a fractal of a "semipermeability," over the course of the directly pertinent Kaeler Metric.
I will continue with the suspense later! To Be Continued! Sincerely, Sam Roach.

Part Six of Session Three of Course 19 -- The Klein Bottle and Orbifold Differentiation

Those Wilson Lines -- that would here directly appertain to the basis of the composition of any respective given arbitrary Klein Bottle eigenstate, tend to behave, in part, like "limp shades" that may often be penetrated by an external force, over a successive series of instantons.  So, as a relatively stable Klein Bottle-related construction works to wobble in any given arbitrary Minkowski-based directoral combination  that includes up to a total of six Njenhuis additional spatial dimensions -- over the course of a tightly-bound Fourier-based translation of the here directly pertinent substringular members -- that would be local to the motion of the here respective given arbitrary Klein Bottle eigenstate of this specific case scenario, those external-based tensoric-related Hamiltonian operators that are to here interact with the said Klein Bottle eigenstate in an acutely Yakawa manner, will here bear a relatively non abelian-based wave-tug/wave-pull upon the so-stated Klein Bottle eigenstate of this case.  This so-eluded-to Njenhuis eigenbase of topological sway, of which is local to a set of tensors that are off of the Real Reimmanian Plane, will tend to be more limited at working to pull or tug at the construction of the said respective given arbitrary Klein Bottle eigenstate.  This tendency is on account of the condition that the so-eluded-to holonomic structure --that is here to bear the said Njenhuis eigenbase of a relatively non abelian wave-tug/wave-pull, that is projected at a relative distance upon the Gliossi-based phenomenology of the so-stated Klein Bottle eigenstate, would here be locally proximal to a substringular neighborhood that is then here situated off of the relatively Real Reimmanian Plane.  It would then follow here, that the directly corresponding cohomological eigenbase of that phenomenology -- that would here be applying the Njenhuis topological sway upon the said Klein Bottle eigenstate -- will here tend to bear a higher scalar degree of a Ricci Scalar-based index that is then of a Doubolt cohomology, than that phenomenology that would, instead, be more directly related to that cohomological framework that is directly corresponding to the physical memory that would here be formed by the holonomic substrate of the said respective given arbitrary Klein Bottle eigenstate of such a case,itself.
To Be Continued! I will continue with the suspense later!  Sincerely, Sam Roach.

Part Five of Session Three of Course 19 -- the Klein Bottle and Orbifold Differentiation

As to the specific how and the when that the specific kinematic activity, that is of any given arbitrary Klein Bottle eigenstate, is to wobble -- over the course of any respective given arbitrary iteration of group-related instanton, in which such a so-stated eigenstate is undergoing an iteration of one group-metrical course of the Kaeler Metric -- is dependent, in part, upon the multivarious external factors, that work to effect the environment of the internal Ward-Caucy conditions that are of the Fourier Translation of such a substringular composition.  This multivarious interconnection of external factors, that come together in so as to work to effect the kinematic activity of the said Klein Bottle eigenstate -- in a tightly-bound extrapolatable gauge-metric, that is involved with any one specific respective given arbitrary instanton in which such a Klein Bottle is here working in so as to provide the adequate substringular environment, so that the directly corresponding discrete quanta of energy that enter such a so-eluded-to composition may be able to re-attain the condition of working to bear their fractals of discrete energy -- so that there may be a continued existence of discrete energy or energy period -- is, in part, dependent upon both the holonomic-substrate-based existence and the Fourier-based activity of those substringular eigenmembers of the proximal local substringular region, when such a consideration, as well, works to include the consideration of those relatively loosely constructed Wilson Lines that work to form the framework of the holonomic substrate of the so-mentioned Klein Bottle of such a case, itself.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Four of Session Three of Course 19 -- the Klein Bottle and Orbifold Differentiation

Any given arbitrary Klein Bottle eigenstate, only kinematically differentiates as an operator of the Kaeler Metric -- during the course of each successive iteration of group-related instanton.  This is involved with the general Ward-Caucy-based conditionality, that any respective given arbitrary Klein Bottle eigenstate tends to remain in a relatively stable Majorana-Weyl-Invariant manner, during the course of any specific given arbitrary Kaeler Metric -- in which such a Shotky-based construction is being utilized as such -- when not including the wobbling that is involved with the immediately correlative Fourier-based activity of such a so-stated composition of eigenstate, that would be at the Poincaire level of the so-eluded-to composition, that works here in so as to help with the re-attainment of discrete energy.  Any respective given arbitrary Klein Bottle eigenstate may -- conditionally depending -- differetiate kinematically, either transversely, radially, and/or in a spin-orbital manner, over the course of any specific given arbitrary iteration of group-related instanton -- that is here directly corresponding to the coherent flow of any directly corresponding flow of a respective given arbitrary Kaeler Metric.  Again, the Kaeler Metric, per specifically related cite, is involved in a Gliossi-based manner, to a successive series of 191 consecutive iterations of group-related instanton.  Yet, when one is to here extrapolate the overall Kaeler Metric -- when including the whole involvement of the Fischler-Suskind-Mechanism, that is immediately coherent to the motion of any directly corresponding respective given arbitrary Klein Bottle eigenstate -- as it is moving in such a manner in so as to work to help in the re-attainment of discrete energy for any specific cite of superstrings within a substringular neighborhood -- is involved with 384 successive iterations of group-related instanton, -- 381 realatively abelian-based iterations that are Yakawa to the so-eluded-to locus, and 3 iterations that are here directly involved with the needed re-positioning of any correlative Klein Bottle eigenstate.  The just mentioned re-positioning is utilized, in so as to work to prepare the said generic Klein Bottle eigenstate of any such case, for a potentially ensuing Kaeler Metric.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Even More As To The Appendageing of Singularities

All unfrayed substringular phenomena that is kinematic per iteration of group-related instanton, is interconnected by the holonomic substrate of mini-stringular-based phenomenology.  So, the existence of homotopy always tends to work to involve the consistent interconnection of superstrings -- through the overall existence of unfrayed space-time-fabric -- by the topological entity of the so-stated mini-stringular phenomenology  This works to be the case, per each successive iteration of the said activity of instanton. So, as any set of one or more superstrings is undergoing a specific proximal cite of as to where these so-stated substringular phenomena are undergoing the Kaeler Metric -- the so-eluded-to "appendageing" of singularities, for each of such directly corresponding substringular phenomena -- is done in such a manner in so as to produce a multiplicit condition of the correlative mini-stringular phenomenology, that is most Poincaire to the core-field-density of the said discrete quanta of energy, that are to here work to re-attain their full potential, to be able to move in the direction of being brought into an optimum abelian Ward-Caucy state of differential wave-tug/wave-pull, that is to here be a fractal of a Hamiltonian operation that is to here work to  form the most locally present ideal conditions for the said discrete quanta of energy to be most free in their ability to be translated as eigenstates in their directly corresponding Hamiltonian operands of spatial freedom.
To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

More About Appendages of Singularity

Both the manner and the pulsation of what would here amount to what I have earlier named of as those "appendages" of singularity -- of which are topologically mapped upon the holonomic substrate of superstringular phenomena, this of which acts as the additive re-attainment of those fractals of discrete energy  that are integrated upon those substringular phenomena that would here be undergoing the Kaeler Metric -- happens in such a way in so that such "appendages" are here enacted upon the said substringular phenomena, in a manner that is metaphorically like an imprint of the resultant of certain exterial phenomena that is pressed upon the so-stated pliable phenomena, in such a way in so as to work to form the said appendageing of singularity, that is here necessary in order to work at causing substringular phenomena to re-attain their discrete quanta of energy.

Part Three of Session Three of Course 19 -- The Klein Bottle and Orbifold Diferentation

The specific behavior of any given arbitrary Klein Bottle eigenstate -- in the process of such a substringlular composition as acting in the group-metrical manner, that is intrinsic to the correlative Kaeler Metric-associated Fourier-based activity -- may vary, both per iteration of group-related instanton in which such a respective Klein Bottle eigenstate is being mobilized in, as well as per specific general locus in which such a directly corresponding Kaeler Metric is undergoing its translation, in so as to work at causing the proximal correlative discrete quanta of energy, that have been exhausted from bearing their needed "appendages" of singularity per so-stated iteration of group-related instanton -- to be able to re-attain those fractals of discrete energy, that these said quanta of metric-gauge-based holonomic substrate need to go through -- in order for these so-stated quanta to proceed at being sustainable discrete quanta of energy.  Both superstrings of the particle-based nature of discrete energy permittivity, their directly corresponding counterparts of the wave-functionability-based nature of discrete energy permittivity, their correlative Fadeev-Popov-Trace eigenstates of the particle-based nature of discrete energy impedance, and their directly corresponding light-cone-gauge eigenstates of the wave-functionability-based nature of discrete energy impedance -- are operational, as I have just respectively mentioned -- over the course of each successive iteration of group-related instanton.  Yet, the just mentioned discrete units of both the respective particle-based permitttivity and the wave-functionability of discrete energy permittivity, &, the respective particle-based impedance and the wave-functionability of discrete energy impedance -- tend to behave as added substringular commutative phenomenology to its immediate suroundings, that is made as integrable quanta to other of such related phenomenology -- that is pulled out of the course of the general tense of substringular pulsation, over the course of the respective given arbitrary iterations of the here directly corresponding generally unnoticed durations of Ultimon Flow.  To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

As To The Appendageing of Singularities

What I meant by the "appendageing" of singularities, in any given arbitrary case, is the specific mini-stringular norm-state projections -- that work to tie into the multivarious superstrings of discrete energy -- in such a manner in so that the here directly corresponding superstrigular phenomenology is perturbated, in either a harmonic and/or in an annharmonic manner.  This happens in so as to work to bear some form or another of a relatively Laplacian-based topological sway, that would here involve some sort of a fractal of an angular momentum-based wave-tug/wave-pull -- that is contingent to a directorial-based Hamiltonian operation, that may here be integrated with the other of such so-stated "appendages" -- to where the resultant cross between the overall fractal of angular momentum and the overall  fractal of spin-orbital momentum, will here work to help define the Ward-Caucy-based Ricci Scalar eigenbase of the so-eluded-to superstring.  This happens, as the said stringular phenomenology is interdependantly interacting with the correlative Rarita Structure eigenstate -- that is of such a respective given arbitrary case.  Such an interdependant interaction, will here work to help cause the said superstring to bear a discrete relationship to its local eigenbase of homotopic structure -- as the said superstring is moving as a Hamiltonian operator, over time, in the correlative respective lattice or manifold that the so-stated superstring is undergoing its kinematic differentiation in, in lu of the said superstring's directly corresponding Majorana-Weyl-Invariant-Mode, over time.
To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

An Aside To As To The Fractals Of Discrete Energy

So, here is the general gist of as to how discrete quantum-based increments of energy are pulled through the Kaeler Metric, in so as to re-attain those discrete fractals of both the particle-based genus and the wave-based genus of both discrete energy permittivity and discrete energy impedance -- this process of  re-attainment of which is necessary, in order for the correlative discrete energy to be able to sustain the condition of being the multiplicit holonomic substrate of the said quantum eigenbase of energy.  A superstring, its counterstring, its correlative Fadeev-Popov-Trace eigenstate, and its correlative light-cone-gauge eigenstate, are pulled out of BRST into the Minkowski-based surface of the relatively norm-to-forward-holomorphic cite -- of the locus of a directly corresponding Klein Bottle eigenstate.  Upon entering the Ward-Caucy bounds of the said Klein Bottle eigenstate, the so-eluded-to eigenstate shuffles around eight times back-and-forth at its relatively Laplacian-based locus, during the relative ending duration of an iteration of group-related instanton.  The Klein Bottle, as a holonomic substrate, bears an intrinsic Wilson linearity in its physical structure.  As the so-stated Klein Bottle eigenstate of the here so-mentioned example of this given arbitrary case, shuffles back-and-forth eight timed each (a total of 16 overall topological sways of the whole said Klein Bottle eigenstate), there is just the needed "appendage" of singularity amended upon the quantum entity of both the respective discrete energy permittivity -- in terms of both the particle and the wave-based function of quantum energy, -- as well as upon the quantum entities of both the respective discrete energy impedance in terms of both the particle and the wave-based functions of quantum energy, to where one of the discrete fractals of discrete energy -- in terms of both the particle and wave-quantum needs for permittivity and the particle and wave-quantum needs for impedance, may then have here  imbued upon the topological-based structure of their general holonomic substrate, -- one discrete quantum of energy.  This happens over the course of the needed 191 successive iterations of group-related instanton, in which the superstrings that are directly involved with the correlative Kaeler Metric are Gliossi to the so-stated Klein Bottle eigenstate of this here respective given case.  The Kaeler Metric happens, so that each discrete quantum of energy that is to be needed to undergo this said group metric -- may go back to becoming fully equipped with its necessary fractals of discrete energy -- so that energy may persist upon being energy.  To Be Continued!  Sincerely, Sam Roach.

Part One of Session Three of Course 19 -- The Klein Bottle and Orbifold Differentiation

Did you ever wonder how any given arbitrary Klein Bottle eigenstate -- as being put together in the manner of a Schotky Construction -- could be physically maintained in the substringular, without bearing any significant substringular perturbation acting upon it, in such a manner in so that a Njenhuis-based Klein-Gordan-Mechanism could spontaneously here be working upon it in a viabley perturbative manner, over time?  The Klein Bottle -- as being put together as I have described in my blog, as in the manner of the Schotky Construction -- differentiates in a Fourier-based manner per each succeeding iteration of group-related instanton.  Such a so-mentioned Fourier-based differentiation happens in both a transversel-based manner, a radial-based manner, and also in a spin-orbital-based manner -- via those Ward-based coniaxials, of which here work to define the spatial structure of any respective given arbitrary Klein Bottle eigenstate, over a successive series of instantons in which the said eigenstate is moving through what is known of as the Kaeler Metric.  In so long as the correlative discrete energy that is involved here, is only of a Noether-based flow over a successive series of group-related instantons, both those superstrings of discrete energy permittivity and also those Fadeev-Popov-Trace eigenstates of discrete energy impedance, that enter any respective specific given arbitrary Klein Bottle eigenstate, through each succeeding iteration of the directly corresponding Kaeler Metric -- in which such quantum eigenstates of discrete energy are here re-attaining their fractals of discrete respective permittivity and impedance, are pulled into the here directly associated given arbitrary Klein Bottle, in a methodical-based manner -- in so as to undergo the re-attainment of all of their fractals of discrete energy that these need, in order to be fulfilled as being the respective discrete energy permittivity and discrete energy impedance, after the succession of the directly corresponding individually taken eigenmetric of the said proximal Kaeler Metric.  This activity of the Kaeler Metric, as well, works to cause both the wave-functionabiltiy of discrete energy permittivity as is in counterstrings -- and also causing the wave-functionabililty of discrete energy impedance as in light-cone-gauge eigenstates, to re-attain their discrete fractals of their intrinsic entity -- in so that both the particle-based nature and the wave-based nature of discrete energy -- may remain as a continual existence of energy, over time.
Later, I will discuss as to how the so-eluded-to motion of any respective given arbitrary Klein Bottle eigenstate works to cause such a said re-attainment.
To Be Continued!  I will continue with the suspense later! Sincerely, Sam Roach.

Part Ten of Session Two of Course 19 -- The Klein Bottle and Orbifold Differentiation

Take an extrapolation of as to the substringular scenario that I metaphorically painted, over the "course" of my last post.  Such a multi-angled wave-tug/wave-pull that I had pictured with words in that post, will here tend to work to overcome part of the fractal modulus that is directly associated with the here proximal light-cone-gauge eigenstates -- that are of the so-eluded-to general substringular locus of this particular case.  Such a tendency often tends to work in the direction of increased entropy,  over time.  Yet, the interactivity of neutrinos -- that may often work upon a respective given arbitrary general substringular locus -- can, at times, work to act as a kinematic Fourier-based operation, that may often tend to be able to repair part of that detriment -- that is often associated with that general genus of perturbations that are here directly associated with a relative increase in the local eigenbase of entropic substringular-based metric-gauge-based eigenstates.  This latter-mentioned tendency, is here, partially due to the condition -- that any respective given arbitrary neutrino is a constantly kinematic fermionic operator of an orbifold eigenset -- that behaves in such a manner, in so that it bears both partially hermitian and partially perturbative singularities, that act in so as to work at forming a holonomic substrate, that is of a Njenhuis tense of being of a "Yau-Exact" d-brane --when this is taken in terms of its composition, even though such a genus of an orbifold eigenset tends to behave as if it were actually a p-brane.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.