The Third Part of Session 10 of Course 19 -- The Klein Bottle and Orbifold Differentiation

If any given arbitrary sub-atomic particle acts as an orbifold eigenset, that works to bear a core-field-density via its respective Laplacian Transformation -- that exists as an F-field, in time and space -- then, if the directly corresponding spatial parameters of dimensionality that work to bear both a respective given arbitrary length, width, thickness, plus a Njenhuis tensoric spatial parameter of dimensionality -- that is correlative to an orbital-based coniaxion, then, there will resultantly tend to be no added Njenhuis tensoric spatial parameters of dimensionality --  that would otherwise be respectively corresponding to either: an added Gliossi-oriented spin-based coniaxion upon the holonomic substrate of the said F-field at the Poincaire level, an added Gliossi-oriented radial-based coniaxion upon the holonomic substrate of the said F-field at the Poincaire level , nor, would there be a respective corresponding added Gliossi-oriented transversel-based coniaxion upon the holonomic substrate of the said F-field at the Poincaire level, each of which would then act (as I have said, if this were Not directly of the nature of an F-field) in so as to behave as an individually taken Njenhuis tensoric spatial parameter of dimensionality, in time and space.  This is because of the respective given arbitrary situation, in this case, that we are dealing with a postulative F-field, and, an F-field only works to describe a Laplacian-based sub-atomic field that would tend to directly involve four spatial parameters of dimensionality -- over the course of the said Laplacian-based set of conditions. Yet, if one were to consider the said orbifold eigenset as, instead, differentiating over a Fourier-based transformation, over time, then, if the so-stated orbifold eigenset were to move into a perturbative environment, that would then involve an overt alteration in its Gausssian-based eigenbase of the index of its correlative Majorana-Weyl-Invariant-Mode -- then, the so-mentioned F-field would then possibley be moving through a Lagrangian, in the process of the holonomic substrate of the said F-field acting as a Hamiltonian operator moving through its correlative Hamiltonian operand, work to bear an external decompactification of spatial dimensionality -- that would then help the said F-field to bear a potential spatial orientation with either a spinor-based coniaxion, a radial-based coniaxion, and/or a transversel-based coniaxion -- as the so-stated F-field is to move in a kinematic manner, over time.  Such coniaxions that I have just mentioned, may be thought of as a tense of cyclic permutative indices of decompactification.  Yet, the Poincaire-based presence of such permutative indices would theoretically be of a relatively transient nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Two of Session 10 of Course 19 -- The Klein Bottle and Orbifold Differentiation

The protons of any given arbitrary atom, tend to be theoretically shaped in a basically parabolic manner -- when this is taken in a Laplacian-based manner.  For those atoms that work to bear the existence of neutrons as well, in the nucleus of the said respective atoms -- the so-stated neutrons, as well, also tend to be theoretically shaped in a basically parabolic manner -- again, when this is taken in a Laplacian-based manner.  If one were to spatially integrate one added so-eluded-to spatial parameter of orbit, to the dimensionality of the so-stated tendency of the nucleons of an atom -- that is, if one were to spatially integrate one Njenhuis-based tensor, in the form of an orbital-based coniaxion, to the spatial parameters of dimensionality of the said theoretical parabolic-based topological-based contour -- that is of the so-mentioned nucleons of any respective given arbitrary atomic structures, that have been eluded-to in this post, then, one would get a topological contour that would be of a four-dimensional spatial entity, that may here be described of as a genus of a set of given arbitrary multiplicitly taken F-field-based structures.  Such F-field-based structures that I have mentioned here, are described of in this respective given arbitrary case -- in terms of their differential clause as being in a timeless-based orientation.  This is due to the condition, that any holonomic substrate of topological-based phenomenology -- that exists in the form of an F-field, will bear a minimum of four spatial parameters of dimensionality -- in any minimum Fourier-based Transformation, in which such a so-stated F-field is differentiating in a kinematic manner, over time.  Any F-field that works to indicate the existence of a core-field-density, that is Gliossi to the directly corresponding holonomic structure, at the Poincaire level -- that would here consist of a set of superstrings, that operate in so as to perform one specific function, is an orbifold.  So, any respective given arbitrary proton, and, any respective given arbitrary neutron, when individually taken, exist as each working to bear the existence of being of an orbifold eigenset -- that will tend to exist at the general center, or, in other words, at the nucleus, of the respective atom -- in which such so-stated protons and so-stated neutrons are tending to be existing at -- over their correlative tense of a correlative Majorana-Weyl-Invariant-Mode.  (This is the tendency, in so long as their is not a directly appertaining mode of radioactive decay, that is then occurring to the directly appertaining atoms in question.)

I will continue with the suspense later! To Be Continued!  Sincerely, Sam Roach.

The First Part of Session 10 of Course 19 -- The Klein Bottle and Orbifold Differentiation

If one were to make a supremum of a postulative point particle -- one may then be able to get a postulative sphere, in a respective given arbitrary case scenario.  Both protons and neutrons are nucleons.  Nucleons are examples of F-branes -- these of which may be described of as existing in what may then be termed of as F-fields -- that differentiate in their respective Laplacian and Fourier-based fields in time and space.  The existence of F-fields may often be considered as being in the form of manifolds, or, in other words, in membranes or the so-stated "branes."  A superstringular manifold is a configuration of superstrings of discrete energy permittvity -- that have both the characteristics of bearing a fractal of electrical-based field and as well as bearing a fractal of magnetic-based field, when such a consideration is then working to consider the genus of a membranous manifold to be of either an F-field, a d-field, a p-field, etc... .  The premise of the existence of a given arbitrary field -- as existing to form the fractal-based existence of both an electrical-based field and a magnetic-based field -- is the manifested characteristics of what I have termed before as being of an orbifold eigenset.  An orbifold is a set of superstrings that operate in so as to perform one respective given arbitrary function.  An orbifold eigenset is a set of orbifolds that operate in so as to perform one respective given arbitrary function.  So, an orbifold eigenset is a manifold, or, a membrane of superstrings -- that have come together in so as to form both a fractal of an electrical-based field, as well as a fractal of a magnetic-based field -- that then operates in so as to work together as being of one overall "brane" or manifold, that tends to be of either an F-field, a d-field, or, of a p-field, as such an overall field or manifold is to act as a membrane of the here correlative superstrings of discrete energy permittivity, over time.  The fractal of a magnetic field is more directly involved with permittivity than impedance.  Therefore, it is the superstrings and their correlative counterstrings themselves that work to make-up an orbifold, that are more directly associated with the activity of an orbifold.  (Superstrings form the pointal-basis of the functionability of discrete energy permittivity, and, their correlative counterstrings form the wave-basis of the functionability of discrete energy permittivity.)  And, it is the directly corresponding Fadeev-Popov-Trace eigenstates as well as the directly corresponding light-cone-gauge eigenstates -- that work here to act as the respective pointal-basis of the functionability of discrete energy impedance and the respective wave-basis of the functionability of discrete energy impedance -- that are directly tied to the so-stated superstrings, that work to form the electical-based fields of their directly affiliated orbifolds.

Part Four of Session 9 of Course 19 -- The Klein Bottle and Orbifold Differentiation

The activity that is directly associated with the duration that happens during what I term of as the "space-hole," works to help allow for those mild re-connections to be able to happen to the multiplicit condition of homotopy -- so that those adjustments may be able to be made, so that those directly affiliated tenses of differentiation, that are correlative to the Gaussian normalization of superstrings as these are taken interdependently among the discrete quanta-based increments of substringular entities that inter-relate between each other -- may be brought into an ensuing iteration of group-related instanton (after the initially ensuing instanton-quaternionic-field-pulse-mode), that would then work to involve a correlative general condition of homotopy -- to where the directly associated quanta of discrete energy will then be able to both not be intruding upon each other, as well as this working to allow for the norm-based relations of substringular phenomenology to bear their encoded norm-based relationships, as this would tend to be happening as is according to the multiplicit delineatory indices, that work to pull the then initiated displacement conditions, that are then likewise imbued upon the all together group-related general eigenbase of what may be here described of as the forging of the inter-relative continuation of the activity of discrete energy. In the process, the activity of the inter-relationship of the "space-hole" with what I term of as the Bases of Light, works to bring the multiplicit Klein Bottle -- the summed up relationships of each Klein Bottle eigenstate that is to inter-play with superstrings that are to partake of any then ensuing Kahler-Metric -- into a spatially proximal differential locus, with those strings that need to work to re-attain those fractals of discrete energy quanta, in order for actual discrete energy quanta -- both the pointal-functional and the wave-functional eigenbases of discrete energy perimittivity, and the pointal-functional and the wave-functional eigenbases of discrete energy impedance -- to be able to remain as operational as holonomic substrate-based eigenstates of discrete energy quanta, so that energy may then be able to both persist and exist.  In case you wondered, with the way that I generally term of as a duration of actual "time," is a duration that is of a Real-based nature -- that would here work to involve a sequential series of instantons.  So, the Njenhuis part of Ultimon Flow & those gauge-metrics that happen in a more brief nature than an iteration of instanton, are not metrically comprised of an integration of discrete time.  (The first part of what I described of in the last sentence is outside of Real-based time, while, the latter part of what I described of in the last sentence is from within a fractal of actual time.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Three of Session 9 of Course 19 --- The Klein Bottle and Orbifold Differentiation

All space that is made kinematically differentiable upon, during each successive series of the iterations of group-related instanton, works to include at least some directly corresponding relationship with the general Real Reimmanian eigenbase of time -- since the general Real Reimmanian eigenbase of time is the so-eluded-to successive series of group-related instantons that travel through their correlative Hamiltonian operands.  Yet, the action of the generally unnoticed cycling of Ultimon Flow -- which includes both the cycling of substringular phenomenology through both the world-tubes as well as through what I term of as the Main Heterotic Stringular Fabric, the space-hole -- of which happens during what I term of as the Bases of Light happens to happen, and, the instanton-quaterionic-field-pulse-mode -- does not happen during the so-stated successive series of the iterations of group-related instantons, since this happens outside of the general Real Reimmanian eigenbase of time.  So, superstrings of discrete energy permittivity and their correlative quanta of discrete energy impedance ( of which works to include both the particle-based functionability and the wave-based functionability of those quanta of space-time-fabric, that work to form each individual overall quanta of discrete energy in time and space), iterate as individual pulsations of Hamiltonian-based operation -- in such a manner in so that the integration of such pulsations will here work to form the spontaneous successive series of the respective Hamiltoniain indices of individual substringular "packages", that come together per each of such so-eluded-to substringular delineations, in so as to form what we perceive of as the flow of actual viable energy in time and space.  The actual viable energy in time and space, happens, in what may be described of as the phenomenon of  Real-based time, while, the generally unnoticed durations of Ultimon Flow, happen in what may be described of as the phenomenon of Imaginary-based time.  The just eluded-to Njenhuis eigenbase of time, functions in so as to coordinate the encodement of the substringular -- with the resultant sequences of the multiplicit substringular delineations, that are extrapolatable over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part Two of Session 9 of Course 19 -- The Klein Bottle and Orbifold Differentiation

When one is to take a supremum of a line of point particles, that are of a relatively non-kinematic eigenbase of Fourier-based Transformation -- one may then potentially get a postulative sphere that would then bear an additive spatial parameter of dimensinonality, that would here potentially be of a tensoric spatial dimension, that would directly appertain in this given arbitrary case to a spinor-based coniaxion --  that could here be attributed to the spinning of the so-stated spherical phenomenology of this scenario, happening here around the conformally invariant central conipoint of the directly associated coniaxial, of which is correlative to the physical existence of the holonomic substrate -- that may here be described of as the said spherical-based entity of this given arbitrary case scenario.  The here additive spatial parameter of tensoric dimensionality, that is directly associated with the said spinor-based coniaxion of the directly previously mentioned case, would then be of a relatively minimal Njenhuis-based nature -- since the condition of four spatial dimensions, works to involve one more spatial parameter of dimension than what is generally conceived of in a more macroscopic manner -- yet here only, in so far as an f-field is concerned.  An f-field may be typified of as the spatial dimensionality of the nucleus of an atom -- it works to concern the existence of four spatial dimensions plus time.  This would then be able to work to explain the existence of the first four relateable spatial dimensions that exist at the atomic and/or at the subatomic level, as being what may be deemed of as four relatively extended or stretched-out dimensions -- that are not of a nature that may be overtly conceived of as curled-up.  Yet, when one works to conceive of the existence of additional spatial parameters of dimensinonality -- one will then run-across physical dimensions that tend to be of more of a curled-up nature of dimensionality.  This curled-up nature would work to describe some of the content of both d-fields and p-fields.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

Part One of Session 9 of Course 19 -- The Klein Bottle and Orbifold Differentiation

If one were to take a supremum of a postulative point particle -- one could tend to get a theoretical sphere as a resultant, since a sphere has incorporated into it three more spatial dimensions than an initially stated point particle.  If one were to take a supremum of a postulative sphere -- one could tend to get a theoretical spherical shape that would have three added spatial dimensions, these three dimensions here being both a spinor-based tensoric spatial parameter, that would here be directly associated with a spin-based coniaxion, an orbital-based tensoric spatial parameter, that would here be directly associated with an orbital-based coniaxion, and, a radial-based tensoric spatial parameter, that would here be directly associated with a radial-based coniaxion -- these so-stated spatial-based parameters of dimension, that would be additive to the initially so-stated spherical-based shape of this given arbitrary example, of which would be both codifferentiable, codeterminable, and covariant to the kinematic Hamiltoniain operation of the said initially said sphere of this respective given arbitrary case scenario.  Again, a supremum is the condition of the activity -- that is directly associated with the integration of three added spatial dimensions, to any initially given arbitrary case in point.
To Be Continued!  I will continue with the suspense later!  Sincerely, Sam Roach.

Part Three of Session 8 of Course 19 -- The Klein Bottle and Orbifold Differentiaton

Let us say that one were to double supremumize a postulative sphere,  -- that worked to bear an initially added spatial parameter of dimensinoality, that would here be of a radial-axion-based manner.  Let us than say that one were to double supremumize a postulative sphere -- that worked to bear an initially added spatial parameter of dimensionalilty, that would here be of an orbital-axion-based manner.  Let us then say that one were to then double supremumize a postulative sphere -- that worked to bear an initially added spatial parameter of dimensionality, that would here be of a transversel-axion-based manner.  A supremum works to add three spatial dimensions to an extrapolated phenomenology.  So, a double supremumization works to add six spatial dimensions to an extrapolaed phenonology. Let us now consider a postulative integration of all three of theses ten dimensional spaces -- these spatial parameters of dimensionality, of which would here work to involve a Hodge-based adding of all of the resultant dimensional-based indices, as in the form of a compactification of all of the directoral-based topological sways that would here be necessary, in so as to work to form a potential extrapolation of an orbifold that would then be existent in a Fourier-based manner in 30 spatial dimensions plus time -- in any kinematic-based setting in which such a so-eluded-to extrapolation of an orbifold would then be moving through a discrete Lagrangian, through its here directly corresponding Hamiltonian operand, over the respective given arbitrary time period in which such an eluded-to extrapolation of a respective given arbitrary set of superstrings that operate in so as to perform one specific function would exist as such.  Now, let us say that a perturbative substringular force were to form a then resultant exterial tensoric topological sway -- that would then work to pull as a Minkowski-based Njenhuis wave-tug-wave-pull, that would cause a torsional-based rocking of the initially so-stated 30 spatial dimension-related extrapolated orbifold-based phenomenology. -- as the said orbifold that I have here denoted as potentially existent, would be moving in time and space, through a then resultant Njenhuis Hamiltonian operand that would work to bear a Doubolt cohomology -- that would then be spontaneously existent in the relatively proximal field that is of the directly corresponding Majorana-Weyl-based field, that would be directly related to the relatively locally cyclically permutative indices, over time. The then resultant Fourier-based covariant, codeterminable, and codifferentiable space -- that would directly appertain to the correlative Ward-Caucy conditions of the combined existence and motion of the so-eluded-to orbifold eigenset of this given arbitrary case -- that would then work to involve a 32 spatial parameter-based dimensionality, over the correlative successive series of group-related instantons, in which such a said orbifold eigenset would be functionable as I have here described.  This here eludes-to the condition -- that an individual set of parallel universes works to involve a realm of 32 spatial dimensions plus time.  (A spatial dimension is Not to be directly confused with a layer of reality or a parallel universe.)  This would here correspond to the condition -- that an individual set of parallel universes works to bear an overall Minkowski space of a total of 26 spatial dimensions plus time, plus, an additional 6 Njenhuis-based dimensions, of which works in so as to complete the  "second-side, second-edge" of the Mobiaty of space-time phenomenology.  This works to make space-time-fabric of more of a volumed space than of a flat space, as the fabric of space and time is completed in its Laplacian-based flow, over time.  To Be Continued!  Sincerely, Sam Roach.

The Next Part of Session 8 of Course 19 -- The Klein Bottle and Orbifold Differentiation

If one were to majorize a basic sphere that had an added spatial parameter of dimensionality, of which would here directly appertain to the addition of a tensoric orbital axion, as a given arbitrary postulate of what could exist in this given case in the substringular -- one would then have here, in this arbitrary case, a sphere that could then exist as appertaining to it then bearing two additional tensoric axions -- in the form of a physically extrapolated space, that could here have a spatial orientation that would have an added tensoric spinor-based axion and an added tensoric radial-based axion, that would then be ammended to the originally mentioned orbital-based sphere of the said initial conditions of this respective given arbitrary case scenario.  If, instead, one were to majorize a sphere that had two initially added spatial parameters of dimensionality, of which would here directly appertain to the initial existence in this respective given arbitrary case of both a tensoric orbital-based axion and a tensoric spinor-based axion -- one could then get, as a resultant extrapolation -- a sphere that would then work to bear the then Gliossi-based presence of both a tensoric orbital-based axion, a tensoric spinor-based axion, a tensoric radial-based axion, and, as well, the presence of a transversel-base axion, with the latter two of such tensoric axions being made present by the process of the just mentioned process of the majorization of the so-stated initial postulation, that was here implied in the earlier part of this sentence. These last two posts of which elude-to the substringular existence of ten spatial dimensions plus time for photons -- as existent in any respective given arbitrary p-field -- of which woulf then be the minimal number of spatial dimensions that would exist for small particles that would then tend to move in such a p-field, as would be the case in any actual limited Fourier-based Transformation in which any of such respective given arbitrary individually taken orbifold eigensets that would exist spatially in a p-field, would bear a directly corresponding existence in, over any alloted given arbitrary time, as such a so-eluded-to particle would then exist as such in the said p-field, as a general tendency in any of such respective given arbitrary case scenarios.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam.

Part One of Session 8 of Course 19 -- The Klein Bottle and Orbifold Differentiation

Let us say that a majorization was the process of double integrating the spatial parameters of a given arbitrary initial phenomenology -- this being done without an alteration in the directly corresponding time-based integrand, this said spatial alteration of which would be correlative to the change in the supposition of the Ward-Caucy-based conditions of such a respective given arbitrary case scenario. So, if one were to majorize the state of a point particle-based phenomenology in time and space  -- one would get, as a result in this given arbitrary case, a basic planar-based phenomenology in the here renewed postulation of the substringular.  If one were to majorize a basic linear-associated phenomenology from an initial of such a so-eluded-to postulation -- one would get, as a result in this given arbitrary case, a parabolic phenomenology (often, of a spherical phenomenology) in time and space.  If one were to majorize a planar phenomenology from an initial postulation --one would get, as a result in this given arbitrary case, a parabolic entity that is to here bear, let's say, an orbital tensor in time and space (as may be denoted by the extrapolation of an added orbital-based axion here).  If one were to have majorized a parabolic-based configuration from an initial postulation, or, in this case, if one were to majorize a spherical-based configuration from the so-stated initial postulation -- one would get, in this given arbitrary case, a sphere with the two added tensoric spatial entities in time and space, that would here directly appertain to the addition of both a spinor-based axion and an orbital-based axion, in the so-eluded-to changed consideration of the substringular -- this being the denoted spatial alteration, that may be considered here as a change in the postulation of the spatial parameterization of the so-stated initial conditions of the holonomic substrate -- as going from the so-eluded-to phenomenology that was initially of the said basic spherical-based nature, To the so-eluded-to changed extrapolation of the Ward-Caucy-based conditions that would be of this eluded-to case scenario in the substringular.  I will continue with the suspense later!  To Be Continued!  Sincerely, Sam.

Another Interim In-Between Sessions 7 and 8 of Course 19 -- The Klein Bottle and Orbifold Differentiation

When one is to consider any given arbitrary set of fermionic superstrings of discrete energy permittivity -- that would here come together in so as to work to comprise a fermionic orbifold eigenset -- the existence of such open strand associated superstrings of the said nature, would, as the respective orbifold eigenset that these work to comprise, work to bear the nature of having a fractional spin.  Over the course of when such a so-stated open-strand-based superstring is to undergo the Kahler-Metric, this would then tend to imply that the directoral-associated topological sway of those Hodge-based indices that would here work to comprise the integration of the summed fractal-based partials -- that are of the quantum discrete energy angular momentum-based permittivity, that would be directly associated with the Hamiltonian-based operation of the so-eluded-to one-dimensional superstring of discrete energy permittivity -- would tend to bear a relatively annharmonic pulse-like flow, during the individually taken iterations of BRST in which such a respective given arbitrary superstring is metrically propagated through, over a sequential series of instantons -- to where the so-stated flow of the so-eluded-to Hodge-based indices of the fractals of discrete energy permittivity, that would here come together in so as to work to form a discrete quantum of energy permittivity, would tend to bear more of a tendency to acquaint with an orbifold eigenset, of which will here involve more of a perturbative distribution of the individual superstrings that work to make it up -- in the process of their delineation towards their contingent Klein Bottle eigenstate -- to where such a tendency would then work to imply the need for the relatively local existence of potentially additional Klein Bottle eigenstates, in so as to be able to fascilitate the activity of the here needed Kahler-Metric to occur at the inferred proximal related general region at hand in such a case.  To Be Continued!  Sincerely, Sam Roach.

An Interim In-Between Sessions 7 and 8 of Course 19 -- The Klein Bottle and Orbifold Differentiation

Let us say that we are here discussing a bosonic superstring of discrete energy permittivity, that is of an orbifold eigenset -- that is differentiating in a kinematic nature -- at group-related instanton.  The said given arbitrary orbifold eigenset -- as each of the superstrings that work to comprise the respective orbifold eigenset -- is of a bosonic sub-atomic nature, to where the so-stated orbifold eigenset works to bear the nature as to having a whole spin, over any correlatively corresponding sequential series of affiliated group-related instantons, in which such a set of bosonic superstrings is of the so-stated substringular nature.  Since the orbifold eigenset that is being describe of here is entirely comprised of superstrings that are of a bosonic nature, each of the superstrings that would here work to comprise the said orbifold eigenset, would work to bear a whole spin, over the course of each individually taken iteration of BRST that is affiliated with the directly corresponding iterations of the said group-related instantons that are here to be considered.  This would be affiliated with the condition -- that each of the individually taken superstrings of discrete energy permittivity that would here work to comprise the so-stated orbifold eigenset of this respective given arbitrary case, would tend to oscillate in a harmonic nature, during the course of each individually taken iteration of BRST -- that is here directly affiliated with the correlative iterations of group-related instanton -- in which both the constituent superstrings and the orbifold eigenset that these substringular members work to make-up is active as a Hamiltonian operator, that is to perform one given arbitrary function in the substringular, over time.  Since the so-eluded-to orbifold eigenset of this given arbitrary case is here comprised of superstrings that are tending to oscillate in a harmonic manner during each individually taken iteration of BRST, then, the individually taken partials that would here work to comprise the Hodge-based fractals of the discrete energy -- that would work to comprise the sum of the discrete quantum of energy, that each of such superstrings works to make-up -- would then tend to bear a higher probability of working to bear a relatively unitary directoral-based flow of angular momentum-based permittivity.  So, if such a tendency is to be incorporated into the overall flow of the directorial-based flow of the angular momentum-based permittivity of the directly associated orbifold eigenset of this case as well, then, there is here more of a likely-hood of there being less of a need for extra Klein Bottle eigenstates to be able to facilitate the activity of any potential proximal Kahler-Metric -- if such a Kahler-Metric is to then be needed to be performed by the substringular members that are in the set relative general locus in which such a so-stated respective given arbitrary orbifold eigenset is to be differentiating in in a kinematic nature, over the so-eluded-to correlaltive sequential series of instantons.  To Be Continued!  Sincerely, Sam Roach.

Orbifolds and the Klein Bottle

Generally, when a superstring of discrete energy permittivity is to undergo the Kahler-Metric, all of the superstrings that work to comprise the directly corresponding orbifold eigenset -- that operate in so as to perform the correlative function, of which the initially stated respective given arbitrary superstring of this case is interdependantly active in the process of the attainment of such a so-mentioned genus of operation  -- will be tending to be worked upon by one or more directly affiliated relatively proximal Klein Bottle eigenstates, these of which will here be situated -- in so as to act as the respective tense of a holonomic substrate, that is to be utilized here in so as to allow for such correlative superstrings of discrete energy permittivity to be able to reattain those fractals of their discrete energy permittivity, that are essential in order to cause the continuation of the condition of such a case in that such substringular entities may then still be able to act as discrete units of energy permittivity, over time -- in so as to work to bear a common ground of the state of which is appertaining to the condition, that the partials of any unique and specific given arbitrary orbifold eigenset, will tend to always be recycled in such a manner -- in so as to bring a tense of unity to the indistinguishably different recycling mode of any specific respective given arbitrary Hamiltonian operation -- that acts as operating in such a manner that happens as it does, in order to perform one specific substringular function in the realm of time and space.
To Be Continued!  Sincerely, Sam Roach.

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

A supremumization, taken eight times, of a majorized initially pointal-based reference frame, or -- if one were to integrate an initially pointal-based reference frame 26 times spatially, under a Laplacian-based set of conditions -- one would get what would be the equivalent of a maxed-out Minkowski space, or, a maxed-out flat space, that would here bear 26 spatial dimensions, when this is not including time.  If one were to spatially integrate an initially pointal-based reference frame, 32 times spatially, under a Laplacian-based set of conditions -- one would get a Hilbert space that would here be maxed-out for the directly corresponding Ward-Neumman boundary conditions, that would here appertain to the correlative spatial dimensions of one set of parallel universes.  Another way of looking at things, is that a supremumization -- taken three times, of an initially one-dimensional-based reference frame -- will work to form a ten spatial dimensional reference frame, of which, when majored, will form the twelve-spatial dimensional field that is often correlative to the spatial dimensionality of a worm-hole. I will continue with the suspense later!  To Be Continued!  Sam.

Part Four of Session Seven of Course 19 -- The Klein Bottle and Orbifold Differentiaion

A supremumization is when one integrates a physical space into three extra spatial dimensions.  So, if one were to take a supremumization of a supremumization of an initial six spatial dimension-based Minkowski Space -- one will then have a twelve dimensional-based Minkowski Space.  Such a just eluded-to twelve-dimensional Minkowski surface or flat-based surface may often be considered as a volume-based space or a Hilbert Space,  instead.  (A Minkowski Space is a flat-based space, and, a Hilbert Space is a volume-based space.)  So, if one were to be initially considering a ten-dimensional Hilbert Space -- that is subsequently double-integrated into two additional spatial dimensions, into what will then be a twelve-dimensional Hilbert Space -- then, what this will here amount to, is the generally taken Laplacian-based condition of having the extrapolation of a majorization of a ten-dimensional volume-based space into a twelve-dimensional volume-based space.  One can have a flat space that may have up to 26 spatial dimensions, plus time.  The condition as to whether or not one is dealing with the consideration of either a flat-space or a Minkowski-based space or a volume-space or a Hilbert-based space, is whether or not one is either to be able to or to not be able to treat the space-time-based fabric in which one is to go through, over time, as a contortable sheet that is not viably travelled through in a transversel-based manner otherwise, or, instead, if one is to treat the space-time-based fabric in which one is to go through, as actually being a viably travelled through operand -- that would here be traveled through in a transversel-based manner, respectively.  A volume-based space or a Minkowski Space is most associated with a worm-hole that would -- in this case -- bear all of its additive source of velocity to the condition of the bending of space-time-fabric.  Yet, if any of the additive source of the velocity at all that is caused by the activity  of traveling through a given arbitrary worm-hole is due to a respective given arbitrary tense of a tachyonic propulsion, then, the manner of describing the nature of the space that would here be traveled through, would be a twelve-dimensional volume-based space or a twelve-dimensional Hilbert space -- when this is not including the dimensionality due to time itself.

The Third Part of Session Seven of Course 19 -- The Klein Bottle and Orbifold Differentiation

When one is to spatially majorize a basic planar surface that acts as a Hamiltonian-based operand in time and space, that is of a simple flat-space-like configuration,  when this is in terms of what the tendency of what you will physically get in the process -- one will tend to have a three-dimensional physical field that works here to bear an added tensoric-based genus, that will here tend to be related predominantly to the physical existence of a spin-orbital-based coniaxioin -- to where this said spin-orbital-based coniaxion will here tend to curve in so as is the relatively local general curvature of the directly related space-time-fabric would then have a tendency to curve as such.  When one is to then here work to extrapolate a majorization of the directly previously mentioned three-dimensional spatial field -- that would here have an added spin-orbital coniaxion that is incorporated as had been eluded-to into the Hamiltonian operand of that particular eigenstate of space that is to bear any of certain given arbitrary Hamiltonian operators, that would here be functional from within the just-eluded-to general region, one will then get a set of two additional tensorsic-based operators "on top of that"-- that will here tend to be related predominantly to the physical existence of both a transversal-based coniaxion and a radial-based coniaxion -- this said set of both a transversal-based coniaxion and a radial-based coniaxion of which will here tend to curve, in so as is the here relatively local general curvature of the directly related space-time-fabric would then have a tendency to curve as such.

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

When one is to majorize the Laplacian-based Lagrangian scalar magnitude of the integrative Hodge-based index of a plane of one respective given arbitrary set of superstrings, that operate in so as to perform one specific substringular function over time -- one will here then tend to be able to extrapolate from this, a surface of topological-based holonomic substrate -- from the integration of the directly affiliated cohomological mappable tracings that are thence formed -- that will here directly appertain to at least three spatial dimensions plus time -- this here multidimensional-based planar topological surface -- of which will tend to curve in such a manner, that is most effectual to the Laplacian-based existence of the here given arbitrary intrinsities of the local genus of the curvature of space-time-fabric.  This would then mean, that -- when one is to majorize the Laplacian-based Lagrangian scalar magnitude of the integrative Hodge-based index, that is of a plane of one respective given arbitrary orbifold eigenset, this of which would thereby operate in so as to perform one specific substringular function over time -- one will then here tend to be able to extrapolate from this, a surface of a topological-based holonomic substrate, from the integration of the directly affiliated cohomological mappable tracings that are thence formed -- this of which will here directly appertain to at least three spatial dimensions plus time -- to where this here multidimensional-based planar topological surface will then tend to curve in such a manner, that is most effectual to the Laplacian-based existence of the here given arbitrary intinsities of the local genus of the curvature of space-time-fabric.
Such a said multidimensional spatial-based surface, that is formed here as a physically resultant "memory" of both the existence and the activity of phenomenology of discrete energy permittivity -- of which works as an interdependent and subsequent correspondence to both the existence and the activity of discrete energy impedance -- will here be contorted and torqued -- as a set of cohomological-based indices -- into a membranous manifold, this of which may then here be deemed of as a Gliosi-Shirk-Olive ghost, that behaves as either of a Calabi-Yau manifold, a Calabi-Wilson-Gordan manifold, or, as a Calabi-Calabi-manifold.  I will continue with the suspense later!  Sam Roach.

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

A point particle of a discrete size -- that is of the smallest conceivable volume in the substringular -- may be thought of as being called a third-ordered point particle.  It is third-ordered point particles that work to come together -- in so as to form what may thought of as second-ordered point particles.  It is second-ordered point particles that come together -- in so as to form what may be here considered metaphorically as tiny beads -- which is needed in so as to form what I describe of here as "mini-stringular" segmentation.  The so-stated mini-stringular segmentation integrates in the correlative multiplicit loci, where these are at, in so as to act as the core-field-density of substringualr fields.  It is the said mini-stringular segmentation that is pulled together in a compactified parabollic grouping, in so as to work to form the holonomic substrate of what may here be called first-ordered point particles.  And, when the just-mentioned first-ordered point particles are pulled into a tense of allignment, these tend to often form superstrings of discrete energy permittivity -- these of which are either of a hoop-like nature or of a strand-like nature (generally, of a hoop-like nature), and, as well, these tend to form the correlative counterstrings that act here as the counterparts of the said superstrings.  So, when one is to majorize the connectivity of the so-stated first-ordered point particles, along a Laplacian-based Lagrangian path -- at a given locus, during the course of an arbitrarily given instant in which such a group-related instanton is occuring, one will often tend to be able to derive the resultant Laplacian-based existence of the multivarious superstrings of discrete energy permittivity that exist in time and space -- in such a manner in which this existence works, at least in part, to help define the correlative respective Minkowski-based regions, that would here be iterating, in so as to work to form the activity of discrete particle-based energy, that is simply needed in order for energy to be able to remain as energy, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.