Beti Action Jacobian Stabilization

 When what I term of as being, the “ ‘sub-force’ mini-string-related (de)compactification,” — that is here to be of the directly applicable multiplicity of the Ward-Cauchy-related conditions, of a correlative given arbitrary respective superstring of discrete energy permittivity, to simply be: i*(i*PI(Del) Action)*(Zero-Point-Energy), when taken over the course of a respective iteration of group-related instanton; it consequently follows, that the directly corresponding superstring of discrete energy permittivity, that is thus effected, will tend to not work to bear neither any dimensional compactification, nor any dimensional de-compactification, as the number of spatial dimensions, that such an inferred superstring is here to work to exhibit, will consequently tend to not be in the process of changing, over such a proscribed brief duration of discrete time, —  to where there will consequently tend to be a greater probability, for such a said discrete quantum of energy, to thereby work to bear a more stable tense of a metric-related nature. I call such a Noether-related situation, in which there is here to be no proximal local gauge-metric-related activity of dimensional (de)compactification, due to the physical condition of a minimized absolute value of such a “sub-force,” (as taken at the Poincare level, that is here to be appertaining to the nature of such a fractal of discrete energy) that is here to be related to the nature of such mini-string-related gauged-action, — over the general course of (de)compactifaction, to thereby consequently bear such a general condition of a non-perturbative tense, to where I will thereby name such a super-string-related situation, to be: the Beti-Action-Jacobian-Stabilization (BJS). Sincerely, SAM ROACH.

Anharmomic Vibration And Stringular Compactification

When an orbifold eigenset is to compactify by one given arbitrary number of spatial dimensions, then, all of the superstrings that are of the same one respective given arbitrary orbifold eigenset of such a case, will compactify by the same number of spatial dimensions.  So, all of the individually taken superstrings of discrete energy permittivity, that are here to work to comprise one correlative given respective orbifold eigenset -- will be vibrating in an anharmonic manner in a holomorphic manner, in the same number of spatial dimensions, -- at that general point in duration, that is here to be at the general moment that is to be taken right before the start of the correlative beginning of one specific iteration of group-related instanton.  So, if one individually taken superstring of discrete energy permittivity, is to be orientable during a correlative iteration of the Beti Action, -- then, all of the individually taken superstrings of discrete energy permittivity that are of the same orbifold eigenset, will be orientable during the self-same correlative iteration of the Beti Action.  Consequently -- if one individually taken superstring of discrete energy permittivity, is to be unorientable during a correlative iteration of the Beti Action, -- then, all of the individually taken superstrings of discrete energy permittivity that are of the same orbifold eigenset, will be unorientable during the self-same correlative iteration of the Beti Action.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Unorientable Superstrings Become Tachyonic

Let us initially consider a superstring of discrete energy permittivity -- that vibrates annharmonically in an odd number of spatial dimensions, in a relatively holomorphic-based manner, right before BRST,  -- as well as such a superstring of discrete energy permittivity to be vibrating in an odd number of spatial dimensions, in a relatively antiholomorphic manner, during the immediately ensuing correlative iteration of the directly corresponding Regge Action eigenmetric.  This would not only work to help at causing the said string to both compactify in an odd number of spatial dimensions right before BRST, as well as to work to help at causing such a superstring to decompactify in an odd number of spatial dimensions during the immediately ensuing correlative iteration of the directly corresponding Regge Action eigenmetric, -- yet, such a general tense of activity, would then work to cause the application of an odd-functional pulse -- to be incurred upon the field that would then exist in-between the said string and its correlative counterstring, during both the Beti Action & in its immediately ensuing iteration of the Regge Action eigenmetric.  This would then work to cause such a cohesive field, that is in-between the said string and its counterstring -- to then be heteromorphic, instead of it being homeomorphic.  This would then work to instigate a potential deviation from the general tendency, as to the conservation of homotopic residue -- if such a superstring were to remain of a Noether-based flow, -- since the field that I had just mentioned would then be in a state of a Cevita-related perturbation.  (Here, like a Cevita interaction -- yet, at a level that is here on a smaller scale (a fractal), than an interaction that would exist between bundles of discrete energy quanta.)  Such an annharmonic perturbation, would then tend to work to form an alteration from the general tendency of a conserved exchange amongst that phenomenology of which  I name of as "partition-based discrepancies."  Keep reading, this is nifty!  Homotopic residue is to tend to be conserved for unfrayed substringular entities, that are of a Noether-based flow.  This would then tend to make the here just discussed discrete energy packet, to then to have become unorientable during both BRST and in its immediately ensuing Regge Action eigenmetric -- to where, this would then tend to make the here just discussed discrete energy packet to then ensue to become tachyonic.!
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Some Stuff As To Homeomorphic Field And The Beti Action

The Beti Action works to help at making a superstring of an orientable nature, in so that the said string may continue to differentiate in a Fourier-related manner -- in a Noether-based manner.
A superstring is to be made orientable during BRST by the Beti Action -- when the field that is here to exist in-between a given arbitrary superstring and its correlative counterstring, is said to be homeomorphic during a respective iteration of BRST.  A superstring is said to work to bear a homeomorphic field -- in-between itself and its correlative counterstring -- when the asymmetry that is to exist amongst the phenomenology that is of the dual-state that exists between the proximal local delineation of the partition-based discrepancies of the said superstring, & the proximal local delineation of the partition-based discrepancies of the said counterstring, -- is to be maintained with an even-functional-based pulse -- at the topological surface, that is Poincare to the region that is here to exist in-between the said superstring and its said counterstring.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Some Interesting Stuff About The Beti Action

What the Beti Action happens to be, is that activity that is to happen, in so that there may potentially be a homeomorphic field between a given arbitrary superstring and its correlative counterstring, when there is of an even-function-related translation between the initial compactification and the ensuing correlative decompactification of the so-eluded-to discrete energy quantum - over the course of that general duration, that is to transpire from right before BRST, until the directly corresponding iteration of the Regge Action, -- to where then, the said superstring is said to be orientable, and thus, the said superstring may be ensue in so as to be of a Noether-related Ward-Caucy nature.  When the Beti Action -- when going into an iteration of BRST -- is to be of an even number (if that compactification that is to happen, right before BRST, is to work to involve a decrease in spatial dimensions by an even integer number of such discrete spatial dimensions), then, the immediately ensuing Beti Action will work to involve the Ward-Cauchy-related conditions, of there being a homeomorphic field subtended between a given arbitrary superstring that is of a Noether-based flow, and its directly corresponding counterstring, to where, the correlative superstring is to then to be said to be of an orientable nature.  If a given arbitrary superstring is unorientable during the Beti Action, by working to involve a decrease in spatial dimensionality by an odd number of spatial dimensions right before instanton, and, as well, if the immediately ensuing correlative iteration of the Regge Action, is here to work to bear an increase in spatial dimensionality by an odd number of spatial dimensions, then the said given arbitrary superstring will become unorientable during both the Beti Action and in its correlative Regge Action, and thus, such a said superstring will then immediately ensue to become of a tachyonic nature.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Beti Action and Annharmonic Vibration Of Superstrings

If a superstring of discrete energy permittivity is to be vibrating annharmonically in a holomorphic manner, in an odd number of spatial dimensions right before BRST, -- then it will tend to not work to bear a homeomorphic field between itself and its counter-string, during the immediately ensuing correlative Beti Action eigenstate.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Integration Of Segmentation, And The Polyakov Action

Let us here initially consider a bosonic superstring of discrete energy permittivity, that is fully Lorentz-Four-Contracted -- over the course of one given arbitrary iteration of a respective metric of BRST. The Polyakov Action eigenstate that is to here happen to this said given arbitrary superstring, is to here happen to this said superstring, in a manner that will not bring about the substringular condition of any net decompactification to then happen to the so-eluded-to discrete quantum of energy permittivity -- during the course of such an eluded-to iteration of BRST. Due to this general classification of there being relatively no tense of net decompactification to happen to the topological holonomic substrate of such a fully contracted increment of discrete energy -- there will thereby be no net additional mini-stringular segmentation to be added to the Gliosis-based indices, that are to be involved with the Ward-Neumman bounds of the topological eigenindices that are of the said superstring of discrete energy permittivity, that is to here be stationed at the general locus to where the so-stated quantum is to here be simultaneously be undergoing the Beti Action -- via the vantage-point of a central conipoint.  This will then here work to be involved with that condition, that the main homotopic stemming -- at which there is here to be a tense of static equilibrium to be happening here -- to where, when this is taken in terms of the equal flow of that enterence of the holonomic substrate of mini-stringular segmentation, that is to be evenly paired with an equal flow of the exiting of the holonomic substrate of mini-stringular segmentation -- this will then happen in such a manner, of which will then bear its eminent locus of the convergence of zero net aquisition of core-field-density-based eigenindices, at the Ward-Neumman-based locus, to where its single "partition" would here be existent at such a so-stated locus, as a holonomic substrate that is involved with a relatively Laplacian-based Transform, that such a said superstring is to here be differentiating through as.  Such a "partition" is here to act as a separation from a condition of bearing a unitized Lagrangian-based flow -- at a proximal localized spot, that is of a relatively Laplacian-based manner.  This so-stated locus, to where this is here to be at such a "partition," is to then be homotopically bound to the cite, -- to where it is topologically intertwined, -- as a tied set of mini-stringular segmentation-based eigenindices, that act in a relatively flexible manner during BRST, by interchanging an equal number of Hodge-based eigenstates to be brought into the Gliosis-based core-field-density of the topological stratum -- that is of the here differentiating bosonic superstring of such a respective given arbitrary case, in an even symmetrical manner towards the interchanging of the same relative Hodge-based quantity of the same genus of the tense of the scalar magnitude of the eigenstates, that are here, to instead, be brought out of the Gliosis-based core-field-density of the topological stratum, that is of the here differentiating respective given arbitrary bosonic string of such a case.  This so-stated Laplacian-based condition, may be thought of here as an occurrence -- that is to happen during a tightly-knit array of kinematic activity, that is to happen here, from within the Ward-Caucy bounds of one discrete increment of time.  Time is the successive series of group-related instantons, and, an iteration of BRST is involved with the first 6hbar increments of the 2pi hbar increments of one discrete instanton.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.

Another Interim In-Between Parts Of Session 12 Of Course 19 -- The Klein Bottle Differentiation

When any two-dimensional superstring of discrete energy permittivity is undergoing an iteration of BRST, which is when both the Beti Action and the Polyakov Action are taking place -- the vibrational oscillation of the said given arbitrary respective so-eluded-to bosonic superstring, is to then be undergoing a sub-Fourier-based differentiation -- in which the directly corresponding superstring and its correlative counterstring are to then be radially vibrating back-and-forth during the so-stated iteration of BRST.  Such a semi-Laplacian-based topological sway, that is of the so-eluded-to genus of the vibrational oscillation of such a respective superstring of discrete energy permittivity -- will here tend to be of more of a spin-orbital-based nature than the genus of the vibrational oscillation that would instead tend to be exhibited by the sub-Fouriier-based differentiation of a respective given arbitrary one-dimensional or a fermionic superstring that is of discrete energy permittivity, during its respective genus of a semi-Laplacian-based activity -- that would tend to happen when such a one-dimensional superstring is to iterate during its correlative activity, that is to here be directly involved with an iteration of BRST.  This is in part the reason why the vibrational oscillation of a two-dimensional superstring during BRST will always tend to be of a harmonic topological sway during the directly associated sub-Fourier-based activity that would here be represented by the Calabi-based motion of a bosonic superstring -- during the main thrust of any respective given arbitrary iteration of the directly corresponding iterations of group-instanton, in which a bosonic superstring is iterating as a discrete quantum of energy permittivity.  This is  related to the condition that bosonic superstrings exhibit -- what may be termed in an individually taken manner, as a whole spin.  Next -- why fermioinic superstrings of discrete energy permittivity tend to vibrate in a enharmonic manner during BRST.
I will continue with the suspense later!  To Be Continued!  Sincerely, Sam Roach.

As To What The Grassman Constant Is

Any given arbitrary superstring of discrete energy permittivity, over the course of BRST -- is acommadated by the Laplacian-based existence of its directly corresponding counterstring.  The said respective superstring of discrete energy permittivity works to mainly act as the particle-based presence of discrete energy permittivity, while its directly corresponding counterstring works to mainly act as the wave-based presence of discrete energy permittivity.  During BRST and/or during the Regge Action -- the respective superstring and its directly correlative counterstring are to work to bear a homeomorphic field, or else the said respective superstring will ensue to not be orientable.  The constant that works to bear any respective superstring of discrete energy permittivity, to act in a Laplacian-based nature in so as to then have the condition of obtaining a homeomorphic field -- when in terms of that field that is formed in-between the said respective superstring and its directly corresponding counterstring -- may be thought of as the Grassman Constant.  When the Grassman Constant is not maintained in both the Beti Action eigenstate of one given arbitrary respective iteration of BRST -- and in the directly ensuing Regge Action eigenstate that is of the self-same given arbitrary respective iteration of BRST, then, the superstring will immediately tend to ensue in so as to temporarily alter from working to be of a Noether-based flow.  This is because, when the Grassman Constant is not maintained during both the Beti Action and its directly correlative Regge action -- the superstring is then said to not be of an orientable nature.  A superstring that is not of a Noether-based flow is not orientable, and will then tend to temporarily be of a tachyonic nature.  Therefore, a superstring that is said to not bear the Grassman  Constant over both the course of a respective eigenstate of the Beti Action as well as during the ensuing iteration of the directly associated Regge Action eigenstate, in so as to make the directly correlative discrete quantum of energy to not be orientable, then, that self-same superstring of discrete energy permittivity is to then tend to temporarily become of a tachyonic nature.
To Be Continued!  Samuel David Roach.

Part Six Of Session 12 Of Course 19 -- The Klein Bottle And Orbifold Differentiation

Any given arbitrary worm-hole works to bear a Laplacian-based Grassman Constant -- that is both of a Njenhuis and of an unorientable nature.  The Laplacian-based condition -- that the Grassman Constant of a worm-hole is of a Njenhuis nature, is due to the physical quality that a worm-hole is the equivalent of the annulus of a bending and of a warping, of what was an initially Real Reimmanian space. The Laplacian-based condition -- that the Grassman Constant of a worm-hole is of an unorientable nature, is due to the physical quality, that a worm-hole is of the same general genus of space-time-based fabric as substringular phenomenology that is of a tachyonic-based nature.  This is true, even though a vast majority of the added velocity that any respctive worm-hole works to bring to any physical entity that is to be accelerated to go "faster than light," actually tends to be due to what is here to be just due to the so-stated condition of the fact that a worm-hole is a contorsioning or in other words of a bending of space-time-fabric -- that works to pull space-time-fabric into a further scalar locality of space, even if the actual speed that an entity itself that is pulled through such a said worm-hole, is not even moving close to light speed.  A worm-hole's speed actually tends to be basically due to the condition that the directly appertaining space-time-fabric that is of the said worm-hole -- is what is moving "faster than light," and not the respective holonomic substrate that is transported through it to be being transported "faster than light."  Yet, unorientable superstrings do always tend to become spontaneously tachyonic -- once these work to neither bear an orientable Grassman Constant during both the directly corresponding Beti Action and the directly corresponding Regge Action.  This is due to the condition that such a so-stated unorientable superstring is to here be temporarily altered -- from working to bear an initially  Kaluza-Klein light-cone-gauge topology into then working to bear instead a Yang-Mills light-cone-gauge topology.  This is due to the condition that a mass that works to bear a Kaluza-Klein topology, would need to bear an infinite fractal modulus in order for it to actually go at the speed or light or faster -- to where it would then need to bear all of the mass of the Continuum.  Yet, if one were to cause the so-eluded-to and temporary alteration of the light-cone-gauge of a mass-bearing superstring of discrete energy permittivity -- to alter into then work to bearing instead a Yang-Mills or in other words a non abelien light-cone-gauge topology, then, such a mass-bearing phenomenology can indeed go at the speed of light or faster.  Such an alteration of the correlative light-cone-gauge topology, is what will always tend to occur -- when the directly corresponding superstring is unorientable during both its directly corresponding Beti Action and its correlative Regge Action.  This is when a superstring will actually become tachyonic. I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

About The Entry Of Discrete Energy Quanta Into Klein Bottle Eigenstates

Let us initially consider a superstring of discrete energy permittivity, that is inextricably bound to its directly corresponding counterstring that is at its relative forward-holomorphic side, -- and with its directly corresponding first-ordered light-cone-gauge eigenstate and its correlative Fadeev-Popov-Trace eigenstate, that are here being positioned just to its relative reverse-holomorphic side -- during the course of one specific given arbitrary iteration of BRST, of which is happening over a substantiable portion that is of the most part of a respective given arbitrary iteration of instanton, that is at a set locus in the substringular.  As the so-stated superstring of such a case is decompactified to the inverse of the scalar magnitude of its directly corresponding Lorentz-Four-Contraction -- the directly affiliated counterstring, that is of what mainly acts as the wave-based characteristic of the said discrete energy permittivity-based quantum -- is decompactified over the course of the respective eigenmetric of the Polyakov Action, as its directly associated superstring that mainly acts as the pointal-based characteristics of the said discrete energy permittivity, is working to bear its Laplacian-based condition over the respective given arbitrary iteration of BRST that I am here working to describe in this case scenario.  If any given arbitrary discrete quantum of energy is to then be undergoing what is known of as the Kahler-Metric -- over the course in which the said respective given arbitrary discrete energy is in the need of re-attaining those fractals of discrete energy that the said discrete energy quanta need -- in order for the said discrete energy quantum to both exist and persist as discrete energy, -- the discrete energy of such a given arbitrary case, will, right after a correlative iteration of BRST, fall into a proximal localized eigenstate of the holonomic substrate of a Klein Bottle eigenstate.  As the said discrete quantum of energy is to here be pulled into a proximal localized Klein Bottle eigenstate -- the directly associated superstring and its counterstring will then have its correlative Polyakov Action-based scalar magnitude of its correlative tense of decompactification, to be undone -- in the process of going into its entry upon the Gliosis-based bounds of the so-stated holonomic substrate of the said Klein Bottle eigenstate, that I have here inferred.  The discrete energy -- during the directly associated eigenmetric of the Kahler-Metric, will spend (2pi-6)/2) of a Planck-Bar affiliated duration of metric -- in the Ward-Neumman bounds of the said Klein Bottle eigenstate -- right after the initial 6 Planck-Bar duration of the generally noticable span of the directly corresponding period, in which the respective given arbitrary discrete energy were to be iterating in both the simultaneous Polyakov Action and the Beti (Bette) Action, that had happened during the so-stated iteration of BRST that is thus differentiable upon -- over the course of all but (2pi-6/2pi) of the whole duration of the so-eluded-to iteration of such a respective given arbitrary sub-Fourier-based translation of instanton.  (This is via the vantage-point of a central conipoint.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.