Anharmonic Homotopic Dispersion -- Spurious Tense Of Entropy

 The greater that the "thrust" of the anharmonic dispersion of homotopic residue is to be, at a given arbitrary covariant proximal local region, the more spurious that the consequentially formed respective entropy will therefore tend to be. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAMUEL DAVID ROACH. 

Perturbation In The Tense Of The Dispersion Of Local Homotopic Residue

 Often, when there is to be a spontaneous perturbation, in the relative tense of the dispersion of a local superstring-related set of homotopic eigenstates, that are here to be eminently related, to the course of the kinematic activity, of a directly corresponding Noether-Based mass-bearing cohesive set of discrete energy quanta, this will often work to alter the relative course of motion, of which such a directly associated gauged-action, that the just eluded-to "team" of mass-bearing energy, was here to have initially been interdependently acting in conjunction with, to where both the del of the gauged-action appertaining most eminently with the Hamiltonian, as well as the del of the gauged-action appertaining most eminently with the Lagrangian, is thence to be enacted upon as well, to where, this will thereby often have the general tendency, of working to alter the dimensional-related-pulsation of the earlier said Noether-Based mass-bearing cohesive set of discrete energy quanta, to where, this will often tend to work to help form, a consequentially resultant set of metric-based Chern-Simons singularities, of which are here to often tend to be produced, when there is to become the existence, of a definitive viable proximal local presence, of such an inferred genus of perturbation, as incurred upon the initially stated superstring-related correlative respective set of homotopic eigenstates. TO BE CONTINUED! SINCERELY, SAMUEL ROACH. (1989).

Asymmetrical Homeomorphic Covariant Mappable Fields

 When any given arbitrary Noether-Based superstring of discrete energy permittivity, is to be orientable, during the general respective course of the Betti Action, the directly associated proximal local superstring, is here to tend bear an asymmetrical homeomorphic covariant mappable field, when this is here to be taken, in relation to its (the superstring's) counter string's covariant mappable field. Sincerely, Sam Roach.

Reversed Direction Of Net Spin-Orbital Momentum -- Reversed Direction Of Dispersion

 When a given arbitrary mass-bearing cohesive set of discrete energy quanta, is to spontaneously work to bear a reversal, in the direction of the directly corresponding net tense, of its directly corresponding spin-orbital momentum, -- this general type of a common occurrence, will often tend to result, in a consequentially occurring case scenario, in which there is here to be the ensuing display, of an exhibited reversal in the net direction, of the dispersion of those particular eigenstates, that are here to be expended outward and away From the proximal local field-density, that is to be of the said respective mass-bearing cohesive set of discrete energy quanta, which is here to be considered, over the general durational course, of that kinematic activity, in which those correlative respective tangentially flowing eigenstates, that are here to tend to be formed, by the enactment of the directly corresponding Chern-Simons-Invariants, are to be generated, in a relatively homotopic manner, over the span of a sequential series of group-related instantons. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAM ROACH.

Attenuated/Augmented Ricci Curvature

The given arbitrary covariant proximal local presence, of a cohesive set of inverted gravitational waves, often tends to be directly associated, with a Ricci Curvature, that is here to be attenuated, from a heuristically flat Ricci Curvature. Whereas; The given arbitrary covariant proximal local presence, of a cohesive set of amplified heuristic gravitational waves, often tends to be directly associated, with a Ricci Curvature, that is here to be augmented, from a heuristically flat Ricci Curvature. SAM ROACH. (1989).

Inverted Gravitational Wavelengths -- Fraction-Related Ricci Curvature

 The proximal local covariant kinematic presence, of a cohesive set of one or more inverted gravitational wavelengths, often tends to be associated, with the respective proximal local presence, of the general genus of a Ricci Curvature, that is to work to bear a scalar magnitude, that is to be heuristically described of as a fractional value. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL ROACH. (1989).

A Little As to When A Discrete Quantum Of Energy Is Gauge-Invariant

 In the general procedural course of "events," in which a given arbitrary discrete quantum of energy is to remain gauge-invariant, -- there is thereby to be the eminent resultant given arbitrary physical tendency, in which the directly associated kinematic flow of the respective local sequential series, in which one is here to be considering the "plucking" action of those directly applicable gauge-bosons, as these are here to be made Gliosis upon the topological surface of those directly corresponding second-order light-cone-gauge eigenstates, to where these said second-order eigenstates, that are here to work to make-up the holonomic substrate, of what basically amounts to being the proximal local presence of the wave-based nature of discrete energy impedance, -- will thence tend to occur in such a general manner, to where this inferred flow of a resultant formation of a set of Schwinger-Indices, that are here to externally propagate, in so as to interact with their infringed upon environment, in such a manner, to be able to form the forces of nature, to where this will therefore tend to work to form, in this particular genus of a case, a homeomorphic flow of force-related eigenstates, over a directly corresponding period of time. Sincerely, Samuel David Roach. (1989).

Non Abelian/Abelian Vector Bundle

 Let us, at first, consider the holonomic substrate of a given arbitrary cohesive set of discrete energy quanta, -- to act as being the overall energy, of a given arbitrary respective Ward-Cauchy-related system. This implied overall energy of a system, is often referred to as being called, the Hamiltonian Operator. The general physical attribute, of the group action-related behavior of a holonomic entity, may be thought of as being the general characteristic of isotropism. In this particular case scenario; let us minimize the focus upon the potentially proximal local presence, of any invariably latent Nijenhuis tensors. Let us next think of the general case scenario, in which the just mentioned Hamiltonian Operator, (in which the earlier stated cohesive set of discrete energy quanta, is here to act as the overall energy of the respective system), is to potentially directly interact, at the Poincare level, with the topological surface, of an ulterior Ward-Cauchy-related manifold, -- to where one may consequently say, that the said respective cohesive set of discrete energy quanta, that is here to be of the initially inferred general case at stake, is then to work to bear a potentially Gliosis contact, with the earlier inferred topological  manifold, that is here to act as the general type of a phenomenology, that is here to be potentially struck in a covariant manner, by the eminent impact of the motion of the said respective cohesive set of discrete energy quanta -- that I had initially brought-up in this discussion. Let us next call the direction-related tense of the holonomic entity, that is of the initially inferred set of energy quanta, to act as the Hamiltonian manner, of a kinematically delineated vector bundle. If the potentially impending direct contact of the Hamiltonian-related vector bundle, as interacting with the topological surface of that manifold, which is here to be potentially eminently struck, were to more than likely spontaneously work to bear the relative proximal local presence, of a tense of isotropic "slippage," then, one may consequetnly say, that the general characteristic of the reductional tense, of such an implied genus of a holonomic vector bundle, is then to be of the respective reductional nature, of acting as a Hamiltonian-related non abelian vector bundle. However; if the potentially impending direct contact of the Hamiltonian-related vector bundle, as with the topological surface of that manifold, which is here to be potentially eminently struck, were to more than likely spontaneously work to bear a relative lack of isotropic "slippage," then, one may consequently say, that the general characteristic of the reductional tense, of such an implied genus of a holonomic vector bundle, is then to be of the respective reductional nature, of acting as a Hamiltonian-related abelian vector bundle.  To Be Continued, As "Advertised"  -- "At A Computer Near You!" SAM.

More As To The Importance Of The Light-Cone-Gauge

 The continuity of Casimer Invariance, is primarily due to the general tendency, of the ever pervasive presence of homotopy. The continuity of homotopy, is primarily due to the general tendency, of the ever pervasive presence of the conservation of homotopic residue. The continuity of the conservation of homotopic residue, is primarily due to the general tendency, of the basically ever pervasive perturbative presence of the Polyakov Action. (Alterations in the Polyakov Action, work to help to allow, for orbifold eigensets that are comprised, eminently by Yau-Exact superstrings, that are to alter in their motion in relationship to light, to be able to better accommodate for the needed flow of the i*PI(Del) Action, in so as to work to help to allow for the general processes of relativity). The Polyakov Action, is primarily due to the general tendency, of the ever pervasive presence of the innate reaction of the light-cone-gauge, towards any correlative changes in the delineation-related allocation of discrete energy quanta --  in their directly corresponding relationship to the motion-related presence of electromagnetic energy. Homotopy -- is the general tendency of discrete energy quanta, to work to bear a web-like field, that is here to work to inter-relate all un-frayed superstring-related phenomenology, via the multiplicity of the interdependent inter-connections, of what I perceive of as being the general tendency, of the ever pervasive presence of mini-string-related segmentation. Sincerely, Samuel David Roach.

Some Stuff As To What An Abelian Association Is

An Abelian association, is one -- in which a given arbitrary Ward-Cauchy-related eigenstate is to have a direct wave-tug-like interaction with that phenomenology --  in which it is to be coming into contact with.  So, -- an abelian geometry, is that general differential geometry -- that is here to relate to such a substringular situation, in which any respective given arbitrary Ward-Cauchy-related eigenstate, is to have a direct wave-tug-like interaction, with some other substringular stuff.  Often -- this refers to phenomena -- that tend to be extrapolated, as to here be in the process of adhering to the general cohomology-related shell, that is here to be proximal to the topology of a superstring of discrete energy permittivity, -- particularly if such a so-eluded-to discrete quantum of energy permittivity, that is to work to bear such a set of composite eigenindices, is of a closed-looped nature.  This is because -- whenever something is, as for all otherwise apparent observation that may be deduced --  to be "stuck" to the surface of another phenomenon, -- such a potentially interdependent binding, is one general genus of such a situation, to where one is here to have one entity, that is to work to  bear a direct wave-tug-like interaction with another entity that it is to be touching, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Physical Re-Delineation Of Masses

Let us consider a set of discrete masses.  Let us say that the masses that are to be considered here, are in a relationship that is to then involve the initial Laplacian-based condition of three basic hydrogen atoms.  In this given arbitrary case scenario, one is to here be considering the fundamental sub-atomic particles that are to then work to comprise the three so-stated basic respective hydrogen atoms -- that I have eluded-to in this given arbitrary case.  What I am more specifically referring to as the physical substrate of each of such individually taken discrete masses -- of which are to be considered here as the eigenmembers of this respective given arbitrary case scenario, are the two fundamental basic cases of what always exist in any stable atom, by which I am simply referring to as the initial Laplacian-based condition of the existence of one relatively stable proton, that is being surrounded by the kinematic-based orbiting of one relatively stable electron, -- that are of the nature of as to being of either the holonomic substrate of a proton, or of the nature of being of the holonomic substrate of an electron.  Let us say that all three of such mentioned fundamental hydrogen atoms (each of which are a stable atom that is comprised of one proton that is being orbited by one electron), are to then each become positively charged all of the sudden -- by losing their respective multiplicit electron -- due to a proximal localized group-attractor.  The then resulting three loose protons would then tend to move towards whatever loose negatively charged adjacent source, is most aptly to be able to bring this so-eluded-to loose set of three positive charges into a state of optimum rest.  In the course of such a basic situation -- one is to then have a re-adjustment of the local delineation of the distribution of the proximal gluonic force of this specific case scenario -- since the three directly corresponding protons of such a basic case that I have described here, are made unstable, in order to move into a changed delineation, in so as to move into the respective individually taken spots where these are then to be at more of a state of optimum rest.  Individual protons each consist of two quarks that bind to one lepton.  Any given quark has a gluon that is situated within the Ward-Neumman bounds of its topological-based holonomic substrate.  Gluons -- of which are an example of what works to act as being a metrical-gauge-based Hamiltonian operator of the strong force -- are an example of a general condition as to the cite as to where there is a centralized knotting of the Rarita Structure.  (Where there is a gluon, there is an eigenstate of the centralized knotting of the Rarita Structure.)  So, whenever a proton is re-distributed in so as to form a re-delineation of its component gluons that are directly associated with the here so-eluded-to  Ward-Caucy bounds of the so-stated respective proton -- there is then to be a re-delineation of an eigenstate of the strong force.  So, whenever there is a re-delineation of the strong force -- there is thereby a directly corresponding re-delineation of an eigenstate of the centralized knotting of the respective multiplicit Rarita Structure eigenstate.  I will continue with the suspense later!  To Be Continued!
Sincerely, Samuel David Roach.

As To The Integration Of Superstrings Into Orbifolds

Let us here consider a given arbitrary superstring of discrete energy permittivity, that is differentiating in a Fourier-based manner through a discrete mean Lagrangian path -- in a medium that is of a "pure" vacuum-based Hamiltonian operand.  Let us next consider in this particular case, that what is here to be the general substringular region of this scenario -- is here to be composed of a relatively large Hodge-Index of other superstrings of discrete energy permittivity, these individually-based superstrings of which, as well, are also differentiating in a Fourier-based manner through a discrete mean Lagrangian path -- in which each of such multiplicit-based superstrings of this case, is, as well, in this scenario, to be going through a medium that is of a "pure" vacuum-based Hamiltonian operand.  Let us next say that there is some tense of a group-attractor, that is proximal localized in what is here to be the general substringular region in which the many superstringular metrical-gauge based Hamiltonian operators -- are here to be moving towards each others field-density, in a greater scalar amplitude of potential collision, over a relatively transient duration of time.  Let us then say, that in this respective given arbitrary case -- once the relatively large quantum of superstrings that are here to each be initially acting as their own orbifold eigenset, are here to then be infringing upon a relatively close to Gliosis-based multiplicit proximal locus to the each others core-field-density -- the velocity that each of such superstrings had been bearing, as a scalar amplitude of their relative and respective genre of Noether-based translation, will be significantly lowered in scalar magnitude, as such superstrings are then to be pulled (actually pushed, in part, by gravitational waves from the other side) into a codifferentiable, codeterminable, and in a covariant manner, in such a manner, to where all of the here so-implied superstrings of such a case -- that were initially of the respective different independent orbifold eigensets, are now to be of the same larger overall so-eluded-to orbifold eigenset.  At this point, the overall quantum as to the composition of what is now to be one larger set of superstrings, that are to then perform one group-related function -- is to then to tend to work to bear a relatively more steady-state tense of a Majorana-Weyl-Invariant-Mode, than the initially so-stated individual superstrings of discrete energy permittivity that I had started out mentioning, were to have had at the respective start of this given arbitrary case scenario.
 I wil continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Converging Phenomena From Parallel Universes

Let us initially consider a set of many orbifold eigensets, that are each individually taken -- as distinct given arbitrary respective orbifold eigensets, that are each from different universal based settings.  Let us say, that -- for each of the said orbifold eigensets that are each from different universes -- there is a Hamiltonian operator that acts as a group-attractor, that all work to pull each of these said individually taken sets of superstrings that operate in so as to perform one specific function, per each of the said individually taken orbifold eigensets -- in a manner that works in so as to pull the holonomic substrate of the said orbifold eigensets together, into a proximal localized set region -- that is of a relatively tight Laplacian-based setting, over a relatively transient duration of time.  Let us then consider such an interaction, as the Fourier-based activity of the kinematic motion of a certain set of orbifolds, that are initially relatively spatially separated -- to be brought into the same general substringular region -- by the Fourier-based activity of a separate physical entity, that works to cause the Ward-Neumman constraints of each of the different given arbitrary individually taken orbifold eigensets, to be converged towards a region that is much more proximal and of a localized conformally invariant-based setting.  Let us next consider the condition that would exist, if each of the then brought relatively close together orbifold eigensets -- were to still each work to bear a different tense of a Gaussian-based Li-Algebra spatial-related setting.  This would mean, that -- although each of these said orbifold eigensets were to then be spatially convergent, in a relative tense, -- the Fourier-based activity of each of the said orbifold eigensets, would still not be viable upon each other, over a relatively transient duration of time.  To Be Continued!  Samuel David Roach.

Part Two of the Interim In-Between Sessions 7 and 8 of Course 18

If the proximal encodement of the superstrings of the scenario that we have been dealing with here is maintained over the sequential series of group instantons of the so-stated group-related metric, then, the general condition of the first-ordered point particles that have worked here -- in so as to help to cause the directly corresponding superstrings to be of such a conformally invariant nature, in so as to be near each other, in such a tense of a Majorana-Weyl invariant nature, will work to allow for the so-stated point particles to bear  of a relatively proximal nature to a certain extent as well.  This is when this is taken in consideration of their correlative neighborhoods in the globally distinguishable.  Yet, if the directly corresponding reverse-fractaled tense of the electrostatic nature that is propagated from the directly corroberative superstrings will then here bear a divergent tense of residual homotopic Hodge-based indices, over the so-eluded-to sequential series of group instantons that work to correspond to the time in which the correlative superstrings are here being associated -- in the course of the so-eluded-to tense of superconformal invariance of this corroberative scenario, then, there will here be at least some sort of alteration in the localization of some of the superstrings that were directly associated with the so-stated group metric of this general scenario.  Yet, if the correlative superstrings are to remain relatively unchanged locally after each iteration of group instanton -- when in terms of their respective codeterminable codifferentiation, over each corresponding discrete increment of time that is to be metrically mapped-out in so as to work to help determine the genus of the specific tense of superconformal invariance that is involved here, then, the index of the prior tense of the respective perturbation of electrostatic differentiation is to be nullified in consideration.  The higher the Dirac factor is in terms of the non-local substringular phenomena -- that is to bear an exterial spin-orbital and/or a transversel effect upon the more directly involved interial-based phenomena, of such a format of a scenario, in spite of the degree and/or the level of the scalar magnitude of the physical separation that may exist here, the more assymetrical that the correlative superstirngs will tend to covariantly be propagated through in a kinematic manner -- relative to one another, over the so-eluded-to group metric -- when such a tendency is considered time-wise through a coniaxion that is centered at the convergent-based loci of the directly corresponding Fadeev-Popov-Trace eigenstates.
I will conclude with this interim later! To Be Continued!  Sam Roach.