De Rham Cohomology -- Isotropic Stability -- Homeomorphic Field

 Let us initially consider a mass-bearing cohesive set of discrete energy quanta, that is here to be working to form the mappable tracing, of a De Rham cohomology. If both the said mass-bearing cohesive set of discrete energy quanta, As Well As the given arbitrary particular Legendre (co)homology, that is here to be working to kinetically transfer the said set of discrete energy that is of such a case, are to both bear the general physical condition, of being of an isotropically stable nature, then, it will follow, that the resultant Lagrangian-based flow of motion, that is in this particularly mentioned case, to be directly associated with the mapping-out of a De Rham cohomology, will then consequently have a greater chance of working to bear the general physical condition of being of a homeomorphic nature, than if both the mass-bearing cohesive set of discrete energy that is here to be transferred, And, that Legendre (co)homology, that is here to be in the respective process of working to kinetically transfer it, through its correlative Hamiltonian operand, were to otherwise Not be of an isotropically stable nature. To Be Continued! Sincerely, SAMUEL ROACH. (1989).

Present Tenses Of Chern-Simons Singularities

 Although one may often have a superstring-related situation, in which there may be the general kinematic activity, to where a metric-based Chern-Simons singularity may be formed, Without the simultaneous covariant presence (via the vantage-point of a central locus) of a proximally local formed Lagrangian-based Chern-Simons singularity being initialized, at the exact same locus of occurrence; since due to the general mechanics of normal Noether-related physical constrains, it tends to be more highly probable, for there to often be the tendency of that general Ward-Cauchy-related condition, that when there is to be the covariant proximal local presence of the formation of a Lagrangian-based Chern-Simons singularity, there will often be the general tendency, for there to be present, at the same moment (at the vantage-point of a central locus) of the covariant formation of a metric-based Chern-Simons singularity. This is on account of the general physical condition, that although a set of discrete energy quanta may often change in its direction and or in its rate of delineation, Without necessarily working to form an alteration in more derivatives of motion than the number of spatial dimensions, that such a set is to be traveling through; yet, if a set of discrete energy quanta is to be changing in more derivatives of motion than the number of spatial dimensions that such a said set is to be traveling through, it will be more than likely to be altering in either its direction and or in its rate of speed, in relation to light, in the process of doing so — to where such a said set of discrete energy quanta, will thereby “simultaneously” tend to be altering in its dimensional-related pulsation, over the course of this self-same inferred process. TO BE CONTINUED! Sincerely, SAM ROACH.

Recursively Gliosis To The Kahler-Metric

 The quicker that a cohesive set of discrete energy quanta, is to reverberate in a Ward-Supplemental manner, at the microscopic level, the more of a relatively rapid rate, in which such a said cohesive set of discrete energy quanta, will thereby consequently tend to become recursively Gliosis to the Kahler-Metric. SAM ROACH. 

Recursively Smooth Display Of Anti Holomorphic Kahler Conditions

An isotropically stable mass-bearing cohesive set of discrete energy quanta, that is here to be reverberating,  from within the Ward-Cauchy-related physical bounds of a set region, as in a Ward-Supplemental manner, will tend to exhibit a more recursively smooth display of anti holomorphic Kahler conditions, than an isotropically unstable mass-bearing cohesive set of discrete energy quanta, that is otherwise to be behaving in a similar general mode of activity. I will continue with the suspense later! SAM ROACH.

Dimensional-Related Pulsation, And The i*PI(Del) Action

 Whenever a given arbitrary Noether-based mass-bearing cohesive set of discrete energy quanta, is to alter in its dimensional-related pulsation, -- not only will it consequently tend to work to bear a metric-related Chern-Simons singularity, at the proximal locus, at which such a said alteration in dimensional-related pulsation is to occur, yet, such an inferred set of discrete energy, as such a change is here to be occurring, will simultaneously (at the proximal locus of a central coni-point), tend to be undergoing an alteration, in either its speed and/or in its directional delineation, in relation to light, in the process of doing so. It follows then; that whenever  there is to be a gauged-action, by which there is to be the proximal local occurrence, at which there is to be the eminent presence of a metric-based Chern-Simons singularity, this general type of a common occurrence, will tend to be directly associated, with the eminent presence of what I term of, as being a general physical phenomenology, that I call here, the i*PI(Del) Action. Sincerely, SAM ROACH. (1989).

Smooth Ricci Flow And Thrust

 Let us initially consider an isotropically stable mass-bearing cohesive set of discrete energy quanta, that is here to work to bear a general rotational motion of spin — to where such an inferred “spinning,” is here to work to bear a recursively smooth Ricci Flow. The quicker that such a said spinning motion, of a recursively smooth Ricci Flow, is to accelerate, per terrestrially-considered time, the more of an orthogonally delineated thrust, that will consequently tend to be impelled, upon the earlier stated isotropically stable mass-bearing cohesive set of discrete energy quanta; Whereby, it follows — that the quicker that such an earlier stated spinning motion, of a recursively smooth Ricci Flow, is to decelerate, per terrestrially-considered time, the less of an orthogonally delineated thrust, that will consequently tend to be impelled, upon the earlier stated isotropically stable mass-bearing cohesive set of discrete energy quanta. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL DAVID ROACH.

Recursively Smooth Ricci Flow And Charge Generation

Isotropically stable mass-bearing cohesive sets of discrete energy quanta, that are here to work to bear a recursively smooth Ricci Flow, -- tend to reverse-fractal into physical phenomenology, that are here to work to bear a greater probability of generating a relatively large quantum of electrostatic charge, than isotropically stable mass-bearing cohesive sets of discrete energy quanta, that instead, are Not to work to bear such a recursively smooth tense of a Ricci Flow. To Be Continued! Sincerely, SAM ROACH. (1989).

Conservation Of Homotopic Residue -- Casimir Invariance

 The multiplicity of the Noether-based general physical condition, as to the conservation of homotopic residue, -- is necessary, in order for the multiplicity of the general tendency of Casimir Invariance, to be able to take hold. I will continue with the suspense later! To Be Continued! Sincerely, SAM ROACH.

Nature Of Lagrangian-Based Paths And Conservation Of Homotopic Residue

 When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a unitary Lagrangian-based path -- then, each correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work to bear a unitary directoral. When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a binary Lagrangian-based path -- then, each correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work to bear a binary directoral. When an accelerating mass-bearing cohesive set of discrete energy quanta, is here to be spatially transferred -- via a tertiary Lagrangian-based path -- then, each  correlative individually taken dimensional-related variable, that is here to work to help in describing the nature of the directly corresponding homotopic residue, that is here to tend to be conserved, will consequently tend to work bear a tertiary directoral; etc... . To Be Continued! Sincerely,  SAMUEL DAVID ROACH. (1989).

More About Recursively Smooth Ricci Flow

 When a recursively smooth Ricci Flow is to be displayed, by a directly corresponding spinning isotropically stable mass-bearing cohesive set of discrete energy quanta, — the magnetically associated gravitational-like energy, that is here to be exhibited at the proximal local external shell, of such an inferred cohesive set of energy, is thenceforth to be stretched back-and-forth — like a metaphorical set of harmonically interactive “rubber-bands.” This general activity of such a respective type of a Fourier-related activity — in which the recursive kinematic manner of the general reiterative process, in which the given arbitrary tense, in which the back-and-forth manner, that is here to be of the gravitational curvature-related deformation of the magnetic-associated spin-orbital indices, — will consequently often tend to enhance the general probability, of an increased chance, for an enhanced ability of a consequential resultant transversal thrust, that is here to often tend to help facilitate an increased ability, for the said mass-bearing cohesive set of discrete energy quanta, to be tugged into a relatively strong scalar amplitude, of a transversally inclined tense, of a Lagrangian-based drive, in its directly corresponding angular momentum.

Sam Roach.

Recursively Smooth Ricci Flow

 The more homeomorphic that the flow of the rotational motion is to be, that is here to be of the Fourier-related spatial translation, of an isotropically stable mass-bearing cohesive set of discrete energy quanta, -- the more recursively smooth, that the directly corresponding Ricci Flow will consequently tend to be. SAM ROAH. 

On The Dispersal Of Superfluous Drawn-In Magnetism

 Let us initially consider a given arbitrary Noether-based highly magnetic mass-bearing cohesive set of discrete energy quanta, that is thence to tend to adhere to be exhibiting a relatively strong tense, of consequently working to bear a high scalar amplitude, of a correlative Majorana-Weyl-Invariant-Mode, -- over a proscribed duration of time -- to where the directly corresponding flow of such an inferred general type of a Fourier-Related Transform, --- is thereby to occur, over an evenly-gauged Hamiltonian eigenmetric. The inferred isotropically stable set of energy quanta, in such a respective given arbitrary case, is to be engaged in such a manner, to where it will work to bear, both a homeomorphic rotational spatial translation over time, as well as this working to bear a homeomorphic transversal spatial translation over time. The quicker that such an inferred tense of a mass-bearing cohesive set of discrete energy quanta, is to be spinning, in a relativistic tense, in its relationship to the motion of light, -- the more that the topological manifold, of the implied tense of such a stated discrete set of energy quanta, is consequently to have an increased probability of resulting, in an ensuing dispersal, of the otherwise drawn-in superfluous  eigenstates of magnetic residual charge, that would tend to be of a potential hindrance to the motion, of the said set of discrete energy quanta -- if such a mentioned Fourier-related activity, of a relatively high scalar magnitude of rotational acceleration, were instead, to not be occurring. To Be Continued! Sam Roach.

Homeomorphic Isotropic Stability — High Tense Of Majorana-Weyl-Invariant-Mode

 Isotropically stable mass-bearing cohesive sets of discrete energy quanta, that are here to be spatially transferred in a homeomorphic manner, — by the kinetic assistance of a Legendre tense of (co)homology, tend to work to bear a relatively higher scalar amplitude of a Majorana-Weyl-Invariant-Mode — to where this will often tend to be associated in one manner or another, with a charged particle, that is here to be in the process of being spatially conveyed, with a relatively low scalar magnitude of electrical resistance. SAM.

Electricity Of Low Impedance

 Electricity of low impedance (low resistance), tends to conduct well, — specifically speaking here, in Majorana-Weyl-Invariant-Mode sub-atomic-related structures. TO Be CONTINUED! Sincerely, SAMUEL DAVID ROACH. (1989).

Highly Magnetic Cohesive Set Of Discrete Energy Quanta

 A given arbitrary Noether-based mass-bearing cohesive set of discrete energy quanta, that is here to be of the nature of a specific given arbitrary Hodge-Index of a quantum energy state, -- is to tend to be of a highly magnetic nature; when it is both to work to bear an isotropically stable homeomorphic rotational spatial translation, over a proscribed duration of time, as well as when it is to work to bear an isotropically stable homeomorphic transversal spatial translation, over that same eluded-to proscribed duration of time. Sincerely, SAM ROACH. (1989).

Correlative Decrease In Torsional Force Of Set Of Discrete Energy Quanta

 When a given arbitrary Noether-based mass-bearing cohesive set of discrete energy quanta, that is here to be working to display the mapping-out of a De Rham cohomology, is here to ensue in displaying a relative decrease in the scalar magnitude, that is appertaining to the net rate of the spatial transference, of its directly corresponding spin-orbital tensors, this will then often tend to result, in a consequentially lowered "drive," in the scalar amplitude of its directly corresponding angular momentum.  This is on account of the reductional physical condition, that since added torsion upon a topological manifold, will often lead to a stronger drive in a  direction; it will consequently follow, that a lowered torsion upon a topological manifold, will  often lead to a weaker drive in a direction. To Be Continued! Sincerely, SAM ROACH.

Isotropic Flow And Capacitance/Conductance

 A banded group of isotropically stable cohesive sets of discrete energy quanta, tends to be more facilitated  at working to form a homeomorphic flow; than a banded group of isotropically unstable cohesive sets of discrete energy quanta does. Furthermore; the homeomorphic flow of a banded group of isotropically stable cohesive sets of discrete energy quanta, tends to bear both a greater capacitance and a greater conductance; than the homeomorphic flow of a banded group of isotropically unstable cohesive sets of discrete energy quanta does. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL.

Homeomorphic Flow Of Isotropically Stable Phenomenology

 A homeomorphic flow, that is of a banded group of isotropically stable cohesive sets of discrete energy quanta, tends to work to display, both a relatively higher capacitance and a relatively higher conductance; than a heteromorphic flow, that is of an otherwise similar banded group of isotropically stable cohesive sets of discrete energy quanta. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL DAVID ROACH. (1989).

Isotropic Transfer Of Mass-Bearing Energy

  A given arbitrary tense of an Isotropically stable Legendre (co)homology, (which is, in this particular case, as appertaining to a set of open-looped isotropic superstrings, of discrete kinetic energy permittivity),  has a stronger capacity, of working to transfer its respective correlative given arbitrary mass-bearing cohesive set of discrete energy quanta, when the just mentioned respective mass-bearing cohesive set of discrete energy quanta, is also, as well, to work to display an isotropically stable nature. I will continue with the suspense later! Sincerely, SAM ROACH.

Isotropic Stability And Structural Integrity

 Individually taken cohesive sets of discrete energy quanta, that work to bear a high scalar amplitude of isotropic stability, have a "habit" of tending to work to bear a greater structural integrity, -- than if such said cohesive sets of discrete energy quanta, were, instead, to not work to bear such a tense of isotropic stability. I will continue with the suspense later! To Be Continued! Sincerely, SAM ROACH. (1989).

Homeomorphic Tense Of The i*PI(Del) Action

 When an isotropically stable mass-bearing cohesive set of discrete energy quanta, is to evenly accelerate towards the speed of light -- while such a said set of discrete energy quanta, is here to work to bear a consistent directional tense of angular momentum in the process, -- then consequently; such a respective inferred genus of a mass-bearing cohesive set of discrete energy quanta, will thereby tend to work to bear a homeomorphic tense of a gauged-action, in its correlative i*PI(Del) Action. Sincerely, Sam Roach. 

Potential Exchange Differential

 The greater that the given arbitrary scalar amplitude is to be, of that potential exchange differential, that is here to be pertinent to the correlative respective alterations in the number/delineation of those directly corresponding partition-based discrepancies (of superstrings), that are here to be kinematically re-distributed, in one manner or another, in relation to the motion of light, — in so as to work to facilitate the eminent covariant proximal local presence, of the respective correlative i*PI(Del) Action, — thereby, the higher that the reverse-fractal-related tense of the directly corresponding magnetic flux potential will consequently tend to be, — when this is here to be taken, relatively speaking,  at a significantly more “macroscopic” level. (As this is thence to be taken at more of a molecular level, instead of at the superstring-related level.) SAM.

Density Of Formative Superstring-Related Forces -- Density Of Correlative Schwinger-Indices

 The denser that the given arbitrary formative superstring-related forces, that are here to be initiated at a covariant proximal local region, of which is here to be present at the correlative respective Ward-Cauchy-related level, -- this will then tend to result in a situation, to where it will consequently follow, that there will thereby be the covariant proximal local presence, at the previous inferred kinematic cite, of a greater  scalar amplitude of wave-like topological sway, as expressed by an increase in the respective directly corresponding density, that is of those correlative Schwinger-Indices, that are here to be of the nature of consequently appertaining to that general classification, as being of the essence of that general topological manifold, which is here to be of the nature of those vibrational oscillations, that are here to be formed, by the "plucking" of second-order light-cone-gauge eigenstates, by their directly associated gauge-boson eigenstates.  I WILL CONTINUE WIHT THE SUSPENSE LATER! TO BE CONTINUED! SAM. (1989).

When the Betti Number Is Zero -- For A Specific Given Arbitrary Set Of Discrete Energy Quanta

 Let us initially consider one given arbitrary mass-bearing cohesive set of discrete energy quanta, as taken over the course of one given arbitrary iteration of group-related instanton. For all of those individually taken superstrings of discrete energy permittivity that work to comprise such an implied tense of a cohesive set of discrete energy quanta, each of such said strings are to work to bear the exhibition of the same Betti Number going Into the earlier mentioned iteration of group-related instanton, (as being either "0," or as being of a "positive" integer here); as well as that each of such individually taken superstrings of discrete energy permittivity that are here to work to comprise such an implied tense of a cohesive set of discrete energy quanta, are to work to bear the exhibition of the same Betti Number going Out of the earlier mentioned iteration of group-related instanton (as being either "0," or as being of a "negative" integer here). If the Betti Number is here to be "0" during both the general process of both going Into the said respective iteration of group-related instanton, as well as if the Betti Number is also to be "0" during the general process of going Out of the said respective iteration of group-related instanton, then, both each of the given arbitrary individually taken respective superstrings of such case , as well as the entire mass-bearing cohesive set of discrete energy quanta, will remain of as working to continue to display the same number of spatial dimensions, in the general process of this to be occurring. SAM ROACH.

Spinning Of Isotropically Stable Set Of Discrete Energy Quanta

 When a given arbitrary isotropically stable mass-bearing cohesive set of discrete energy quanta, that is here to basically be transversally fixed, over a discrete duration, that is here to be contingent upon the flow of a respective sequential series of group-related instantons, -- as this is here to be associated with a proscribed evenly-gauged Hamiltonian eigenmetric, -- as such a general type of a topological phenomenology, is thereby to work to maintain a constant rate of a rotational flow, in relation to light, in all of its applicable directly corroborative spin-orbital tensors, then, over the duration of the inferred period of time in which this is here to be occurring, such a said isotropically stable mass-bearing cohesive set of discrete energy quanta, will, during the course of this inferred case scenario,  consequently tend to lack the eminent proximal local presence, of imparting the general genus of that reductional type of a Fourier-Related activity, of which I tend to term of as being called, the "i*PI(Del) Action." (This is with the exception, of the potential recursively iterative alterations in the corroborative delineation-related indices, that are appertaining to those contingent partition-based discrepancies of such a respective case, of which is here to be due to that general type of an activity, whereby those directly associated changes in the direction, of which such an inferred cohesive set of discrete energy quanta is to impart, is to consistently be altering, (in relation to the motion of light), as it is here to work to bear a constant flow, in its net tensor-related oscillation(s.)) I will continue with the suspense later! To Be Continued! Sincerely, Samuel David Roach. 

Electricity, And High Generation Of Cohomology

 Let us initially consider a certain given arbitrary mass-bearing cohesive set of discrete energy quanta, that is here to be of the holonomic substrate of a moving electron (as appertaining to a discrete increment of electricity). Let us next say, -- that such an inferred flowing electron, is here to be approaching a velocity, that is at just under the speed of light. The larger the number of partition-based discrepancies, that are here to be exchanged, for the composite sum of the overall net gauged-action, that is of the correlative net behavior of the individually taken mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise the herein stated electron, both the lower that its consequential electrical resistivity will tend to be, and also, the greater that its directly corresponding cohomology-related generation will consequently tend to be, as well. TO BE CONTINUED! Sincerely, SAMUEL DAVID ROACH.

As to High Resonant Vibration

 Let us initially consider a mass-bearing cohesive set of discrete energy quanta, of which is here to be working to display a relatively high elastic modulus, that is also to be working to exhibit a relatively large number of spatial dimensions. The more partition-based discrepancies, that are to be exchanged per iteration of group-related instanton, of which are here to be directly affiliated with those individually taken mass-bearing superstrings of discrete energy permittivity, that are here to work to comprise such a said respective mass-bearing cohesive set of discrete energy quanta, the higher that the resulting directly corresponding scalar amplitude of the correlative resonant vibration, of the interplay of such an inferred set of discrete energy quanta, will consequently tend to be exhibiting. To Be Continued! Sincerely, SAMUEL DAVID ROACH.

Probability Of A Homeomorphic i*PI(Del) Action

When a given arbitrary mass-bearing cohesive set of discrete energy quanta, is to evenly accelerate in its velocity, when this in its relation to the motion of electromagnetic energy, this will thereby tend to work to increase the probability, for the directly affiliated i*PI(Del) Action, to thereby have an increased ability, of working to exhibit a homeomorphic tense of behavior. To Be Continued! Sincerely, SAM ROACH.

Spinning Heuristic Calabi-Yau-Related Field

 When the i*PI(Del) Action is to be eminent, upon a given arbitrary spinning intrinsic heuristic Noether-based Calabi-Yau-Related field, this inferred tense, of such a general genus of a Fourier-Related activity, will consequently tend to work to effect the scalar amplitude, as to the covariant proximal local effect, of the correlative decrease/increase, in the effectual gravitational impedance, that is thenceforth to be latent, upon the topological manifold, that is here to be of that respective inferred mass-bearing cohesive set of discrete energy quanta, that is here to work to be exhibiting such an inferred innate tendency, of displaying such a tense of a heuristic Calabi-Yau-Related field. If such an inferred tense of the correlative i*PI(Del) Action, is to work to bear a relative decrease in the number of partition-based discrepancies, that are here to be present, for those individually taken superstrings of discrete energy permittivity, that are here to work to comprise such a said mass-bearing cohesive set of discrete energy quanta, then, such an inferred case of an accelerative phenomenology, will simultaneously (via the vantage-point of a central locus), tend to result, in a lowered gravitational impedance. However; if such an inferred tense of a the correlative i*PI(Del) Action, is to work to bear a relative increase in the number of partition-based discrepancies, that are here to be present, for those individually taken superstrings of discrete energy permittivity, that are here to work to comprise such a said mass-bearing cohesive set of discrete energy quanta, then, such an inferred case of a deccelerative phenomenology, will simultaneously (via the vantage-point of a central locus), tend to result, in a heightened gravitational impedance. Reminder: As those individually taken superstrings of discrete energy, that are here to work to comprise a respective mass-bearing cohesive set of discrete energy quanta, are to Decrease in the number of their correlative partition-based discrepancies, then, this general phenomenology of an inferred set of discrete energy quanta, of such a respective given arbitrary case, will consequently tend to proportionately increase, in the number of mass-bearing superstrings, that are here to work to make-up such a said set of discrete energy quanta. Furthermore; as those individually taken superstrings of discrete energy quanta, that are here to work to comprise a respective mass-bearing cohesive set of discrete energy quanta, are to Increase in the number of their correlative partition-based discrepancies, then, this general phenomenology of  an inferred set of discrete energy quanta, of such a respective given arbitrary case, will consequently tend to proportionately decrease in the number of mass-bearing superstrings, that are here to work to make-up such a said set of discrete energy quanta. To Be Continued! Sincerely, SAMUEL ROACH. (1989).

Homogeneous Ricci Flow -- Less Gravitational Impedance

 Let us initially consider a Noether-based mass-bearing cohesive set of discrete energy quanta, that is here to be undergoing a homogeneous Ricci Flow, -- to where it is here, to tend to be exhibiting, what may be termed of as being a "flat" Ricci Curvature. The faster that such a said mass-bearing cohesive set of discrete energy quanta, is thereby to be traveling, when this is here to be in its relationship to the correlative motion of electromagnetic energy, -- the less that the force of impedance, by which the adjutant proximal local gravitational forces, that are here to be immediately surrounding the general whereabouts of such an inferred set of discrete energy quanta, will consequently tend to exhibit -- to where such an inferred tense of a cohesive set of discrete energy quanta, will thereby tend to result, in working to bear a lower gravitational inhibition, in the overall net "momentum" of such a said mass-bearing cohesive set of discrete energy quanta. This general tendency tends to be facilitated, by the general kinematic activity, in which such an inferred transversally moving phenomenology of a mass-bearing cohesive set of discrete energy quanta, is to be spinning, as it is to be simultaneously moving along its given arbitrary correlative Lagrangian-Based path. SAM ROACH. YES, I GRADUATED FROM PINCKNEY HIGH;  (1989).

Spinning Field -- Heuristic Calabi-Yau-Related Nature

 A spinning mass-bearing Noether-related field, that is here to work to bear an intrinsic heuristic Calabi-Yau-Related nature, -- will tend to work to bear a greater potential, of exhibiting an affinity for working to display a tense of anti gravity, than an ulterior field, that is instead, to tend to work to Not bear such an inferred tense, of an intrinsic heuristic Calabi-Yau-Related nature. To Be Continued! Sincerely, SAMUEL  ROACH. (1989).

Homogeneous Ricci Flow -- Flat Ricci Curvature -- Heuristic Calabi-Yau-Related Field

 The more homogeneous that the Ricci Flow is to be, at a given arbitrary region in time and space, the flatter that the directly corresponding proximal local Ricci Curvature is to tend to be, at that respective given arbitrary said region, in time and space. The flatter that the Ricci Curvature is to be, at a given arbitrary region in time and space, the more probable, that any one given arbitrary directly corresponding cohesive set of discrete energy quanta, that is here to be proximal local to that said respective region of space-time fabric, is thence to tend to work to bear a heuristic Calabi-Yau-Related field. Therefore; the more homogeneous that the Ricci Flow is to be, at a given arbitrary region in time and space, the more probable that any one given arbitrary directly corresponding cohesive set of discrete energy quanta, that is here to be proximal local to that said respective region of space-time fabric, is thence to tend to work to bear a heuristic Calabi-Yau-Related field. I will continue with the suspense later! Sincerely, SAMUEL ROACH. (1989).

A Little As To Why Yau-Exact Behavior Is As It Is

 What I term of as being the "partition-based discrepancies" of Noether-based superstrings of discrete energy permittivity, act as the directly correlative indices, of what I term of as being the general phenomenology of "homotopic residue." Such individually taken sets of such inferred indices of homotopic residue, in a way, act as a tense of what may be thought of as being a general genus of "kinks," that are here to be delineated, in an adjutant manner,  that is basically pretty much proximal local to the core-field-density, that is here to be mappable in a covariant manner, along the contour of the topological manifold, of those individually taken directly corresponding mass-bearing superstrings of discrete energy permittivity, that are here to have the intrinsic capacity of tending to bear a Yau-Exact nature. The faster that such individually taken mass-bearing superstrings of discrete energy permittivity are to travel -- in their relationship to the motion of electromagnetic energy -- the more that such inferred strings are to require an affiliation with less of the so-stated "kinks," in order to be able to work to bear a quickened piecewise continuous process, of being able to generate as much cohomology as these are here to degenerate, -- per each recursively associated iteration of an evenly-gauged Hamiltonian eigenmetric.  Homotopy is to be conserved, in order for the universality of superstring-related fields, as a whole, to thenceforth be able to bear an eminent inter-connection amongst one another (which is necessary, in order for Casimir Invariance to be able to be upheld). Thereby; as a cohesive set of discrete energy quanta (which may be thought of as being basically a "team" of superstrings), is to increase in its speed of relative motion, in its relation to light, the consequential decrease in the inferred presence of what I term of as being "partition-based discrepancies," as this is here to be among the correlative composite individually taken superstrings of discrete energy permittivity, is thereby to be resulted, in a proportional increase in the number of mass-bearing  superstrings of discrete energy permittivity, that are here to work to comprise such a said "team." This is part of the reason, as to why a mass-bearing phenomenology is to increase in its scalar amount of mass, as it is to increase in its velocity, in relation to light.  To Be Continued! Sincerely, SAM ROACH. (1989).

Flat Ricci Curvature And De Rham Cohomology

 A cohesive set of discrete energy quanta, is more likely to work to map-out a De Rham cohomology, if the Hamiltonian Operand that it is here to be transferred through, is to work to bear a flat Ricci Curvature, -- than if such a said cohesive set of discrete energy is, instead, to be transferred through a Hamiltonian Operand, that is here to work to bear a spurious tense of a Ricci Curvature. To Be Continued! Sincerely, Samuel David Roach. 

Ricci Flow And Hermitian-Related Cohomology

 A cohesive set of discrete energy quanta, is more likely to work to exhibit a hermitian-related cohomology, if it is to work to bear a homogeneous Ricci Flow, than if such a said cohesive set of discrete energy quanta were, instead, to work to bear a heterogeneous Ricci Flow. Sincerely, SAM ROACH. (1989).

Sound, Heat, And Isotropic Stability

 Isotropically stable vibrational interactions, among mass-bearing cohesive sets of discrete energy quanta, tend to have more of a probability of working to form sound than heat; whereas, isotropically unstable vibrational interactions, among mass-bearing cohesive sets of discrete energy quanta, tend to have more of a probability of working to form heat than sound. I will continue with the suspense later! I will continue with the suspense later! Sincerely, SAMUEL DAVID ROACH.

Thought Waves And Isotropically Stable Energy Quanta

 Thought waves tend to be able to harmonize MORE with isotropically stable cohesive sets of discrete energy quanta, than with isotropically unstable cohesive sets of discrete energy quanta. SAM ROACH.

Recursive Manner Of Smooth Ricci Flow

 When a relatively smooth Ricci Flow is to be exhibited, by a cohesive set of discrete energy quanta, --  that is here to recursively go back-and-forth, from working to display a radial-related sway, to working to display a transversal-related sway, to working to display a radial-related sway, and so on, -- this general type of a kinematic-related activity, will often consequently tend to work to cause a relatively heightened drive -- in the respective given arbitrary angular momentum, that is here to be directly appertaining to the holomorphic wave-tug, of the Hamiltonian fractal of "thrust," that is here to be exhibited, by the Lagrangian-based motion, of the Fourier Transform, that is here to be correlative to the spatial transference of the earlier mentioned cohesive set of discrete energy quanta in question. SAMUEL. (1989).

Radial-Related Sway, Of Correlative Ricci Flow

 The more of a radial-related sway, that the Ricci Flow is to work to impart, -- upon a given arbitrary cohesive set of discrete energy quanta, that is to be accelerating in its respective motion, when this is to be taken in relation to light, -- the more likely that a tense of a potential torsional force, will often consequently tend to be imparted, upon the correlative i*PI(Del) Action, that is here to be directly associated with the physical attributes, that are characteristic of the general activity of the Polyakov Action (which is here to act as that general type of an activity, that is inversely associated with the Lorentz-Four-Contraction). I will continue with the suspense later! To Be Continued! Sincerely, SAM.

Isotropic Stability, And The Ricci Flow

 The smoother that the correlative Ricci Flow is to be, for a given arbitrary cohesive set of discrete energy quanta, the more likely that this respective physical condition of a smoother Ricci Flow, -- will consequently tend to work to help, in allowing for a stronger scalar amplitude of isotropic stability. SAM.

Isotropic Stability and Torsion Upon i*PI(Del) Action

 Let us initially consider a mass-bearing cohesive set of discrete energy quanta, of which is here to be in the process of having a viable tense of torsion, being applied upon its directly corresponding i*PI(Del) Action eigenstates.  The more isotropically stable of a physical condition, that such a herein mentioned cohesive set of discrete energy quanta is to be exhibiting, over a proscribed discrete duration of time, -- the more eminent of an effect, that the inferred twisting of the correlative i*PI(Del) Action, will tend to work to bear, upon its immediate environment. To Be Continued! Sincerely, SAMUEL DAVID ROACH. (1989.)

Rapid Change In Direction And Torsion Upon i*PI(Del) Action

Let us consider a given arbitrary mass-bearing cohesive set of discrete energy quanta, that is here to be increasing in its rate of speed, at a constant rate. The more rapidly that such a said respective given arbitrary cohesive set of discrete energy quanta, is to be altering in its direction of motion in the meanwhile, -- the more torsion that will consequently tend to be applied, to the directly associated inferred covariant tense, of its correlative eminent i*PI(Del) Action. I will continue with the suspense later! Sincerely, SAMUEL ROACH.

As To A Different Nature Of Schwinger-Indices That Is Produced

 Let us consider two different covariant superstrings of discrete energy permittivity, that are here to both be working to exhibit basically the same nature of behavior, -- except, that one of such superstrings is to be vibrating in a slightly different manner, than the other of such inferred strings is to be exhibiting. This will consequently tend to result, among other things, that these two different distinct covariant superstrings of discrete energy permittivity, will consequently tend to have a strong probability, of tending to form two different distinct respective genre of Schwinger-Indices, -- as such said "Schwinger-Indices" are thence to be produced, by the correlative "plucking" of the correlative gauge-bosons  -- that are here to be directly corresponding to each of the two said respective individually taken superstrings of discrete energy permittivity -- Upon the topological substrate of their directly corresponding second-order light-cone-gauge eigenstates, -- in the process of working to form those vibrational oscillations, that are to be propagated along the general Rarita Structure, in so as to work to facilitate the conveyance of the existence of the reductional forces of physical nature. I will continue with the suspense later! To Be Continued! Sincerely, SAM. (1989).

Idea, As To What Works To Facilitate The Reductional Forces Of Physical Nature

 Here is a general idea (an overview, if you will), as to what works to help, at facilitating the physical presence, -- as to the existence of the reductional forces of physical nature.:

The multiplicity of discrete energy is spatially translated, over the general course of a sequential series of group-related instantons. In the meanwhile; the corresponding second-order light-cone-gauge eigenstates, that are here to be most directly involved, with the proximal local presence of such an inferred tense of discrete energy quanta, are to be "plucked" like a "harp," by their directly corresponding gauge-bosons. The said second-order light-cone-gauge eigenstates, are thence to consequently work to bear a tense, of a proximal local vibrational oscillation. This just mentioned tense of vibrational oscillation, is then to propagate outward, -- due to the reductional physical condition, that superstring-related fields, tend to be inter-bound by the general condition of homotopy. This outward propagation of vibrational oscillation, is consequently to work to interact with other Ward-Cauchy-related phenomenology, in order to thereby work to indirectly cause the multiplicity, of the general vibrational oscillation, of mini-string-related fabric -- along the general topology of space and time. The multiplicity of mini-string-related fabric, is what works to both act and direct, the proximal local existence, of the respective reductional entity and motion, that is here to be of the kinematic inter-play, of the overall net interaction of discrete energy quanta. And it is the overall net interaction of discrete energy quanta, that works -- in one manner or another -- to help in the facilitation, of both the presence and in the gauged-action, of the proximal local existence of the reductional forces of physical nature. Therefore; this works to consequently indicate, that the earlier mentioned general vibrational oscillation of mini-string-related fabric, is a key factor, as to what helps in working to facilitate the reductional forces of physical nature. To Be Continued! Sincerely, SAM ROACH.

The Four Main Functions Of The Rarita Structure

 The four main functions of the Rarita Structure, are:

1) To act as the main entity, which works to form the general substrate of superstring-related fields.

2) To guide the directional attributes, of the correlative fields of discrete energy quanta.

3) To facilitate the conveyance, of the reductional forces of physical nature.

And;

4) To act as that general medium, by which the substrate of pressurized vacuum, may then consequently take a viable effect, upon discrete energy quanta.

I will continue withe the suspense later! To Be Continued! Sincerely, SAMUEL DAVID ROACH.

As To Smooth Topological Contour

 The smoother that the topological surface of the external “shell” of a cohesive set of discrete energy quanta is to be, as this is here to be taken at a Laplacian-related condition, over the course of an applicable given arbitrary iteration of group-related instanton, — the more likely that such a said cohesive set of discrete energy quanta, is to work to bear the nature, of acting as a diffeomorphic topological manifold. SAM.

As To Gain/Loss Of i*PI(Del) Action Increments

 The gain and/or loss of i*PI(Del) “increments” (partition-based discrepancies),  per instanton, as this is here to be considered, for those individually taken superstrings of discrete energy permittivity, that are here to work to comprise an individually taken cohesive set of discrete energy quanta, — as this is likewise to be considered, when given what the specific given arbitrarily correlative Lorentz-Four-Contraction/Polyakov Action eigenstate happens to be, in such a general type of a case scenario, — often tends to work to facilitate the general oscillation-related effect, of helping to “manage” the general structural integrity of the spatial dimensionality, of such a respective given arbitrary cohesive set of discrete energy quanta. As you may have already guessed, such an inferred oscillation-related effect, is here to be referring, to the E(8)XE(8) string-related oscillation-based-mode. Sincerely, SAM ROACH.

Homeomorphic Nature And Scattering

 When the Motion of a cohesive set of discrete energy quanta, is to be brought Into a tense of working to display a homeomorphic nature, this often tends to be the case, of a general genus of a  Riemann scattering. Furthermore; when the Motion of a cohesive set of discrete energy quanta, is to be brought Out of a tense of working to display a homeomorphic nature, this often tends to be the case, of a  general genus of a Rayleigh scattering. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL DAVID ROACH. (1989).

Diffeomorphism And Scattering

 When a cohesive set of discrete energy quanta, is to be brought Into a condition of diffeomorphism, this often tends to be the case, of a general genus of a Riemann scattering. Furthermore; when a cohesive set of discrete energy quanta, is to be brought Out of a condition of diffeomorphism, this often tends to be the case, of a general genus of a Rayleigh scattering. To Be Continued! Sincerely, SAMUEL DAVD ROACH. (1989). 

Isotropic Stability And Homeomorphic Field

 The more isotropically stable, that the Fourier Transform, that is here to be of a Noether-based mass-bearing cohesive set of discrete energy quanta, is to be translated as, while it is here to work to bear the general manner of exhibiting the workings of a De Rham cohomology -- while such a herein stated cohesive set of discrete energy quanta, is here to be transferred through time and space -- from one spot to another, -- the more likely that the mappable-tracing, that is here to be of the cohomology-related projection, of the inferred directly corresponding propagated path, that is correlative to the direction of the Lagrangian-based path, that the earlier mentioned mass-bearing cohesive set of discrete energy quanta, is here to be traveling along, over a duration, that is here to work to involve a sequential series of group-related instantons, (as taken, over an evenly-gauged Hamiltonian eigenmetric), this will thereby often consequently tend to result, in the exhibition or display, of the propagation of a respective genus of a homeomorphic field. I will continue with the suspense later! Sincerely, SAMUEL ROACH. (1989).

Alteration In Tense Of Escalation/Attenuation -- Chern-Simons Singularities

 Whenever an escalating/attenuating expansive Lagrangian, that is here to be appertaining to the manner of the motion, of a cohesive se of discrete energy quanta, is either to be dampened or augmented, in the scalar attribute of its inferred escalation/attenuation, -- there will consequently tend to be a covariant proximally local presence, of a set of one or more metric-related Chern-Simons singularities -- since either of such an inferred respective dampening or augmentation, would thus tend to work to cause an alteration, in the dimensional-related pulsation, that is here to be appertaining to the manner of the spatial transference, of the directly corresponding inferred Fourier-related propagation, of such a said cohesive set of discrete energy quanta. I will continue with the suspense later! To Be Continued! Sincerely, SAMUEL ROACH.

Convergent Dampening Of Escalating Expansive Lagrangian

 When an escalating expansive Lagrangian, that is here to be of the motion of a given arbitrary cohesive set of discrete energy quanta, is to work to bear a convergent attenuation, of its regional proximal local attritional attribute, of the inferred dampening of such a respective tense of an escalating expansion, -- this will thereby tend to consequently result, in a decrease in the correlative demonstrable exponential rate of Ricci-related flow, whereby the initial tense of such an inferred escalation, is then to tend to result, in a relative decrease in the rate of its escalation, over the durational course of a sequential series of group-related instantons, -- as this is here to be taken, over an evenly-gauged Hamiltonian eigenmetric. SAM. 

Homeomorphic i*PI(Del) Action — Homeomorphic Translation Of Proximal Local Correlative Homotopic Residue

 The more homeomorphic that the i*PI(Del) Action is to occur, at a given arbitrary covariant proximal local region in time and space, — the more likely that the correlative directly corresponding homotopic residue, that is here to be generated at such an earlier stated covariant proximal local region, will thereby consequently tend to be translated through such a said general region, in a homeomorphic manner. SAM.

Diffeomorphic Cohesive Set Of Discrete Energy Quanta -- Compounded Homotopic Residue

 When a diffeomorphic cohesive set of discrete energy quanta, is here to work to bear an expansive escalating Lagrangian, -- that is here to bear, both a lack of any viable spurious Chern-Simons-related Lagrangian-based singularities, As well as to be lacking any viable spurious Chern-Simons-related metric-based  singularities -- in the process, in which the spatial propagation of such a mentioned cohesive set of discrete energy quanta, is  here to be transferred along the said expansive Lagrangian-based path, that is here to be escalating, -- then, the correlative generation, that is here to be of the directly corresponding regionally proximal local compounded homotopic residue, that is here to be appertaining to the correlatively inferred tense of escalation, in which such an inferred trajectory of a discrete holonomic entity, is here to be smoothly spatially transferred, in such an inferred manner of projection, will thereby consequently often tend to bear the tense, of working to exhibit a general genus of a homeomorphic field. I WILL SOON CONTINUE WITH THE SUSPENSE!  Sincerely, SAMUEL DAVID ROACH. (1989). 

Attritional Homotopic Residue

 When a cohesive set of discrete energy  quanta, is here to be displaying a unitary attenuated expanding Lagrangian, -- it will consequently tend to be exhibiting, a tense of a unitary attrition, of its correlative regional proximal local homotopic redidue. When a cohesive set of discrete energy quanta, is here to be displaying a binary attenuated expanding Lagrangian, -- it will consequently tend to be exhibiting, a tense of a binary attrition, of its correlative regional proximal local homotopic residue. Furthermore; when a cohesive set of discrete energy quanta, is here to be displaying a tertiary attenuated expanding Lagrangian, - it will consequently tend to be exhibiting, a tense of a tertiary attrition, of its correlative regional proximal local homotopic residue., etc... . To Be Continued! Sincerely, SAMUEL DAVD ROACH. (FROM PINCKNEY MICHIGAN, HIGH SCHOOL CLASS OF 1989.).

As To Torsion Acting Upon Superstring -- Light-Cone-Gauge Eigenstate

 Whenever a gauged-action, that is here to behave as a torsional force, is here to be imparted, upon a given arbitrary correlative superstring of discrete energy permittivity, -- this general genus of a gauged-action, will consequently tend to work to form a tense of twisting, upon its correlative directly corresponding respective light-cone-gauge eigenstate. I will continue with the suspense later! Be Continued! Sincerely, Samuel David Roach.    

Fortification Of Chi

 When a set of thought waves work to harmonically interact with scalar increments of Yin(g), this general process, tends to work to fortify the said Yin(g). When a set of thought waves work to harmonically interact with scalar increments of Yang, this general process, tends to work to fortify the said Yang. Therefore; when a set of thought waves work to harmonically interact with the general resultant attribute, of the E(8)XE(8) string-related oscillation-based mode, this general process, tends to work to fortify Chi. I will continue with the suspense later! To be continued! Sincerely, SAMUEL DAVID ROACH. (1989).

More Thoughts, As To Conservation Of Homotopic Residue

 In general: For every scalar increment of the compounding of homotopic residue, there is to be an equal and opposite scalar increment of the attrition of homotopic residue, — of which is here to work to bear, either a directly and/or an indirectly opposite tense, — of a direction of subtension. This works to facilitate the general necessary attribute, of the conservation of homotopic residue. Sincerely, SAM ROACH. (1989).

As To “Expand/Contract”

 When determining the “driving-force,” of a Ward-Cauchy-related entity of holonomic substrate:  If the anti-derivative-related Fourier multiplet of kinematic transform — that is here to be of the correlative transferable eigenstate, that is to be displaced in its delineation, in so as to work to bear a Hamiltonian-related fractal of “thrust,” upon its recursively proximal local indistinguishably different environment of topological operand, this will then entail, that the general respective process, will consequently tend to act, in so as to mathematically work to bear a positive inverse-root, upon the Lagrangian-related expression, that is here to be spatial translated, in this particular general genus of a scenario, in so as to work to operate upon the said eigenstate, of such a kinematically transferred phenomenon, to where this will then tend to be referring to an escalation of the motion, of an expansive discrete holnonmic quantum entity of topological stratum; yet, if such an inferred “inverse-root” is to be negative instead of positive, then, this is alternatively to tend to be referring to an Attenuating or attritional nature of potential expansion/contraction, — when this is here to be taken, in terms of the general genus of the proximal local generation of homotopic residue, that is thence to be in regards to the potentially expansive/contractive interplay, that is here to be of the kinematic gauged-action of the correlative discrete holonomic quantum entity of topological stratum — that is, in such a respective given arbitrary case in point, to be acting as the general substrate of Hamiltonian Operation. I will continue with the suspense later! To Be Continued! SAM ROACH. (1989).

Discrete Increments Of i*PI(Del) Action

 Partition-based discrepancies, are always to be determined per instanton, in terms of discrete increments involving i*PI(del).  A Noether-Based mass-bearing cohesive set of discrete energy quanta, will always tend to gain/lose between 8,886,110 to 8,886,112 discrete increments of partition-based discrepancies, (involving the i*PI(del) Action), over the durational span, of each individually taken successive iteration of group-related instanton. I will continue with later! To Be Continued! Sincerely, SAMUEL ROACH. (1989).

Sturdy Discrete Energy Quanta

 Mass-Bearing cohesive sets of discrete energy quanta, that both work to bear a relatively high scalar amplitude of Isotropic stability, — as well as working to display a relatively high scalar amplitude of kinematic permeability, tend to be relatively “sturdy,” — to where such an inferred general genus of mass-bearing cohesive sets of discrete energy quanta, will consequently tend to work to bear a relatively high tense of structural integrity — at a level that is here to be Poincare, to the correlative inferred Ward-Cauchy-related boundary conditions. I will continue with the suspense later! Sincerely, SAM ROACH.

Kinematically Permeative Topological Surface Of Cohesive Set Of Discrete Energy Quanta

 Often -- the more kinematically permeative that the topological surface of a cohesive set of discrete energy quanta is to be, the more likely that it will tend to work to display a greater tense of an elastic modulus. I WILL CONTINUE WIH THE SUSPENSE LATER! To Be Continued! (1989). Sincerely, SAMUEL DAVID ROACH.      

Resonant Static Pulse -- A Tense Of Recursion

What I term of as being a Resonant Static Pulse, is a genus of recursion in the scalar amplitude of the intensity of homotopic residue,  -- that is here to be locally present, at a given arbitrary region of space-time-fabric. In general; this is to where, the scalar amplitude of the intensity of a tense of the homotopic residue, that is here to be present for a certain respective phenomenology, as at a given arbitrary region in time and space, --  is repeatedly to go back-and-forth; from working to bear a greater amount of intensity, to working to bear a lesser amount of intensity, to working to bear a greater amount of intensity, etc... . SAM. (1989).

Resonant Static Pulse

 When an expansive physical phenomenon, that is here to be displaying a tense of an escalating Lagrangian, is to harmonically cycle back-and-forth, — from initially working to bear the general tense of a genus of a compounded homotopic residue, to working to bear the general tense of a genus of an attenuating homotopic residue, to working to bear the general tense of a genus of a compounded homotopic residue....etc., then, — the pulsation of such a herein mentioned expansive physical phenomenon, will consequently, in the process of doing so, tend to work to bear the general tense, of what I will call in such a general case, the nature of a Resonant Static Pulse. To Be Continued! SAMUEL.

Isotropically Stable Set Of Discrete Energy

 An isotropically stable mass-bearing cohesive set of discrete energy quanta, will tend to exhibit a higher fractal modulus, than a similar mass-bearing cohesive set of discrete energy quanta, that instead, is to be exhibiting an unstable isotropic nature. I will continue with the suspense later! SAMUEL ROACH. (1989).

Same Number Of Partition-Based Discrepancies -- Different Delineation

 Let us say one were here to be comparing the Laplacian-related covariant physical condition, that is here to be considered, between two different discrete quanta of energy, during an iteration of group-related instanton -- that is here to be of a simultaneous nature, when this is here to be considered, via the vantage-point of a central locus.  Both of the two said discrete energy quanta, are here to be exhibiting the same number of spatial dimensions, at their different and distinct covariant individually taken loci of delineation, as well as that both of these said discrete energy quanta, are here to be traveling at the same rate, in relation to the motion of electromagnetic energy. Even though both of the correlative respective inferred superstrings of such a given arbitrary case, are thereby to be exhibiting the same tense of a Lorentz-Four-Contraction, to where both of such said strings will also, as well, work to bear the same number of partition-based discrepancies, -- the comparative delineation, of such an inferred dual tense of partition-based discrepancies, may often potentially work to bear two different and distinct Ward Neumman  distributions -- since the angular momentum of their individually taken directions, via which these two different said distinct discrete energy quanta are to be aimed at, may quite often tend to work to bear a viable difference, in the manner of their variation of their parameters. Therefore; this will thereby often tend to make their distinctively different individually taken light-cone-gauge eigenstates, If these are here to work to bear a different delineation of distribution, when this is in the process, of comparing the overall topological contour, of both of such said respective covariant light-cone-gauge eigenstates, to thereby work to bear two different and distinct covariant structural genre of topological manifold -- as this is here to be in comparison, between these two different wave-related quanta of  discrete energy impedance. SAM. 

Gauge-Invariance -- Cohesive Set Of Discrete Energy Quanta

 If all of the superstrings of discrete energy permittivity, that work to comprise a mass-bearing cohesive set of discrete energy quanta, are working to exhibit a gauge-invariant nature, then, the inferred overall mass-bearing cohesive set of discrete energy quanta, itself, is also to be working to exhibit a gauge-invariant nature as well.  Till next time! To Be Continued! Sincerely, SAMUEL DAVID ROACH. (PHS 1989).