"Holonomic Quantum"

 A Noether-Based mass-bearing Hamiltonian Operator, at an internal reference-frame, that is to maintain its general tense of "holonomic quantum," will have the reductional tendency, of conserving its directly associated tense of homotopic residue, in order that the general configuration of its mass-based structure, when this is here to be taken at the Poincare level, to the internal reference-frame of the covariant Neumman boundary, that is localized at the general region that is proximal local to its immediately externalized topological stratum, is thereby to be structurally maintained, when this is here to be eminently considered, in relation to the modular integrity of the net topological manifold, of which is here to be directly associated, with the covariant delineative distribution of the mass, of such a stated Hamiltonian Operator, as such an inferred "team" of cohesive mass-bearing eigenstates, is here to bear a tense of super conformal invariance, at an internal reference-frame, that is Gliosis to the Poincare level of the outer boundary, of such an implied cohesive set of mass-bearing discrete energy quanta. Partition-Based Discrepancies of superstrings, work to act as eigenstate-related phenomenology of homotopic residue. In order for a Noether-Based mass-bearing "team" of energy to not change in its "holonnomic quantum," in so as to also not change, at an internal reference-frame,  in its general configuration of mass-based structure, there needs to be a conservation, as amongst the said "team," of a maintained number or quantum, of such eigenstates, of partition-based discrepancy. This way; The potential for contortion related symmetry, is to be maintained, and, the relativistic mass-based configuration of the said Hamiltonian Operator, at its particular vantage-point, is to not be altered. Teams OF Mass-Bearing Eigenstates, that are increasing in velocity, will have the general tendency, of increasing in the efficiency of their cohomological generation/degeneration, in order to successfully be traveling faster and faster. Mass-Bearing strings also have the general tendency, of generating as much cohomology as these degenerate, over time. This equilibrium of cohomological generation/degeneration, is done in a discretely piecewise continuous manner, with Yau-Exact energy systems. Discrete systems of energy are said to be Yau-Exact, when the Ricci Curvature is flat. The Ricci Curvature is flat, when the gravitational force that a Hamiltonian Operator is to be traveling in, is not changing in its effect. The more efficient that a superstring has to be, the less partition-based discrepancies that it is to have. Yet; The correlative Teams of mass-bearing strings, that such individually taken superstrings are here to work to comprise, are here to maintain the same number of partition-based discrepancies, in order for the structural integrity of such a "team" of mass-bearing states, to thereby be able to be maintained. So; For a team of Noether-Based mass-bearing strings, that are here to maintain their "holonomic quantum," it is generally to be the case, that as such a cohesive set of strings is to increase in speed, it will gain mass-bearing eigenstates, in order to be able to keep the same number of partition-based discrepancies, so that homotopic residue is to be conserved. This, in a "nutshell," is why the relativism of mass, in correlation to its speed, behaves as such. SAM ROACH. 

Also; What I meant by the multiplicity of the term, "holonomic quantum," is the general quantum-related cohesive set of physical attributes, that work to help facilitate the process, that is of the general maintenance of the structural integrity, of a given arbitrary applicably respective Hamiltonian Operator, that is here to work to be assisted in potentially achieving such an inferred tense of an eluded-to equilibrium, via the respective multiplicity, of the general process, of the herein mentioned tense, of the earlier stated general Operation, of the Conservation Of Homotopic Residue.  

The coupling of charge degeneration with the rate of the i*PI(del) Action, may often facilitate the heuristic formation of holonomy. 

When The i*PI(Del) Action Tends To Be Effectual

 The i*PI(Del) Action tends to be effectual, when Ward-Cauchy-Related Chern-Simons Invariant Gauge-Actions are being re-calibrated. Chern-Simons Invariant Gauge-Actions tend to be re-calibrated, when the speed and/or direction of a mass-bearing Hamiltonian Operator is to change, relative to the motion/existence of electromagnetic energy. SINCERELY, SAMUEL DAVID ROACH. 

A given arbitrary De Rham, Lagrangian-Based mappable-tracing, that is of the eminently associated projected path, that is here to be spontaneously delineated, by a corroborative set, of covariant energy-related eigenstates, may often tend to be involving, a harmonic flow, of cohomology-related Hess States. Whereas; A Dolbeault Lagrangian-Based mappable-tracing, that is of the eminently associated projected path, that is here to be spontaneously delineated, by a corroborative set, of covariant energy-related eigenstates, may often tend to work to involve, a sporadic flow, of cohomology-related Hess States.This is here to tend to be taken, at a Laplacian.

 The smaller that the wavelength, of a kinematically propagated thought wave, happens to be, to where such a wave, is here to be of a proscribed transversal rate of delineation transfer, the Greater that its eminently associated Frequency, will often spontaneously tend to be — to where such an implicit relatively high frequency thought wave, will often tend to consequently result, in having a greater import, than an otherwise analogous thought wave, that instead, is of a greater wavelength.  

The kinematic “behavioral” propagation, of the eminently associated general physical attribute, of the fundamental workings, of a p-adic cohomology-related scenario, may often tend to be linked, situation-wise, to the thereupon proximal local presence, of a relatively enhanced scalar magnitude, of a viable degree/amount, of physical entropy.  

What is most reductional associated with the general concept of, “the non abelian vector bundle,” may often tend to be eminently associated, with the tantamount behavioral characteristics, of the general physical phenomenology, of the holonomic Lagrangian -Based differentiation, of ultraviolet radiation, over a timeframe. 

The more spontaneously resolute, that the Fourier-Related-Progression, of an eminently associated, Kahler Hamiltonian Topological Manifold, tends to be, the greater that the expectation value will consequently tend to be, that such a stated Kahler Hamiltonian Topological Manifold, will more likely exhibit, the general physical characteristics, of a gauge-invariant phenomenology. 

A typical sub-atomic mass-bearing topological manifold, may often tend to be relativistically super conformal invariant, when taken at an internal reference-frame, that may be thought of as viably delineated, in a flush metrical span, as this is to be considered, from within a gauged distance of 25 Planck Lengths of the “shell,” which is of the eminently associated mass-on-shell structure, that is corroborative to the covariant externalized entity, of a given arbitrary eminently related Laplacian-Based “snapshot,” of the here to be, viably associated, kinematically propagated mass-bearing holonomic substrate, of net energy-related eigenstate. One may also consider, the added stipulation-related implicit physical feature, that the cross-sectional thickness, of the actual earlier implied “shell,” may often tend to have a minimal flush metrical span, of one Planck-Bar Length, as this latter mentioned general phenomenon, is appertaining to the radial sway, of one Planck-Related Phenomenon. 

The hermitian flow of perturbative pulsation per energy, often tends to intertwine the commutative “communication,” amongst eminently corroborative physical waves, in so as to facilitate a fostering, of a smoothly expansive Lagrangian-Based Trajectory, in which the eminently corroborative Fourier-Related-Progression, is thence to be spontaneously altering smoothly, in a piecewise continuous manner, over a duration of time. 

A highly adhesive, hermitian Fourier-Related-Progression, will often tend to be eminently associated, with the likings, of a conductive, isotropically stable, homomorphically oriented, De Rham Hamiltonian Topological Manifold.

Recursively Generative Harmonic Output Of Metric-Gauge-Related Eigenstates

 Let us consider a given arbitrary Noether-Based mass-bearing cohesive set of discrete energy quanta, that is here to be working to exhibit, at least some sort of a tense, of a viable given arbitrary spin-orbital tense, of an oscillation-related vibrational display, over a proscribed given arbitrary relativistic duration of time. Since the said cohesive set of discrete energy quanta, is working to be exhibiting a viable tense of a spin-orbital display, of a Fourier-Related Lagrangian, it is thence to more than likely be consistently altering in its velocity, in relation to the motion of electromagnetic energy, since when a phenomenology is to be consistently "spinning," it will tend to be consistently changing in its direction, and, when such a general inferred phenomenology is here to be consistently changing in its direction, it is thence to be altering in its velocity, -- since something is said to be altering in its velocity, when either its speed and/or its direction is changing. When a given arbitrary Ward-Cauchy-Related phenomenology, is to be maintaining the same velocity in relation to the motion of electromagnetic energy, it's directly associated correlative Chern Simons Invariants are to be just that -- they are said to be invariant, and thus not change. Yet; if the velocity of such an inferred phenomenology, (let us say here, in this particular case, that such a said phenomenology, is here to be a mass-bearing cohesive set of discrete energy quanta), is here to be altering, (to where, it is either to be changing in its speed, and/or, it is to be changing in its direction, when this is here to be considered, in its relationship to the motion of electromagnetic energy), then, its directly corresponding Chern Simons "Invariants," are then to be said to not be invariant -- to where such an inferred directly correlative physical attribute, of the motion of such an inferred set of discrete energy quanta, is then to be changing. So; If a given arbitrary mass-bearing cohesive set of discrete energy quanta, is to be consistently altering in its direction, in its relation to the motion of electromagnetic energy, then, its directly associated Chern Simons Invariants are said to be consistently changing (altering), or, in other words, its directly associated Chern Simons Invariants, are then said to be consistently undergoing perturbation. When such an inferred Noether-Based "team" of mass-bearing discrete energy quanta, are said to bear Chern  Simons Invariants, that are consistently in perturbation, then, there are basically always to be two general types of residual output, that are here to be emitted by the correlative general gauge-metric-related motion, that is here to be basically attributed to the earlier inferred general tendency, of a directly corresponding consistent perturbation of Chern Simons Invariants: 1) A harmonic output of metric-gauge-related eigenstates. And; 2) An anharmonic output of metric-gauge-related eigenstates. -- The just mentioned harmonic output of such metric-gauge-related eigenstates, tends to reverse-fractal, into what may be perceived of, as being, "charge." While; The mentioned anharmonic output of such metric-gauge-related eigenstates, tends to reverse-fractal, into what what may be perceived of, as being, "entropy." The more recursively generative, that the harmonic output of such eluded-to metric-gauge-related eigenstates is to be, the more that such an inferred Ward-Cauchy-Related situation, will consequently tend to reverse-fractal, into a relatively high scalar amplitude of magnetism. Furthermore; The more recursively generative, that the anharmonic output of such eluded-to metric-gauge-related eigenstates is to be, the more that such an inferred Ward-Cauchy-Related situation, will consequently tend to reverse-fractal, into a relatively high scalar amplitude of entropy. TO BE CONTINUED! SINCERELY, SAM ROACH. (1989). 

Smooth Increase In Scalar Magnitude Of Metric-Gauge-Related Pulsation

 Let us initially consider, a constantly rotating given arbitrary mass-bearing cohesive set of discrete energy quanta, to where such an inferred "team" of energy quanta, is to spontaneously work to bear only the perturbation, of an increased metric-gauge-related pulsation, -- due to what is here, in this particular case, to be a smooth increase, in the correlative scalar magnitude of the reciprocal of e^(the del of the Ricci Flow): -- 

[(1/(e^(del of the Ricci Flow)))]; -- As such a constantly rotating mass-bearing cohesive set of discrete energy quanta, is to only work to bear the perturbation of an increased metric-gauge-related pulsation, as taken over the span of a proscribed respective duration of discrete time, -- this general type of a  kinematic alteration, in the acceleration of the said rotating mass-bearing cohesive set of discrete energy quanta, will consequently tend to work to increase, both the scalar magnitude of the speed of the correlative rotation of such a "team"of energy, as well as working to enhance the isotropic stability of the inferred set of discrete energy quanta, of such a given arbitrary respective case. In turn; such an enhancement in the isotropic stability of the inferred "team" of mass-bearing energy, will consequently often tend to increase the ability, of the said set of discrete energy quanta, to work to display a stronger exhibition, of a tense of resonant vibration. I WILL CONTINUE WITH THE SUSPENSE LATER! TO BE CONTINUED! SAM ROACH.

Chern-Simons Invariance -- Gauge-Invariance

 A given arbitrary discrete quantum of energy, is to tend to work to bear the general proximal local  characteristic, of what may here to be considered as being the Ward-Cauchy-related condition of Chern-Simon Invariance, -- when such a said discrete quantum of energy, is here to also work to bear the general proximal local characteristic, of what may here to be considered, as being the Ward-Cauchy-related condition of gauge-invariance. The general physical characteristic of Chern-Simons Invariance, is only of a heuristic manner of exemplification, when the directly associated discrete quantum of energy, is to be in the process of displaying both a constant rate of spatial translation,And, a constant direction of projected trajectory, as this is here to be taken, When in its covariant relationship with the motion of electromagnetic energy. Likewise; the general physical characteristic of Gauge-Invariance, is only of a heuristic manner of exemplification, when the directly associated discrete quantum of energy, is to be in the process of displaying both a constant rate of spatial translation, And, a constant direction of projected trajectory, as this is here to be taken, When in its covariant relationship with the motion of electromagnetic energy. So; whenever a Noether-based discrete quantum of energy, is to alter in either its speed and/or in its direction, in its relationship with electromagnetic energy, -- such a said quantum of energy, is then to alter out of the general Ward-Cauchy condition of gauge-invariance, -- to where its initial condition of Chern-Simons Invariance, is thereby to become variant in the process. To conclude: Both the physical condition of Gauge-Invariance, And, the physical condition of Chern-Simons Invariance, are only heuristically as such, as a given arbitrary directly corresponding cohesive set of discrete energy quantum, that is here to be in the process of being taken into consideration, is to be maintaining both the same rate of speed, And, a constant direction of its projected trajectory, when this is here to be considered, in its relation to the motion of electromagnetic energy. I will continued with the suspense later! To Be Continued! Sincerely, Samuel David Roach. (1989).

More As To A Derivation Of The Concept Of, “Homotopic Residue”

 Since most, if not all, of those mass-bearing superstrings of discrete energy permittivity, that are here to work to help in comprising their directly corresponding mass-bearing cohesive set of discrete energy quanta, will thereby tend to Not be able to purely move into their “innately desired” Holomorphic Direction, (due to the earlier inferred/stated info), — in which, that it is consequently to be the net overall mass-bearing cohesive set of discrete energy quanta, that is here to get “first-dibs,” as to what direction that the implied Hamiltonian Operator is to move into — such implied strings, will then, often tend to invariably, work to bear the general physical attribute, of something called, “Chern-Simons Invariants.” As I have indicated in some of may previous posts, Chern-Simons Invariants, are only maintained as actually being “Invariant” or unchanging (as being of the same specific nature), When the correlative mass-bearing cohesive set of discrete energy quanta, that is here to be of any one individually taken case scenario, is here to bear, both the same speed and the same direction, when this is here to be taken, in a covariant relationship, to the motion of electromagnetic energy. I will continue with The suspense later! To Be Continued! Sincerely, SAM 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).

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.

Partition-Based Discrepancies And Tachyonic Flow

As a general concept -- when a given arbitrary orbifold eigenset is to alter, from initially working to bear a Noether-based flow Into subsequently working to bear a tachyonic flow, -- those partition-based discrepancies that are here to exist along the topological contour of those superstrings of discrete energy permittivity, that work to comprise the inferred  given arbitrary respective orbifold eigenset, are then to shift Towards the relative reverse-holomorphic positioning from the proximal local designation where these had originally been delineated -- when such an inferred mass-bearing orbifold eigenset is to go from just under the speed of light, to going at or beyond the speed of light.  Samuel David Roach.

More As To The Noether Current

The multiplicit flow of phenomenology that is here to be traveling at the speed of light or slower, that is to act as the Ward-Cauchy resultant of that general type of interaction --  that is to happen between superstrings and physical norm-state-projections in the substringular, may be viewed of here as being one particular manner of consideration -- as to what the Noether Current is to be.  Sam Roach.

More As To Metaphorically "Standing" On A Paraboloid

Let's go back to what I was saying in one post, -- when I had mentioned about metaphorically "standing" on a spinning paraboloid.  Let's next say, that one was to remain perfectly still on this said metaphorical paraboloid.  Consequently, you are now to be in touch with a constantly differentiating norm-vector, that is kept in the sequential pattern of the spinning of the paraboloid.  Consider the rate of the spinning to be holomorphic to the surface area of the paraboloid.  Consider the rate of the spinning to be maintained at a constant speed.  Of course, since you are spinning, your direction is always changing, so that you are constantly accelerating.  Think of the translation of phenomena that is besides yourself -- to where, again, you are staying "put" -- that was at one point touching the paraboloid, from within the physical bounds of the surface area of it, as being proportional to the differentiation in the speed of the correlative spinning.  This would then mean, that the discharge from the said surface, would be transferred at a constant rate.  Consequently -- since this is true for the whole topology given, it is certainly true for the potential spot at which you would be at.  You are in line with a potential discharge of residue, from the surface of the paraboloid, -- which would then be a translocation of the surrounding phenomena.  This would then mean, that the earlier mentioned norm-vector, that is interactive at each point along the surface, would be constant in magnitude -- although it would be constantly changing in direction. Wouldn't this mean, then, that the norm conditions of the surface area of the given paraboloid, would be constantly altering part of the correlative Cauchy-related norm conditions, while yet constantly maintaining the others?  (Additional Cliffhanger).
To Be Continued!  Sincerely, Samuel David Roach.

Velocity And Flow Of Homotopic Residue

Let us initially consider an orbifold eigenset -- that is to here to work to bear one specific theoretical rest mass.  The faster that the velocity of the said orbifold eigenset is to be -- the less partition-based discrepancies that will then exist from within the confines of the individually taken superstrings of discrete energy permittivity that work to comprise the said eigenset, yet, there will tend to here be, as well, a proportional increase in the number of mass-bearing strings that will then be existent from within the confines of the said orbifold eigenset -- so, as the said orbifold eigenset is to increase in its relative speed over a set duration, -- the said eigenset is then to become denser in discrete energy, since mass tends to increase as such a said mass is to increase in its velocity relative to light.  So, even though homotopic residue tends to flow out of the individually taken superstrings of an orbifold eigenset as it approaches light speed -- homotopic residue still tends to be conserved for the said orbifold eigenset, -- since there is here to be a proportional increase in the number of superstrings that work to comprise such a said eigenset.  (Mass increases as speed increases.  Mass is a form of energy.  Therefore, as an orbifold eigenset is to increase in its velocity relative to light -- the number of strings that work to comprise such a said eigenset is to increase in number.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Session 5 Of Course 20 -- Calabi Manifolds And Interactions

Light in a vacuum of space travels at 3.0*10^8 meters per second.  When light enters a medium that is not electromagnetic energy while it is also not a worm-hole, the light will tend to travel at a speed that is less than light speed.  For instance, when light strikes air, the light not only bends to a slight extent, it will also slow down to a correlative extent as well.  Once that light strikes the air, it will scatter -- while then subsequently tending to re-quantize to form light again.  Once the light reforms as light again, it will tend to travel in what amounts to as its given "tense of bend", yet in segmentations that are each of a relatively straight line, -- to where the said light, as it is here to be as is according to Snell's Law, is to then to go just slightly less than what light speed would be in a theoretical vacuum, as the so-eluded-to electromagnetic energy is to travel in the direction of "least time," as it is to only slow down and change direction, after each of such scatterings of the said light upon the so-eluded-to Calabi-Yau phenomenology of the said air molecules that it is to strike in a Gliosis-based manner over time.  For example, let's say that the given air was homogeneous in density, and that the light that I am referring to here did not have to significantly re-scatter again in the air, as the given light is here to be propagated downward toward the earth.  The light in this case is propagated towards the face of a body of water.  When the light strikes the water initially, the light will scatter, while then re-quantizing back into a beam of light that bends as is according to the density of the water -- and slows down as is according to this same density of the water.  The beam of light may be able to do this, if it is also not scattered by any plain kinetic energy, -- as other beams of light are to be inter-playing in this case scenario as well.  This beam of light may propagate until it is fully absorbed, most potentially by some alterior Calabi-Yau  space of mass.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.