Holonomic Substrate

The following is a general genus of physical operation, -- in which the overall system of such a so-eluded-to tense of co-functional energy, is here to be in the process of undergoing a tense and/or a genus of Noether Flow, in so that the propagation of the directly corresponding energy that is of such an overall system of energy, is here to be operating at a speed here, that is Not, in such a general genus of a case, to exceed the speed of light. Furthermore, -- the ensuing mentioned tense, as to what is here to be considered in this given arbitrary case scenario, -- to be the "holonomic substrate," is here to be thought of as, the potentially kinematic disturbance of space-time-fabric, -- that is here to be propagated, as a system that is here to be comprised of one or more orbifold eigensets -- that are each to be both covariant, codeterminable, and codifferentiable, over the course of what is here to be eluded-to, as an evenly-gauged Hamiltonian eigenmetric, that may vary distinctively in its manner or lack of manner of its associated transience.  Well, here is the just described general case, as to what I have prepared for my readers now to consider:
The more that the holonomic substrate of any one given arbitrary Hamiltonian Operator, is to be scattered upon -- particularly, the more that the holonomic substrate of any one given arbitrary Hamiltonian Operator -- is to be scattered upon  by electromagnetic energy, over the course of a tense of linear time, -- the more that the said holonomic substrate, will then tend to display an ever increasing tense of entropy. -- over the course of the so-eluded-to general course of linear time.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Discrete Increments Of Energy, Monopoles

One may think of individually taken discrete quanta of energy, as being monopoles of energy, -- that are here, (since these said individually taken discrete quanta of energy, may only work to bear an integer number of their correlative increment-related tense of energy), to obviously bear a common tense of dimensionality -- to where, if these are to be acted upon,in so as to work to bear a quaternionic-related pulsation, -- then, these said individual discrete quanta of energy, may then be said to bear a Hamiltonian-related tense of energy, that would thence be equivalent to their directly corresponding Lagrangian-related tense of energy.  ((-i)^4 = 1).  This is why, as is as in accordance with my string theory model -- the quaternionic-instanton-field-pulse-mode, of which is here to happen at the respective ending of the generally unnoticed duration of Ultimon Flow, -- is then to tend to work to help at causing every discrete quantum of energy, when these discrete phenomena are here to be taken individually, to then to work to bear a tense of holonomic-related energy, that is to be equivalent in the magnitude of its scalar amplitude, to its directly corresponding Lagrangian-related energy.  Such a general unification, that is of that tense of that energy that is here to be directly corresponding to the "stuff" of energy, with that tense of energy that is here to be directly corresponding to the motion of energy, -- is then here to work, in so as to tend to work at helping to allow for energy, to be the multiplicit delineations of specific vibrations of space-time-fabric, -- that are then to be transferred as multiplicit entities, from one general locus to another, and so on, -- in so as to help at allowing for both the persistence and the continual existence of energy, over the course of time.  To Be Coninued!   Samuel David Roach.

Holonomy And Motion

It is the multiplicit disturbance in space, that had worked upon space-time-fabric near the beginning of time -- as to the occurrences that had happened over the initial origins of the multiverse -- that had worked to form the multiplicit holonomy, that is here of the energy of the said multiverse.
And:  It is the motion of the prior said multiplicit holonomy -- that is here to act as the multiplicit Lagrangian-related phenomenolgy, -- that is here to work to form the basis of the actual activity, that is of the energy of the said multiverse.

So -- it is the general activity of the quaternionic-instanton-field-pulse-mode, -- that works to unify the eminent presence, that is of the correlation of the phenomenology of Holonomy,  with the phenomenology of the Motion of such a so-eluded-to tense of multiplicit holonomic substrate.  This thereby, (the quaternionic-instanton-field-pulsle-mode), is nature's method of unifying the "stuff" of energy with the motion or activity of the self-same energy.

Part-And-Parcel -- as to the aim of the Grand-Unified-Field-Theory-Equation -- is to come-up with an equation, -- that rigorously unifies the phenomena of holonomy withe the phenomena of motion.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Electromagnetic Energy & Heat

The more likely that a set of photons are to scatter upon a mass-bearing system of energy, per time (to where this said mass-bearing system of energy, is here, in this given arbitrary case, to be comprised of --  by the state of one or more atoms) -- the more likely that the resultant scattering, will tend to work to cause those electrons, -- of which are that phenomenology of atoms that tend to be struck, when electromagnetic energy is to scatter upon an atom -- to where, both the condition that there will then more likely be a situation, in which these said electrons will end-up working to release their residual kinetic energy, as discrete quanta of electromagnetic energy,  -- as well as the condition that there is here to be the condition, that there will more likely be a situation, in which there will then tend to be a higher proximal local presence of entropic photons, -- of which will then work to increase the probability, that is here to be the state of an increase of the scalar amplitude, that is of the proximal local presence of heat to then be present, in this said case scenario.  To Be Continued!  I hope that the suspense factor is good.  Sincerely, Sam.

Gauge-Transformations That Work To Produce Heat

Whenever a set of gauge-transformations, works to help at producing an anharmonic vibration of molecules -- this will always tend to be a case, in which the scattering of light upon a Calabi-Yau manifold --  is to be in the process of working to form a certain scalar amount of heat or infrared energy,  over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Unitized Coupling

If two different distinct Hamiltonian Operators, that are to act as monopoles that are here to be of the same number of spatial dimensions, as these so-eluded-to eigenstates, that are of a discrete quantum bearing of divvied-out energy-- that are here to generate the same absolute value of a Lagrangian-related energy, at a given arbitrary conipoint in space and time -- even though these two distinct Hamiltonian Operators, are to bear their respective correlative motion, in a manner that is of a covariant antiholomorphic means of interaction, over an evenly-gauged Hamiltonian eigenmetric, -- to where there is then to be the condition that these two said Hamiltonian Operators, if coupled in such a manner as this would tend to infer, -- would then tend to act, in so as to consequently work to help to form some sort of inter-relationship of those charges or fractals of charges, that are delineated to the electrostatic or fractal of electrostatic Ward-Cauchy-related conditions, that are of such a case scenario, in so as to work to help to cause charged particles to orbit and spin, in the manner in which these do over time.  This is, in part, because -- like I have mentioned before, such a so-eluded-to Coupling is tantamount to, (-i)*i, which is equal to one (1).   This just described tense of activity --thence works to involve unitization, -- and when eigenstates act in so as to be unitized, this will tend to move phenomena into a state or condition of optimum rest. Sincerely Samuel David Roach.

As To Why Certain Elliptical Orbits Are Formed

Aside from the general condition of gravity -- of which exists in the form of correlative sets of Schwinger-Indices (of which are a special genus of a general type of wave-like pattern) that are here to move both transversally and perpendicularly over time, to where this works to make the multiplicit space-time condition, of a more massive tense of phenomenology to warp its relatively topological surface, -- in so as to work to allow for adjacently adjusted phenomena  that are to approach its proximal region, to orbit around it for a while.  This is part of what forms elliptical orbits.
Now consider the influence of another factor, that plays into part of the reason -- as to why such orbital-tendencies are here to be formed over time.  When one is to have two different Hamiltonian Operators of mass, that are here to be approaching one another --  that are here to act as two different monopoles, that are here to work to bear the same number of spatial dimensions -- to where these said Hamiltonian Operators are here to bear two different Lagrangian-based energies, of which are to be of the opposite general tense of scalar amplitude, at a certain general point in space  -- when one is here to arbitrarily to be in the process of comparing the Lagrangian-related energy of one of such Hamiltonian Operators to the other one, -- to where, then, at the point at which the proximity of the less massive system of energy so-inferred is to bear a Yukawa Coupling with the more massive system of energy so-inferred -- by which there is then to be a basically exact Coupling of their Lagrangian-related energy, in which, at this general point of duration, the correlative Hamiltonian-related energy of the less massive Hamiltonian Operator, is to bear (-i) times the energy of its directly corresponding Lagrangian-related energy, -- to where there is here, at this point in metric-related activity, to be an exactly opposite correlative Lagrangian-related energy, that is here at this so-eluded-to point in space, to be generated by the more massive Hamiltonian Operator, to where the said energy of the Hamiltonian-related energy, that is of the more massive state, is to then to be propagated at this general point in space,  to where this is then to equal (i) times the Lagrangian-based energy, that is of the earlier mentioned less massive Hamiltonian Operator, (not "(-i)," because these are being propagated in the opposite direction) that is of this given arbitrary respective case.  At this metric-bearing point in duration, in which the two so-stated Lagrangian-related energies are to be of exactly the opposite scalar magnitude -- which is due to these two said energies to here, to be initially to be going in the opposite direction over time, -- this is to then happen in such a manner, to where this general type of activity -- will then tend to work to influence these energies, to where these will then tend to couple, -- to where there will then proceed to tend to be the effect of the smaller mass-bearing Hamiltonian Operator, acting in so as to make an elliptical orbit around the larger mass-bearing Hamiltonian Operator. (-i)*(i) = 1.  Its Me. Sam Roach.

Relative Holomorphic Direction And Energy

Normally -- the forward-holomorphic direction is considered to be, of a left-moving direction.  Now; let's now consider this just mentioned relatively forward-holomorphic direction -- to be moving directly away from you -- in so as to be moving "into the page."
Let's next say, that one is to have a discrete quantum of energy, to be moving in the said relatively forward-holomorphic direction -- in so as to be moving then, directly away from you ("into the page".  Let us next, elementary determine that -- since the here directly corresponding motion of the said discrete quantum of energy is here to be traveling into the said forward-holomorphic direction -- then, on account of this said condition, -- the directly corresponding Lagrangian is then here to be delineated into the said holomorphic direction, or, in other words, "into the page."  Since the energy of the correlative Lagrangian is here to bear the scalar amplitude of energy, that is here to be equal to -i*(the energy of the Hamiltonian Operator), then, on account of what's been discussed in this just mentioned session -- the vibrating discrete energy, that is here to act as the holonomic substrate of the so-eluded-to system of energy, -- is then to tend to work to bear a main pulsation, at the Poincare level that is Gliosis to the core-field density of those individually taken superstrings and/or orbifold eigensets, that are here to be acting as the "thing" of energy -- that is thence to be sequentially delineated through a tense of its energy of actual motion -- that may here be thought of as the correlative Lagrangian. Superstrings vibrate constantly to one extent or another when unfrayed -- even during the countless processes of BRST.  Consequently, when a superstring is to work to move through the medium of space-time-fabric -- as a tense of the structural-related holonomic substrate that is here to be transferred over a duration, --  while the motion of such a so-stated discrete quantum of energy is to tend to be going, as a ("best-fit 'curve' to the pressures") in a net direction that is affiliated with the holomorphic-related wave-tug that such a discrete quantum of phenomenology is to be tugged-into (in the direction of most rest and/or in the direction of least time), then, as such a said superstring is to be vibrating as it is to work to bear a sequential series of iterations of energy, -- then, this tends to happen, to where a pajority of the "thrust"of that disturbance in space, that is most associated with  that consistently occurring vibrational oscillations, that the so-eluded-to discrete packet of energy is to work to bear, in order to work to help in allowing for the wave-tug of the holonomic substrate of energy to be able to both exist and persist at flowing through the substringular -- will then tend to be excentuated at the relative Nijenhuis-to-reverse-holomorphic side of such a so-eluded-to superstring of discrete energy permittivity.
I will continue with suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Scalar-Related Expressions

Particularly when one is here to be dealing with the transference of energy, that is here to be directly corresponding with the Fourier-related translation of a phenomenology, that is of a Noether Flow -- one may then call the correlative directorial axes, that are here to be centered around a Hamiltonian operator as a phenomenon of wave-tug, that is here to act as an extrapolated entity of a tense of holonomic substrate -- when this centralized set of holonomic-related directorials, may then act as a function as to here to be tugged along the path in which the said Hamiltonian Operator is to be going in, in so as to act as the source of what may here be called a genus of a particular case of a metric-gauge eigenstate.  Furthermore -- when one is here to be dealing with the actual motion of the  transference of a set of one or more discrete quanta of either energy and/or zero-point energy, via a Fourier-related translation of a phenomenology that is of a Noether Flow -- one may then call the  correlative directorial axes, that are here to be centered around the Lagrangian, -- as a phenomenon of wave-tug, that is here to act as an extrapolated entity of a tense of motion -- when this so-eluded-to set of motion-related directorials may then act as a function of here, to be tugged along the path of the said actual motion or  Lagrangian of such a set of one or more discrete quanta of energy, -- in so as to then to be acting as one general genus of what may be termed of here as being a particular case of a gauge-metric eigenstate.  Such a tense of either "metric-gauge" or "gauge-metric,"  -- when one is here to be taking the directorial flow of a phenomenology -- without mathematically working to consider the correlative variables that would otherwise be included,  such phenomenology, when of Noether Flow,  may be termed of as being an example of a scalar euclidean expression.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Majorana-Weyl-Invariance And Spin

When a phenomenon of mass -- of which is to work to bear a Majorana-Weyl-Invariant-Mode, that is super conformally invariant at an internal-reference-frame -- is then to be carried via a correlative Yukawa Coupling -- at a relatively quick velocity at an external-reference-frame, by a tense of a Legendre homology, yet in a transversal manner, over time --  then such a said mass that is here to work to bear a tense of a Majorana-Weyl-Invaraint-Mode, will, at this point of time-based extrapolation, tend to then be generating more and more cohomology, over this said respective so-eluded-to evenly-gauged Hamiltonian  eigenmetric.  Yet -- when such a phenomenon of mass, -- of which is here to work to bear a Majorana-Weyl-Invariant-Mode, that is super conformally invariant at an internal-reference-frame -- is to be carried via a correlative Yukawa Coupling -- at a relatively quick velocity at an external-reference-frame, to where the motion that is thence caused is here to be kinetically driven by a tense of a Legendre homology, yet in a radial manner,  over time, (to where, the so-eluded-to Hamiltonian Operator of such a respective case, will be traveling or spinning around, for example, in either an elliptical or in a parabolic circuit of motion), ( as well as that, there is here to be such a general situation, to where this will work to involve those correlative Ward-Cauchy-based conditions, -- in which the correlative mass -- that is here to be of such a said Majorana-Weyl-Invariant-Mode -- will then be accelerating, due to a constant change in the direction that it is here to be transferred through, over time)  --  in so as to act as such a said mass, that is here to work to bear a tense of a Majorana-Weyl-Invariant-Mode, to where this will, at this point of time-based extrapolation, tend to then be generating as much cohomology as it is degenerating -- although the amount of cohomology that it is to thus be both generating and degenerating quickly, is here to be of a relatively large scalar magnitude of a resultant magnetic energy.  This just said tendency of this given arbitrary respective case -- that is here to be most appertaining to a spinning tense of a given arbitrary Majorana-Weyl-Invariant-Mode -- will consequently work to tend to bear an ever increasing interaction of the directly corresponding initially inferred to phenomenology -- that is here to be of the Reimman Curvature -- upon the proximal local eigenstates of the Rarita Structure, (to where this will, as well, work to cause an ever increasing interaction of the directly corresponding initially inferred to phenomenology that is here to be of the Reimman Curvature -- upon the proximal local eigenstates of the Rarita Structure) -- in so as to work to make the then resultant Ricci Curvature to be increased in its correlative scalar amplitude.  This overall general process -- will then do this general type of activity,  in a mathematical sense -- by increasing the directly corresponding value of "lambda," in so as to help at making the "lambda*gravitational force" to increase in its correlative scalar amplitude, -- in such a manner, to where there will then tend to be neither any proximal local lower boundary nor any proximal local upper boundary to the directly corresponding Ricci Curvature.  In such a case, the tendency will be -- that the Ricci Curvature will then consistency be, in such a respective case, of the nature in so as to work to equate to the said "lambda*gravitational force."  This will then tend to work to mean, that the tense of Legendre homology, that is thus to work to carry such a Majorana-Weyl-Invariant-Mode, via a Yukawa Coupling, in the so-inferred radial manner, -- will then tend to be of an isotropically-stable genus of open-loop phenomenology.  This will then, as well, work to allow for such a condition, by which this will then tend to be of such a general nature -- to where the directly corresponding Ricci Flow will then tend to be of a "flat" Ricci Curvature.  To Be Continued Soon!  Sincerely, Samuel David Roach.

Reimman Curvature Versus Ricci Curvature

As a general case, that is here to be the basic tendency in the substringular, -- the metaphorical "snapshot" of the mappable-tracing, as it is here to exist as being of a just completed path, through which a given arbitrary Hamiltonian operator has here to have been moved -- as this just mentioned phenomenology is here to exist as being a tense of a general genus of a re-delineated eigenstate, that is here to be continually re-distributed -- when this general genus of a case is here to be taken via those Ward-Cauchy conditions, -- as it is here to be of the nature of a Laplacian Transformation, -- to where this may be thought of as being of the nature of behaving as an eigenstate, of what may be thought of as being of the nature of that general tense of mapped-out homological stratum (whether one is here to be talking about cohomology that is of a symplectic nature, or whether one is here to be talking about Legendre homology that is of a Khovanov geometry), that is here to be of the general multiplicit nature of the Reimman Curvature.  Whereas -- the Laplacian-Based mappable-tracing --  that is here to have been formed by its existence here, as the resultant of the interaction of the respective given arbitrary Hamiltonian operator, (as such a said Hamiltonian Operator is here, to behave as a system of one or more eigenstates of discrete energy quanta -- that operate to perform one specific function at a microscopic level), With the holonomic substrate, that happens to exist as being of those directly corresponding correlative gravity waves, that are here to exist along the topological interplay of the Rarita Structure --  to where this may then be thought of -- as the multiplicit general state of the existence of the correlative Ricci Curvature, that is here to be of such a general given arbitrary respective case scenario.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Concisely -- Lagrangian Versus Hamiltonian Operator

The Lagrangian is the gauge-metric of a state or system of energy, whereas -- the Hamiltonian operator is the metric-gauge of a state or system of energy.  Therefore -- the Lagrangian is the actual motion of a state or system of energy, whereas -- the Hamiltonian operator is the actual holonomic substrate (the actual substirngular physical entity) of a state or system of energy.
To Be Continued!  Sam Roach.

Right Before BRST

At the ending of any one given arbitrary iteration of the generally unnoticed duration Of Ultimon Flow -- which is during the quaternionic-instanton-field-pulse-mode -- each and every discrete quantum increment of transveral energy (as treated here as a monopole of discrete energy), as well as each and every discrete quantum increment of radial energy (as treated here as a monopole of discrete energy), -- is to bear such a quaternionic-related quantum-related effect, as is to be applied to the just inferred about eigenstates of discrete quantum energy -- to where the energy-based tense of each and every lowest common increment of Hamiltonian operator is then to be synchronous to the energy-based tense of each and every directly corresponding Lagrangian-based motion.  This then works to directly associate the actual "stuff" of discrete energy with the actual "motion" of discrete energy, -- in a manner in which these are to bear a tense of synchronous unitization, so that energy may have any organization at all -- which helps to form the basic general condition of energy to then to be able to both persist and exist at all. To Be Continued!  Sincerely, Samuel Roach.

Imaginary Exchange Of Real Residue Happens During BRST

What I have termed of before -- as to here be of the nature in so as to be described of as "The Imaginary Exchange Of Real Residue," is a to-and-fro genus of topological sway, that is here to occur to discrete energy permittivity -- at a level that is Poincare to the correlative composite first-order point particles, that work to comprise the relative norm-to-reverse-holomorphic end of a quantum of such a said discrete quantum of energy permittivity --  that is here to happen over the entire simultaneous duration in which BRST is to happen.  So -- as both the Polyakov Action and the Bette Action are to occur, which is during a majority of an iteration of the generally noticed duration of what I term of as Ultimon Flow, -- there is then here to be, as to be occuring at that general so-eluded-to classification of eigenmetric, -- this so-stated to-and-fro genus of topological sway.
Here is a general example, as to what "The Imaginary Exchange Of Real Residue" is:

Let's initially say that a superstring of discrete energy permittivity has just completed the quaternionic-instanton-field-pulse-mode, in so as to then to be made Gliosis to the proximal locus of Hamiltonian operand -- in which this said superstring has just been delineated to, in order to then to begin to act as an ensuing iteration of the holonomic substrate of energy, --  that is to bear a sequential series, that is to work to bear a tense of acting here as a Lagrangian-related eigenstate.  Now that such a said superstring is to have now just began the process of BRST, -- this said superstring will now go into both the processes of the Polyakov Action and the processes of the Betti (Bette) Action.  As such a so-state string is to be in the process of going through both the Polyakov Action as well as the Betti (Bette) Action -- such a said superstring will then be simultaneously to be going through this earlier mentioned "The Imaginary Exchange Of Real Residue."  What this wobble-like topological sway amounts to, -- is that the correlative counter string, that is here to be directly corresponding to one given arbitrary respective discrete quantum of energy, is to initially go into a manner of "stepping" into the case specific forward-holomorphic direction of the respective given arbitrary said discrete quantum of energy, to where, as this just stated general genus of activity is to then to act in so as to work to cause the correlative superstring of discrete energy permittivity to then to "step" into that self-same said holomoprhic direction, to where immediately afterwards, -- the equal and opposite effect, that is here to be quite related to the consequent but reasonable strain that this is to bring upon the modulus of the said discrete quantum of energy -- to where the counter string is to then to "step" back into the case specific relative reverse-holomorphic direction of the correlative discrete quantum of energy, while then the correlative superstring of discrete energy permittivity is then to wobble back into this just stated tense of a reverse-holomorphic direction that is of the correlative discrete quantum of energy.  At this point in duration -- the multiplicit Hamiltonian eigenmetric (or, one may possibly perceive this as being a fractal of a Hamiltonian eigenmetric), that I term of as being the "Imaginary Exchange Of Real Residue"is to then to have ended.To Be Continued!  I will continue with the suspense later!  Sincerely, Samuel David Roach.

Ammendment to Comparitive Tenses Of Energy

When I happened to have had eluded-to the other day -- as to that the magnitude of the scalar amplitude of the Lagrangian-based tense of energy, that is of one specific quantum of energy, -- is to be equal to (-i)* (the magnitude of the scalar amplitude of the Hamiltonian-based tense of energy, that is of the self-same specific quantum of energy) -- to where, if one were to take the quaternion of both of these two said tenses of energy, -- one would then work to find out, that the value of the resultant scalar amplitude of both of these mentioned tenses of energy, is to then to be of the same magnitude ---- Tends To Only Be True, first of all, if both of the conditions are here to exist, that one is here to be dealing with a respective discrete set of quanta of energy, that operate to perform one specific function, --  that is here to act as a monopole of discrete energy, And, if both the correlative Lagrangian and the correlative Hamiltonian operator of the said quantum of energy, are here to be acting upon the same total degrees of spatial freedom.  Yet anyways -- either manner in which one is  here to be looking at this general concept -- the quaternion of the energy of the Lagrangian (which is of the respective gauge-metric) of a set of one or more discrete quanta of energy, that are of one respective whole unique system of operation, --  Will always tend to at least be analagous to the quaternion of the energy of the Hamiltonian (which is of the respective metric-gauge), that is of the self-same set of one or more discrete quanta of energy, that are of one respective whole unique system of operation.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Lagrangian Versus Hamiltonian -- Orbiting Of Electrons

I will start off with the obvious, and develop this into an insightful thought.  As Anyone knows -- any  given arbitray electron , that is here to exist in a stable atom -- tends to orbit the nucleous of such a said atom, in an elliptical manner.  Aside from the general condition, that is of the charge-based attraction of an electron with a proton, another part of the reason, as to why there is the tendency of what the directional drive of the holomorphic motion -- that is of the activity of any of such individually taken electrons, happens to be over an evenly-gauged Hamiltonian eigenmetric -- as it is here to generally function, in so as to orbit the nucleus of such a said respective atom in an elliptical manner -- is partially due to the Ward-based condition, that the scalar amplitude of the tense of energy, that is most related to the Lagrangian of a correlative Hamiltonian operator -- is then to tend to be analogous if not equal to the scalar amplitude of the tense of energy, that is most related to the holonomic substrate of the self-same corrlative Hamiltonian operator, when multiplied by (-i).  For example:  The Strong Force is related to Euler's Theorem. The Strong Force is most associated with the gluing together of parts of forming nucleons, via what are known of as "gluons," in so as to have nucleons, -- such as protons and neutrons.
Next to be mentioned, is the general condition -- that, when we as people come into contact with a phenomenon of mass -- what we are generally are observing, is the effect of and the presence of eletrons.  Electrons and protons work to bear the opposite charges (Electrons are negatively charged, and protons are positively charged.)  Let's suppose, that we were to initially here to metaphorically call (1+) to be a value that will work to connitate the presence of a proton, - and let's suppose, that we were to initally here to metaphorically call (-1) to be a value that will work to connitate the presence of an electron.
Next -- since the electron is to have a polar-related orbit and spit (with an elliptical orbit), in multiconsideration with the condition, -- that the tense of the energy of the Lagrangian of a Hamiltonian operator, is equal to (-i) times the correlative force of such a tense of energy of the holonomic substrate of the self-same Hamiltonian operator. Let's initially consider the numerical value associated with the basic expression, that is here to both mathematically associate the electron more to the nature of light And to mathematically associate the proton more to the nature of mass. If one were to re-assign the forward-holomorphic direction of the said light, to be propagated relatively straight ahead, then, its one partition-based discrepancy would be around the center of its relative left side (i*PI position).   Yet, given the forward-holomorphic direction is to be re-assigned to be going straight ahead for a fully Lorentz-Four-Contracted mass-bearing superstring, -- its one partition-based discrepancy would be at its relative right side.  (2*PI) position.  Therefore, let's now compare the following:  e^((-1)*((i*PI) )= (i*e^(i*PI)) = i(-1) = -i.  Whereas:--  e^((-1)*(i*2*PI)) = (i*1) = i.
Next:  So we are here relate (-i) to (-1) and (i) to (1), -- to where, if one were to couple the two given multiplets of (-i) upon (i), one would then have: (-)*(i*i) which would equal: (-1)*(-1) =1.  This is then to bear the general Ward-Cauchy-related condition -- that this is part of why electrons and protons have opposite charges, -- and this is, as well, part of why, for atomic stability, there tends to need to be the same number of electrons as protons in an atom.  (The eminent Yukawa Coupling of electron-based force upon proton-based force works to help at unitizing a tense of its energy, and thereby, helping to work to allow for such an atom to bear more of a rest energy.)
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Boundedness Of Ricci Curvature

Let's initially consider a situation, in which one is to have mass-bearing superstrings that are superconformal invariant at an internal reference-frame, -- yet to where such strings are to be kinematically moved at an external reference-frame, by the activity of superstrings of discrete kinetic energy permittivity.  This just inferred overall system of energy, we will call in this given arbitrary post -- the directly associated Hamiltonian operator.  In this given case -- when the eluded-to Hamiltonian-related Ricci Curvature, that is to be the Lagrangian-Based Tracing of a gravitational-related scalar of force, as taken over a Laplacian Transform  -- that is here to be greater than lambda*gravity, (This will then mean, that the magnitude of lambda*gravity will be Less than the magnitude of the scalar amplitude of the correlative Ricci Curvature.), then, this will both mean, -- that there will tend to be the presence of a proximal local lower boundary in the correlative tracing of the said Ricci Curvature, -- as well as this working to indicate -- that the directly corresponding mass-bearing superstrings, that are here to be carried or moved by the correlative superstrings of discrete kinetic energy -- will then here in this case, act in so as to tend to degenerate more cohomology than it is here to be generating.  Furthermore -- when the eluded-to Hamiltonian-related Ricci Curvature, that is here in this case, to be the Lagrangian-Based Tracing of a gravitational-related scalar of force, as taken over a Laplacian Transform -- that is here to be less than lambda*gravity, (This will then mean, that the magnitude of lambda*gravity, will be More than the magnitude of the scalar amplitude of the correlative Ricci Curvature.), then, this will both mean, -- that there will then tend to be the presence of a proximal local upper boundary in the correlative tracing of the said Ricci Curvature, -- as well as this working to indicate -- that the directly corresponding mass-bearing superstrings, that are here to be carried or moved by the correlative superstrings of discrete kinetic energy -- will then, here in this case, act in so as to tend to generate more cohomology than it is here to be degenerating.  I will continue with  the suspense later!  To Be Continued!  Sam Roach.

Quaternionic Nature Related To Light

When an electron is to jump back-and-forth an energy level -- it is to release its spare energy, into what is to be propagated away from it as a discrete quantum of electromagnetic energy.  An electron exists as behaving as an eigenstate of a d-field -- of which is to be comprised of by a minimum of six spatial dimensions plus time.  A photon (a discrete quantum of electromagnetic energy), exists as behaving as an eigenstate of a p-field -- of which is to be comprised of by a minimum of ten spatial dimensions plus time.  The residual spare energy of an electron that is thence to be released as a photon, is as well, to happen through the Fujikawa Coupling via the Green Function.  To keep this developing concept simple, -- this addition of four spatial dimensions in the process of altering an eigenstate of a d-field into an eigenstate of a p-field, is then to work to form a quaternionic-related condition upon the Hamiltonian operation of the so-eluded-to newly formed discrete quantum of electromagnetic energy.  In turn -- this thence formed quaterionic-related condition, is then to work at tending to help the stated discrete quantum of electromagnetic energy -- when such a said quantum of electromagnetic energy is here to behave as a Hamiltonian operator, to bear the scalar amplitude that is of its directly corresponding Lagrangian-related tense of energy, to then be of such a nature in so as to bear a scalar amplitude of its directly corresponding holonomic-related tense of energy -- to then be of either the same magnitude, or, of at least of an analogous magnitude. This is, in part, what works to help at bringing to cause the innate condition -- that is of the Ward-Cauchy-related manner, in which the magnetic field of a photon that is undergoing a tense of Noether flow, is to tend to curl around the electric field of an electron -- as may be shown of as is according to the right-hand-rule.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Lagrangian Versus Holonomic Substrate Of Energy

Let us initially consider a Hamiltonian operator -- such as in the case as to having a situation, in which there is here to be one given arbitrary respective orbifold eigenset -- that is then to be under consideration.  Let us next consider what the energy of the Lagrangian of this operator is here to be, -- as in comparison with what the energy of the holonomic substrate of this same operator is here to be.  The here considered Lagrangian-based tense of energy, will then tend to work to bear a scalar amplitude, of which will be equal to (-i) times the scalar amplitude of the here considered tense of energy of the holonomic substrate -- that is of the self-same Hamiltonian operator.  Consequently -- if one were to initially to take both the individually taken Lagrangian-based tense of energy of the said Hamiltonian operator And the respective holonomic substrate-based tense of energy of the identical Hamiltonian operator, as two distinct unitary multiplets, -- while then taking and comparing the resultant of the quaternions of both of these said multiplets, in so as then to work to compare the resultant scalar amplitudes of these two said tenses of energy -- that are of the same Hamiltonian operator, -- the magnitude of the scalar amplitude of each of these individually taken tenses of energy, that are of these two different said respective tenses of the same Hamiltonian operator, will then tend to be of the same value.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Flat Ricci Curvature Explanation

Let's say that one were to initially be considering a mass-bearing orbifold eigenset.  It is here to be superconformally invariant, at an internal reference-frame.  Furthermore -- the said mass-bearing orbifold eigenset ,is to be moving, in a kinematic manner -- at an external reference-frame.  Even though the individually taken superstrings of discrete energy permittivity, that work to make up the said mass-bearing orbifold eigenset, are to be of a symplectic geometry, -- the superstrings of discrete kinetic energy permittivity, that work to carry or move the so-eluded-to set of mass-bearing discrete quanta of energy at an external reference-frame, are of a Khovanov geometry.  Let's say that the inferred symplectic Hamiltonian operator, is here to be generating as much cohomology as it is to be degenerating -- over an evenly-gauged Hamiltonian eigenmetric.  This will then work to mean -- that the directly corresponding Legendre homology, that is here to be carrying or moving the said mass-bearing orbifold eigenset, at an external reference-frame -- is here to be of an isotropically stable nature, or, in other words, -- of a Floer homology.  This will then work to mean -- that the directly corresponding Ricci Curvature of the so-inferred resultant Hamiltonian operator, will be of such a nature, in so as to here be analogous to lambda*gravity, which will then work to mean, that the said Ricci Curvature of this case here, is to be locally unbound, and thus, -- one may then say that the so-stated Ricci Curvature is here, said to be described of as being flat.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

The Ricci Curvature -- What It Is

The Ricci Curvature is:

The Lagrangian-Based-Tracing of the generative-related scalar amplitude -- that is of the gravitational force -- when this is here to be taken over a Laplacian Transformation.  To Be Continued!  Sam Roach.

Whether Describing Holonomic Substrate Or Motion

When I mention a tense of an energy-related phenomenology, as being a "metric-gauge-related Hamiltonian operator," what I am here to be referring to, -- is an actual Ward-Cauchy energy-related thing, that is here to be acting, -- in so as to perform one specific given arbitrary function.  Yet, -- if I were to mention a tense of an energy-related phenomenology, as to, instead, to act as being a "gauge-metric-related Hamiltonian operator," what I am here to be referring to, is an Actual Tense of Ward-Cauchy-related Motion, that is here to be the result of the duration-based kinematic activity, which is Of that given arbitrary tense of phenomenology,  of which is analogous to the earlier mentioned general genus -- of what I term of as being a metric-gauge-related Hamiltonian operator.  Consequently, -- anything that is to be divvied-out -- in the form of a tense of an overall energy of a system, -- may be described of as being a metric-gauge-related Hamiltonian operator; whereas, -- the Actual Motion of anything that is to be divvied-out -- in the form of a tense of an overall energy of a system, -- may be described of as a "gauge-metric-related Hamiltonian operator."  Therefore, -- one may then think of what I term of as being the general genus of a metric-gauge-related Hamiltonian operator, -- as the holonomic substrate of an overall tense  of an energy-related phenomenology; -- whereas, -- one may then think of what I term of as being the general genus of a gauge-metric-related Hamiltonian operator, -- as the Lagrangian  of an overall tense of an energy-related phenomenology.  What one is to generally to conceive of as being what is known of as a Hamiltonian operator, -- is usually considered to be the tense of an overall energy of a system, that I have described of as being a metric-gauge-related Hamiltonian operator.  The motion of what is generally conceived of as bieng a Hamiltonian operator, is its Lagrangian.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

As To Phenomenology In General

A disturbance in a vacuum of space-time-fabric, will work to produce motion, to where this motion of which will tend to produce energy -- to where this energy is here to exist, as an inter-relationship between  the presence of discrete energy permittivity and the presence of discrete energy impedance.  Thence -- the superstringular phenomenology of space-time-fabric -- are of the holonomic substrate of such said discrete energy permittivity.  Furthermore, one could consider that the energy-like phenomenology, -- that is here to be the action of the delineation of the Ward-Cauchy-related phenomenology that are to directly partake in instanton -- is an example of a Lagrangian.  The interdependent relationships, that are of the general process of succeeding physical interactions -- that are here to exist, from amongst the multifarious delineations of such phenomenology, that are here to directly partake in instanton, may then be said to be related to what the nature of time happens to be.
Sam Roach.  To Be Continued!

Langlands

What I term of as being "Langlands," are non-abelian GSO eigenindices (a tense of non-abelian groups), that come together to work at helping to form a given arbitrary respective Legendre homology -- of which is here to bear a Khovanov geometry.  Such a set of Langlands that operate, in so as to perform one specific function -- that thus behave as one respective group, are here to act as an overall homology-based eigenstate, thru a kinematic translation, that is kinetic at an external reference-frame -- in so as to help to move mass-bearing discrete energy, in a manner that is heuristic.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Hamiltonian Operators And Phenomenology Divvied-Out

A Hamiltonian operator is often thought of, as being the "overall" energy of a system.  Often -- any Ward-Cauchy-related phenomenology that is comprised of a set of one or more discrete quanta of energy, that operates to perform one specific function ( of which I often term of as being an orbifold eigenset) -- may be thought of as being an example of a Hamiltonian operator.   But recent science has worked to indicate the presence, of what may here be termed of to be the existence of "zero-point-energy."  In my model of string theory, this said zero-point-energy is based upon the presence of what I term of as being "mini-stringular segmentation."  It is this said mini-stringular segmentation (of which is to bear a thickness, that is on the order of being 10^(-129) meters thick in its cross-sectional extrapolation), that is what is here to work to inter-connect the topology of discrete energy, into the eminent presence of the physical condition of what may be thought of as being "homotopy."  Homotopy is that general Ward-Cauchy-related physical condition -- by which all discrete energy, that is not in the process of being frayed from within the confines of a black-hole, is to be inter-connected, either by one means or another, by at least some sort of field.  Superstrings of discrete energy permittivity, are, when individually taken, and when under the stipulations of such a model,  basically comprised of by a bead -- of what I term of as first-order point particles (to where such earlier mentioned superstrings of discrete energy permittivity, may be either closed-looped, open-looped, or open-stranded).  Such first-order point particles are, furthermore, comprised of a "yarn-like" entanglement, of what I term of as being such a so-stated mini-stringular segmentation.  (Segmentation, -- since such a so-eluded-to thread, that is here to be comprised of -- by what I term of as being basically a bead of second-order point particles -- is then to be tied or knotted, at countless multiple spots in the substringular, and thus, it is not an untied pattern of thread-like phenomenology.)  Besides from within the confines of black-holes -- mini-stringular segmentation, of which may be thought of as being the essence of zero-point-energy, is thus to signify the presence of the smallest general classification of phenomenology that may be divvied-out in time and space.  Consequently, one may then say, that the overall system of a tense of phenomenology -- that works to be comprised of by any actual scalar amplitude, of either a tense of zero-point-related energy and/or a tense of Planck-related energy, may be described of as being a Hamiltonian operator.  Therefore -- any Ward-Cauchy-related phenomenon in the substringular,and/or any set of such a so-implied Ward-Cauchy-related phenomenology -- that is here to be divvied-out, to where it is here to potentially to bear at least one operational function or another, -- may often thus be described of, as being a sense of what may be termed of here as being a Hamiltonian operator.  Samuel David Roach.

Correction As To Equation Involving Determination Of Metric-Gauge-Related Pulsation

In the equation that I had mentioned at an earlier time, -- as to how one is to work to determine what the relative metric-gauge-related pulsation is to be, between two different distinct orbifold eigensets, -- there is here to be a correction to the equation that I had utilized:
It should actually be:
3.026*10^(-32)Kg*(m^3/s^2)*(1/e^(del of the Ricci Flow))( which is in terms of (s^2/m^2))
*(the Average angle -- that is here to be considered over a Fourier-related Transformation (that is here to be taken over the duration of a directly corresponding evenly-gauged Hamiltonian eigenmetric), that is here to be subtended between the two different distinct orbifold eigensets, over the time in which one is here to be in consideration as to what the correlative covariant metric-gauge-related pulsation is to be)
*(The actual overall amount of time, in which such a given arbitrary relative metric-gauge-related pulsation -- is thus to transpire).  (Such a said scalar amplitude, that is of a given arbitrary respective metric-gauge-related pulsation, is then to be in units of:  Kg*m*< >*s).
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Yukawa Couplings And Cohomological Generation

When there is an amplification of the action, that is here to be directly associated with the Fourier Transformation of a given arbitrary metric-gauge-related Hamiltonian operator, -- this will then often tend to be associated with the generation of cohomology. Consequently -- when there is an attenuation of the action, that is here to be directly associated with the Fourier Transformation of a given arbitrary metric-gauge-related Hamiltonian operator, -- this will then tend to be associated with the degeneration of cohomology.
I will continue with the suspense later!  To Be Continued! Sincerely, Samuel David Roach.

Yukawa Couplings, Group-Attractors, And Ghost-Inhibitors

A Yukawa Coupling often tends to be of the nature, of acting as the Lagrangian-related operation - that is directly associated with an interaction of a metric-gauge-related Hamiltonian operator -- with the holonomic substrate of a group-attractor. Or, a Yukawa Coupling may often tend to be of the nature, of acting as the Lagrangian-related operation -- that is directly associated with an interaction of a metric-gauge-related Hamiltonian operator -- with the holonomic substrate of a ghost-inhibitor.  A group-attractor tends to work to help at amplifying the kinematic action that is of the Fourier Transformation, that is of the directly corresponding Hamiltonian operator, that is here to be interacting in a Yukawa-related nature with the said group-attractor.  Furthermore, a ghost-inhibitor tends to work to help at attenuating the kinematic action that is of the Fourier Transformation, that is of the directly corresponding Hamiltonian operator, that is here to be interacting in a Yukawa-related nature with the said ghost-inhibitor.
I will continue with the suspense later! To Be Continued!  Sincerely, Samuel David Roach.