Reinforced Drive Of Angular Momentum

 When there is to be an enhancement in the torsion, that is here to be incurred upon the resonant metric, of a directly associated kinetically delineated Hamiltonian Operator, this general process, will often tend to help facilitate a reinforcement in the drive, of the corroborative angular momentum, that is here to be eminently associated, with the Lagrangian-Based motion, of the said respective Hamiltonian Operator. SINCERELY, SAMUEL DAVID ROACH.

Torsion -- Homotopic Convergence/Divergence -- Etale Cohomology -- Slater-Related Recursion

 The torsion that is incurred, upon the homotopic convergence/divergence, of an Etale Cohomological topological manifold, may often tend to work to bear a Slater-Related recursion. SAMUEL ROACH.

Diminishing Field Of Kinetic Energy

A propagated steadily diminishing field of kinetic energy, may often be said to tend to be enacted upon, by a Euclidean-Related torsion, to where the directly associated respective enactment of such torsion, may often be said, to tend to be occurring, via a Poisson-Related recursion. TO BE CONTINUED! SAM.

Diminishing Propagated Beam Of Light -- Clifford-Related Torsion -- Slater-Related Recursion

 A propagated beam of light, of which is here to be steadily diminishing in its field intensity, may said to respectively tend to be spontaneously enacted upon, by a Clifford-Related torsion. The recursively considered torsion, that is here to be heuristically enacted, upon such a beam of electromagnetic energy, in so as to work to facilitate such a steadily diminished hereupon inferred electromagnetic field intensity, may be said to often tend to work to be inherently related, to a directly associated Slater-Related recursive field operation, as taken over a directly corresponding respectively potential proscribed duration of time. SINCERELY, SAMUEL ROACH.

Torsion Applied Upon A Homotopic Divergence/Convergence

 A Euclidean-Related torsion, that is to be applied upon a homotopic divergence/ homotopic convergence, is to work to bear a directly associated Yukawa Coupling, that will often tend to be eminently associated, with a Poisson-Related recursion. Whereas; A Clifford-Related torsion, that is to be applied upon a homotopic divergence/homotopic convergence, is to work to bear a directly associated Yukawa Coupling, that will often tend to be eminently associated, with a Slater-Related recursion. SINCERELY, SAM ROACH. 

Non Perturbative Fadeev-Popov-Trace Eigenstate

 When the flow of motion of a given arbitrary Fadeev-Popov-Trace eigenstate, is to be both non perturbative and free from radial torsion, this will thereby tend to work to increase the probability, that its directly corresponding first-order light-cone-gauge eigenstate, will consequently work at having a heightened chance of being gauge-invariant. TO BE CONTINUED! SINCERELY, SAMUEL ROACH.

Spin-Orbital Momentum Of A Fadeev-Popov-Trace Eigenstate

 The more rapid that the spin-orbital-momentum-related motion of a given arbitrary Fadeev-Popov-Trace eigenstate tends to be, the more torsion that will often tend to be applied upon its directly corresponding respective first-order light-cone-gauge eigenstate. I WILL CONTINUE WITH THE SUSPENSE LATER! SAMUEL. (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.

Torsion Upon Space-Related Vacuum And Dimensionality

 Let us initially consider two different space-related vacuums, of the same three-dimensional volume. Both are to have the same amount of torsion applied to them. One of such space-related vacuums, is to work to bear a higher number of innate spatial dimensions than the other one. That space-related vacuum of the two, of which is here to work to bear a higher number of innate spatial dimensions, will consequently tend to result in working to bear a greater viscosity -- than the other of the two stated space-related vacuums.  Consequently; that space-related vacuum of the two earlier stated ones mentioned, of which is here to work to bear a higher number of innate spatial dimensions, will consequently tend to result in working to bear a greater impedance -- than the other of the two stated space-related vacuums. Samuel David Roach.

As To The Torsion Applied To The Light-Cone-Gauge

 The more torsion that is to be applied to an eigenstate of the light-cone-gauge, -- the more likely that this factor, in and of itself, will influence such an inferred wave-related quantum of discrete energy impedance, to tend to consequently result in working to form anharmonic Schwinger-Indices, as these are here to thereby be formed, at the general proximal local region, at which such an earlier mentioned light-cone-gauge eigenstate, is here to be "plucked" like a harp, by its directly corresponding set of gauge-bosons. Sincerely, SAM ROACH.(1989).

Cyclical Pattern Of Change In The Manner Of The Betti Action

 A cyclically re-iterative pattern of change in the Betti Number, that is here to be exhibited by those individually taken super strings of discrete energy permittivity, that work to comprise a cohesive set of discrete energy quanta, -- tends to work to reverse-fractal into a cyclically re-iterative pattern of change, that is here to be in terms of the spatial dimensionality of the thus inferred cohesive set of discrete energy quanta. Such an inferred cyclical pattern of a toggling back-and-forth motion, that is here to be considered, as initially going from a Ward-Cauchy-related tense of a space-wise dimensional compactification, while then ensuing in so as to be going into a Ward-Cauchy-related tense of a space-wise dimensional de-compactification, may thus often tend to work to help in forming a tense of torsion; -- in which -- if such an inferred cohesive set of discrete energy quanta, is then to be in the process of being spatially translated transversally over time, through the Hamiltonian Operand of a viable direction, that resultantly, such an inferred general activity of torque, will consequently tend to work to form a tense of an added boost, that is here to be of that wave-tug, that is of its directly corresponding angular momentum. To Be Continued! Sincerely, Samuel David Roach.

Rigidity Of Torsion Applied To Mini-Stringular Segmentation

The higher that the scalar amplitude of the substringular pressurized vacuum, that is here to be applied upon a relatively proximal local holonomic configuration of mini-stringular segmentation -- as this is here to be taken over an evenly-gauged Hamiltonian eigenmetric, -- the Greater that the the scalar amplitude will tend to be, of the rigidity of torsion, that will consequently tend to be applied upon the holonomic substrate of such a configuration of mini-stringular segmentation.  Consequently; the lower that the scalar amplitude of substringular pressurized vacuum, that is here to be applied upon a relatively proximal local holonomic configuration of mini-stringular segmentation -- as this is here to be taken over an evenly-gauged Hamiltonian eigenmetric, -- the Lower that the scalar amplitude will tend to be, of the rigidity of torsion, that will consequently tend to be applied upon the holonomic substrate of such a configuration of mini-stringualr segmentation. Samuel David Roach.

Alteration In Hyperbolic-Related Gravitational Sway

Let us theoretically consider a physical entity of mass, that is initially here to bear a hyperbolic-related sway in its Lagrangian-based pah, that is solely due to the influence of anti gravity.
Let us next say, that there is then to be an instantaneous change, -- that is then to work to cause this originally stated given arbitrary respective physical entity of mass, to go into working to bear a hyperbolic-related sway in its Lagrangian-based path, -- that is solely due to the influence of gravity.  This general process, will consequently work to cause a definite tendency, -- of resulting in both a set of Lagrangian-related Chern-Simons singularities As Well As resulting in a set of metric-related Chern-Simons singularities, -- at the locus in which there is here to be the inferred instantaneous alteration in the general tense of gravity, that is here to be physically applied to the initially stated physical entity in time and space -- that is here to consequently tend to both alter in its general tense of hyperbolic concavity, as well as simultaneously (via the vantage-point of a central conipoint) to tend to alter in its dimensional-related pulsation. (This is to where, such a general activity will tend to work to cause an inversion in the general tense of the augmentation/attenuation of its initial torsion, upon its holomorphic state of pulsation.)  To Be Continued!  Sincerely, Samuel David Roach.

Torsion And Attribute Of Metric-Related Singularity

Let us initially consider an orbifold eigenset, that is here to undergo a metric-related Chern-Simons singularity -- via the translation of this said eigenstate, over the course of its motion through space and time.  If the dimensional-related pulsation of the said orbifold eigenset is to be increased in its torsion, the directly corresponding Chern-Simons singularity that it will consequently tend to undergo, via the course of its spatial translation, (for the here inferred eigenset, as a whole), will tend to bear a tense of amplification.  However; if the dimensional-related pulsation of the said orbifold eigenset is to be decreased in its torsion, the directly corresponding Chern-Simons singularity that it will consequently tend to undergo, via the course of its spatial translation, (for the here inferred eigenset, as a whole), will tend to bear a tense of attenuation.  Sincerely, Samuel David Roach.

A Correction To Some Of My Recent Posts

I was recently studying both some of my past work, as well as looking over the math that I had done, as appertaining to a couple or so of my past posts.  It appears, that what I had termed of as being of a "tori-sector-range," is actually more succinctly -- a "dimensional-train," that is here to be of only one layer of reality, that is appertaining to one universe that is out of a set of parallel universes.  It also makes a little more sense, that if you were to consider that the "cross-sectional" thickness of the "dimensional-train," that is of the ever torsion-related windings of one overall universal setting,  is still to be at least somewhat similar to my previous estimation, that this concept; whereby, if you were to consider that a "tori-sector-range" that is to be as a "dimensional-train," that is here to work to represent the ever torsion-related windings of one particular layer of reality, that is of one specific universe; that it may be possible, that, if you were to divide the size of the so-stated "cross-sectional" region of a "dimensional-train" that I had earlier stated, by the number of layers of reality of one universe (from within a set of parallel universes), that this consequential resultant "dimensional-train," could be thought of as being or appertaining to the ever torsion-related linkage, that is here to thereby act, in so as to web together the workings of one specific layer of reality, that is part of one universal setting, -- during each successive iteration of the generally noticed duration-related activity of what I term of as being of Ultimon Flow. Sam Roach.

Torsion Upon Mini-Stringular Segmentation

Mini-Stringular segmentation works to form those superstringular fields, that are here to work to allow for the existence of homotopy (to where all unfrayed superstrings are here to be inter-connected, by means of a multiplicit field).  Mini-Stringular segmentation is formed, by the bead-like inter-connection of second-order point particles -- by a general phenomenology, that I term of as being called "sub-mini-string."  When there is to be the general proximal local presence of a hyperbolic convergence of mini-stringular segmentation, upon any one given arbitrary cotangent bundle that is to be approached in such a manner, there is then to tend to be more of a torsion-like activity that is here to be implemented upon the general topological stratum of such said mini-stringular segmentation, -- than instead, if there is to be the general proximal local presence of a euclidean convergence of mini-stringular segmentation, upon any one given arbitrary cotangent bundle, that is to otherwise to be approached in such a manner. To Be Continued!  Sincerely, Samuel David Roach.

Part Two Of Session 13 Of Course 20

By the way, -- the general condition of the torsion that alters the order of any one said light-cone-gauge eigenstate by 90i degrees, works to cause the correlative composite second-order light-cone-gauge eigenstates to either go from working to bear a sinusoidal delineation -- to working to bear a relatively supplemental delineation, when there is a light-cone-gauge perturbation that is to go from working to exhibit a Yang-Mills or non abelian light-cone-gauge topology, to working to exhibit a Kaluza-Klein or abelian light-cone-gauge topology, or, in the ulterior case, to cause the composite second-order light-cone-gauge eigenstates to go from working to bear a relatively supplemental delineation, to working to bear a sinusoidal delineation, when there is a light-cone-gauge perturbation that is to go from working to exhibit a Kaluza-Klein or abelian light-cone-gauge topology to a Yang-Mills or non abelian light-cone-gauge topology.  Such a said torsioning is necessary, in order to work to allow for electromagnetic energy to initially to be able to re-arrange as entropic photons, when it is first disorganized by a correlative scattering -- while to then to be able to re-group and re-quantize as non entropic photons, once such electromagnetic energy has torsioned back into the general genus of the proximal local electromagnetic radiation.  Once the multiplicit photonic energy is to be re-quantized back into the general proximal local electromagnetic radiation, in so as to here to be having a Yang-Mills light-cone-gauge topology -- its Clifford algebra will then have more of a tendency of going from working to bear a primarily euler and a Dirac geometry, into working, instead, to bear a primarily euclidean and a hermitian geometry, over time.
 I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Examples Of Open Loop Phenomenology

Let us consider two different cases of Ward-Cauchy-based open-loop phenomenology, that exist in the sub stringular -- of which act in such a manner, that may be described of as a manner of being "hook strings."  Let us initially consider the first one that I had in mind.  There is the case of a sub stringular open-loop, that acts as an eigenindex of its own genus of Hamiltonian operation, that is isotropically stable.  This may be termed of as being a "1+1" string (not to be confused with a "2 dimensional" string).   It tends not to bear any significant topological-related torsioning across the "width" of its parametric dimensional symmetries.  There is, as well, the case of another sub stringular open-loop, that acts as an eigenindex of its own genus of Hamiltonian operation, that is isotropically unstable.  This may tend to be termed of as being a "2+1" string (not a 3 dimensional string).  This, on the other hand, tends to bear a significant topological-related torsioning across the "width" of its parametric dimensional symmetries.
I will continue with the suspense later!  To B Continued!  Sincerely, Samuel David Roach.

The Strong Force And The Basis Of Charge

In a stable atom, a positive charge tends to happen -- when Ward-Cauchy-based eigenstates of the centralized knotting of the Rarita Structure, work to bear torsional eigenindices -- that bear a tendency of aiming to act in the operational direction, of pushing themselves into external phenomenology.

In a stable atom, a negative charge tends to happen -- when Ward-Cauchy-based eigenstates of the centralized knotting of the Rarita Structure, work to bear torsional eigenindices -- that bear a tendency of aiming to act in the operational direction, of pushing external phenomenology into the so-eluded-to internal phenomenology of the initially said general genus of Ward-Cauchy-based eigenstates.

So, one may say, that a positive charge is as a "dot-product"-based tendency, whereas, one may say that a negative charge in as a "cross-product"-based tendency.

I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

What Charges Are

Charges are when eigenstates of the centralized knotting of the Rarita Structure, work to bear torsional eigenindices -- that may in one general multiplicit instance, have either the Laplacian-based tendency and/or the Fourier-based tendency, of pushing themselves into external phenomenology, via the multiplicit pulsation of the coiling activity of mini-stringular segmentation (relative negative charges), or, when eigenstates of the centralized knotting of the Rarita Structure, work to bear torsional eigenindices -- that may in one general multiplicit instance, have either the Laplacian-based tendency and/or the Fourier-based tendency, of pushing  external phenomenology upon themselves, via the multiplicit pulsation of the coiling activity of mini-stringular segmentation (relative positive charges).
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel Davie Roach.