Reductional Electrodynamics — A Start

 Whenever a Ward-Cauchy-Based Kahler Hamiltonian Topological Manifold, is to change in either its direction and/or speed, relative to the motion and presence of electromagnetic energy, it will thereupon spontaneously tend to consequently occur, that such a stated Ward-Cauchy-Based Kahler Hamiltonian Topological Manifold, will resultantly have a heightened expectation value, of generating one or more discrete increments, of unitary heuristic-gauge magnetic potential. Such unitary heuristic-gauge magnetic potential, is eminently tantamount, to the corroborative effect, of what I happen to call, the “i*PI(Del)Action.” Such a generation of unitary heuristic-gauge magnetic potential eigenstates, is thereby to spontaneously occur, alongside with the spontaneous occurrence of the re-calibration of Chern-Simons Invariants. Again, as I have mentioned before; Chern-Simons Invariants are only invariant, when both the speed and the direction, of the eminently associated Hamiltonian Topological Manifold in question, is to be maintained in consistency, relative to the motion and presence, of electromagnetic energy. So; When a given arbitrary Kahler Hamiltonian Topological Manifold, is to either alter, in its speed and/or in its direction of motion, when this here is to be considered, relative to both the motion and the presence of electromagnetic energy — namely, relative to the motion and presence of light — , that it will thereupon consequently tend to spontaneously occur, that the Chern-Simons Invariants will spontaneously alter to a different venue, or, in other words, the Chern-Simons Invariants will therefore spontaneously become re-calibrated. 

When the general physical characteristics, of the local homotopic conditions, of discrete energy quanta, are brought into perturbation or alteration, at a reductional Ward-Cauchy level, that it will thereby spontaneously tend to consequently occur, that such a general case scenario, will tend to be highly likely, to result in generating, unitary heuristic-gauge magnetic potential. When such unitary heuristic-gauge magnetic potential, is to physically couple with a viable tense of angular frequency, in a hermitian manner, that the spontaneous result, is physical charge. 

Homotopy basically amounts, to contortion-based symmetry. Contortion is eminently associated with the corroborative bending of a directly associated tense of phenomenology. And symmetry is the general condition, in which stuff on one side of a mathematically centralized configured line, is mappable in likeness to the stuff on the other side of such a self same mathematically centralized configured line, if one were to be in such a metaphorical position, in so as to be able to fold the eminently corroborative phenomenon that bears “symmetry,” at the stated configured line of implicit denotation, inward upon itself. If one could theoretically fold something at its center, and the stuff on one side of the folding matches the stuff on the other other side of the folding, then, the implicit “something” of phenomenology that was folded, is said to be symmetrical. So; To get back to what I was saying, when something that is constantly recursively changing its shape, is to bear a covariant tense of respectively recursive symmetry, in a manner, to where the modus operandi of the bending-of-topological-contour-related symmetry is to all of the sudden be changed, due to the physical condition, that the eminently corroborative Kahler Hamiltonian Topological Manifold, is to be changing in its speed and or changing in its direction of motion, relative to the motion of light, then, this general process, will thereupon often spontaneously tend to facilitate, a single direction spontaneous wave tug upon the time related component of the eminently corroborative space time fabric at hand, in the general manner of a modulae non degenerative puncture, in its re-established forward holomorphic direction, of which, at that small of a level, will thereupon tend to form unitary heuristic-gauged magnetic potential. 

What I term of, here, as being, the “modulae non degenerative puncture,” is a puncturing of the morphology of the implicit topological manifold, yet, Not a puncturing of its eminently associated tense of elastic/fractal modulae. 

When the heuristic-gauge magnetic potential, is to eminently couple with a tense of angular frequency, in a hermitian manner, it will often tend to form charge. Whereas; When the heuristic-gauge magnetic potential, is to eminently couple with a tense of angular momentum, in a hermitian manner, it will often tend to form entropy.

The faster that a Kahler Hamiltonian Topological Manifold is to be spatially transmitted, the Greater that its eminently associated Lorentz-Four-Contraction will tend to be, to where its spontaneously resultant i*PI(Del)Action will tend to have a relative enhancement in its scalar magnitude/amplitude, to where its consequentially resultant probable charge potential will thereby tend to be amplified. 

A Kahler Hamiltonian Topological Manifold, that is to recursively maintain both a constant tense of radial momentum, And, a constant tense of transversal momentum, over a viably proscribed duration of time, will consequently tend to spontaneously manifest a steady state i*PI(Del)Action, to where the resulting expression of its effectual potential magnetism, will thereby tend to not be spontaneously perturbative. 

The more compact the Kahler Hamiltonian Topological Manifold, the more resolute the Fourier-Related-Progression. The more hermitian that the Lagrangian-Based flow of a Kahler Hamiltonian Topological Manifold is to be, the more succinct the Fourier-Related-Progression. 

Ward-Cauchy-Related dimensional alteration, tends to physically utilize, the spontaneous incursion, of an eminently corroborative tense, of imaginary energy. 

The pseudo warping of a super string related field, is eminently associated, with the general physical process, in which the core field density, of the individually taken super strings, is here to spontaneously wind upon itself, locally. 

Reductional physical charges, which are eminently associated with the workings of the Betti Action, tend to be lower in scalar magnitude, than reductional physical charges, which are, instead, to be eminently associated with Riemann-affiliated electrodynamic current. 

The greater the positive Betti Number, the more compact that the eminently corroborative Kahler Hamiltonian Topological Manifold will tend to be, the more imaginary energy that it will tend to exhibit per charge, to where, the less likely that external phenomena may pose as much of a threat to collide, as would otherwise be more likely, since voltage tends to have the physical inclination, of having the capacity, to push away co-tangentially approaching debris. 

The greater the imaginary voltage, the more resolute that the eminently corroborative Kahler Hamiltonian Topological Manifold, will tend to be exhibited as, over the general course of its Fourier-Related-Progression. 

The lower the entropy, the more equivocal Landau Lines that there tends to be present here, the lower the impedance, the more spontaneously efficient that the consequentially resultant electromotive current will thereby tend to be. 

The spontaneous enhancement of entropy, as respectively incurred upon a proscribed Kahler Hamiltonian Topological Manifold, tends to facilitate the physical encroachment of incoming initially external quantum breaches of a spurious nature, of which tends to generally form a tense of electromotive chaos, of which tends to consequently work to act as a crucible of physical distraction for the proscribed innate operations of the implicit electromotive system of flow, thereby decreasing the efficiency of electric flow. 

What Homotopic Transfer And Homotopic Restraint Are

 Homotopic transfer may be thought of, as the propagational permittivity, that is eminently associated, with an entity of contortion-based symmetry. Whereas; Homotopic restraint may be thought of, as the propagational impedance, that is eminently associated, with an entity of contortion-based symmetry. SINCERELY, SAMUEL DAVID ROACH.  

Also; The general coupling, of a heuristic tense of homotopic transfer, with the stratum of electrodynamic power, may often tend to facilitate the mappable formation, of a heuristic tense, of the Lagrangian-Based Trace of electrodynamic pulsation. 

When a De Rham Hamiltonian Operator, works to bear the general tense, of an eminent presence, of recursively re-calibrated Chern-Simons Invariant gauged-action, the inversely dispersive (settling) characteristic, of such a general tense of gauged-action, often tends to facilitate, the formation of electrodynamic charge, whereas, the heuristically dispersive (unsettling) characteristic, of such a general tense of gauged-action, often tends to facilitate, the formation of electrodynamic entropy.  

Gravity waves often tend to ebb, towards the direction of greatest homotopic residue.  

The formation of Noether-Based gravitational waves is often facilitated, by the eminent effect upon space-time-fabric, that is produced, by the effectual propagation of the scalar flow, of homotopic residue-related eigenstates, as taken along the Rarita Structure.  

The heuristic force of gravitational waves, generally tends to be eminently effectual, in the direction of escalating homotopic transport.  

When the homotopic dispersion of the gauge-action eigenstates, of super string-based Chern-Simons-Related homotopic residue, kinematically couples with Ward-Cauchy-Related Frequency, (specifically speaking, with the general frequency, that is eminently associated, with what I term of as being, the E(8)XE(8)String -Related-Oscillation-Based-Mode), this may often tend to work to facilitate, the formation of an oscillation-related output, of which tends to facilitate the formation of certain wave-like patterns, of which are here to be eminently associated, with what may tend to be thought of, as being thought waves.  

Calabi-Yau Manifold With A Lack Of Homotopic Symmetry -- Less Likely To Be Highly Kahler

 A given arbitrary Calabi-Yau Manifold, that is here to express a relative lack of homotopic symmetry, will consequently tend to be less likely to express, the physical condition of being highly Kahler. SAMUEL ROACH. (1989).

Topological Contortion-Based Symmetrism

 In many potential genre of the word, the term, homotopy, may often be thought of as being:

(Interactive) Topological Contortion-Based Symmetrism. LATER ON! SAMUEL ROACH.

Perturbation Out Of Homotopy

 When the isomorphic symmetry of the holonomic metric, of an initially homotopic set of discrete energy, is brought into a perturbative state, this will often tend to incur the general physical condition, to where such a mentioned respective set of discrete energy quanta, is thence to often tend to ensue, in so as to spontaneously be brought out of such a general physical condition of homotopy. SAMUEL ROACH.

More As To Translational And Radial Symmetry

Orbifold eigensets that are here to be working to form a De Rham cohomology, tend to bear a greater tense of either a translational symmetry and/or of a radial symmetry, than orbifold eigensets that are here, instead, to be working to form a Dolbeault cohomology.  Sincerely, Samuel David Roach

Isometric Symmetry Of Superstrings Of Orbifold Eigenset

The more isometric that the symmetry of the cyclical reverberation is -- as to those individually taken superstrings of discrete energy permittivity, that work to comprise one given arbitrary orbifold eigenset, -- the greater that the respective tendency will then consequently be, as to that the said given arbitrary orbifold eigenset to then have a higher scalar amplitude of a respective Majorana-Weyl-Invariant-Mode.  Sincerely, Sam Roach.

Symmetries Of Cohomologies

Let us consider a given arbitrary quantum of discrete energy permittivity, during BRST.  This is when both the Polyakov Action and the Beti Action are happening to the correlative discrete quantum of energy, simultaneously -- through the vantage-point of a central conipoint.  The so-eluded-to superstring and its counterstring, during such a tense of a gauge-metric, are not to then to be in the process of going through a Lagrangian-related genus of motion -- since this is here to be happening, over the course of one discrete instant of time.  As this is happening, -- the said superstring is to be vibrating at the correlative proximal locus of its Sterling Approximation.  During BRST, the said string -- whether the correlative superstring of discrete energy permittivity is here to be either of a bosonic nature or whether it is here to be of a fermionic nature -- is here to form a vibrational oscillation, that is to be either of a respective harmonic nature or of a respective anharmonic nature.  (Such a said vibration is here to be of a harmonic oscillation if it is of a bosonic nature, or such a said vibration is here to be of an anharmonic oscillation if it is of an fermionic nature.)  As an aside:  The topology itself of a superstring at the Poincare level, that is inherent to a discrete quantum of energy permittivity, is extraordinarily smaller in thickness than the respective circumference or its respective length than such a so-eluded-to superstring.  (As a general idea so that you get the jist -- a superstring is on the order of 10^(-43)* as thin, as it is respectively round (bosonic) or long (fermionic.)   So, as such a said given arbitrary superstring of discrete energy permittivity and its directly corresponding counterstring, are vibrating during BRST -- the directly corresponding topology of the holonomic substrate of the said discrete quantum of energy -- is to be interacting in a Gliosis manner with the norm-state-projections that surround it, in so as to work to form what may here to termed of here as a Gliosis-Sherk-Olive cohomology.  Such a GSO cohomology, tends to be of a toroidal-related shape for such a so-eluded-to bosonic string, and such a GSO cohomology tends to be either disc-shaped, washer-shaped ( if the correlative superstring is swivel-shaped), or conical-shaped, for such a so-eluded-to fermionic string.  Consequently, the GSO cohomology of a superstring of discrete energy permittivity, that is bosonic in nature -- tends to be symmetric in differential geometry to its directly corresponding counterstring, during BRST, -- whereas, the GSO cohomology of a superstring of discrete energy permittivity, that is fermionic in nature -- tends to be assymetric in differential geometry to its directly corresponding counterstring, during BRST.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Parity Between Adjacent Scattered Eigenindices

Let us initially consider a cohomological pattern, that had just formed at one given arbitrary locus.  Let us next consider this said cohomological pattern, as a "snapshot" in the substringular -- as being of a Laplacian-related Ward-Cauchy case scenario.  Let us now consider that the norm-state-projections that an orbifold eigenset had acted upon here -- in so as to work to form the said cohomology -- had formed what may be termed of as a Reimman scattering to a respective extent, in so as to form the so-eluded-to generation of cohomology eigenstates.  Now, let us consider two of the eigenindices that have here to have just been formed by the said cohomological generation -- in such a case in which these two respective given arbitrary eigenindices, which are out of the much larger overall Hodge-Index of the overall cohomological phenomenology of such a respective given case, are here to be adjacent to one another, at the proximal locus of the correlative Laplacian Transform.  These two adjacent scattered eigenindices, are of a Reimman scattering -- to where these are to bear an even parity.  This then works to elude to the Ward-based condition, that, if one were to theoretically fold together the two different individually taken eigenindices at their central coniaxion towards one another -- this would work to form a general genus of an isomorphic symmetry, at the point of duration of the correlative "snapshot" of time.  I will continue with the suspense later!  To Be Continued!
 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.

Cohomological Pumping

Let us say, that one is to have a topological source, that is here to bear a tense of a Clifford Expansion -- to where this is to elude to a region, that is here to consist of an initial set of  orbifold eigensets, that are to be expanding outward at a relatively quick rate over time.  Let us say, that the externalized core-field-density of the so-eluded-to topological stratum, that is here to be expanding over time -- is to cycle, from initially working to bear an isomorphic symmetry, to subsequently working to bear an isomorphic asymmetry, to working to bear an isomorphic symmetry, and so on -- as the said Clifford Expansion is to be occurring.  This would then work to mean, that the so-eluded-to holonomic substrate, that was here to consist of the said initial set of orbifold eigensets -- is then to go from mainly generating cohomology, to next to go into mainly degenerating cohomology, to then to mainly generating cohomology, and so forth.  This would then work to infer a tense of a process, that is here to work, in so as to "pump" cohomology back-and-forth -- in the process of a general genus of an overall set of cyclical permutation, that is here to be potentially appertaining to a genus of the formation of the homotopic residue of Calabi-based permutations, over time.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Next As To Implosion Resulting In Explosion

If an imploding orbifold eigenset, that is to work to result in an explosive expansion -- is to go from being drawn inward, into then being decompactified as an expansion that is here to happen in a relatively quick manner, as a Hamiltonian operation of a Clifford Expansion, as a divergent Fourier Transformation that is here to bear a divergent eigenbase of those initially interactive eigenindices, that are here to react to the Ward-Cauchy-based condition of an initial eminent collapse, by being spontaneously tugged outward by a cross-product-based thrust, -- is to bear an externalized expanding core-field-density, that is to work to tend to bear a relatively isometric symmetry, then, such an initially imploding orbifold eigenset, that is now to act in so as to diverge outward, -- will then tend to mainly generate cohomology.  Yet, if such a general genus of an explosion, that is here to result here from an implosion, is to, instead, to tend to work to bear a relatively isomorphic asymmetry, then, such a general genus of a Cevita interaction -- will then have the Ward-Cauchy-based condition of tending to mainly act, in so as to degenerate cohomology in this said ulterior case.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

Extra Stuff About Cyclic Permutations

Let us initially consider a phenomenology that goes through a state of a Fourier-related activity,  that is repeated over and over again -- yet, to where such a so-eluded-to general tendency of a cycle is to work to bear one or more slight changes, over the course of the iterations of each of such a so-eluded-to process or processes of cyclical states.  If the pattern of the cyclical changes, is never symmetrically completed -- in such a manner to where the overall pattern of such a general condition of a cycle is not equivalently iterative, then, such a cyclical pattern is said to diverge.  Yet, if the pattern of the cyclical changes, is to instead, be symmetrically completed in such a manner -- to where the overall pattern of such a general condition of a cycle is to be equivalently iterative, then, such a cyclical pattern is said to converge.  For instance -- let us consider an elliptical pattern, that is cyclical in permutation.  Let us say -- within a here considered tendency of time constraints -- that one physical phenomenology is to orbit around another physical phenomenology, in such a manner to where the tense of such an orbit, per each adjacent iteration of orbit, is to be slightly different is its precise Lagrangian-based contour, -- yet, let us say that in this given arbitrary case scenario, that after one thousand iterations of such an elliptical tendency of orbit, that the whole overall general pattern of a cyclical tendency is to be repeated in the exact same manner again, to where the second set of one thousand iterations of such an elliptical orbital-based tendency is to be exactly the same as the first set of one thousand iterations of such an elliptical orbital-based tendency.  In this just mentioned tense of a condition of cyclical permutation, the cycle is to here be symmetrical in its behavior, and thus, such a so-stated tense of a condition of cyclical permutation is to here be convergent, -- at least over the course of the first two thousand iterations of such a pattern of a cyclical-based permutation-related tense of elliptical orbit.  Furthermore, there are three general genre of Fourier-related cyclical permutations -- of which may sometimes be combined. There are Lagrangian-based cyclical-based permutations, and/or there are metrical-based cyclical permutations, and/or there are contour-based cyclical-based permutations.  I will later discuss what is meant by a Laplacian-related state of conditions, that would work to bear a tense of cyclical permutation.

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