Let us initially consider a given arbitrary superstring of discrete energy permittivity. Given both its general geometry, and, the type of field that it is exhibiting, such a said string will consequently have an innate relative direction -- that it will work to bear a tendency of "wanting" to move into. This may be termed of as being the relative "holomorphic direction," of such a said given arbitrary superstring. Discrete quanta of energy, often tend to move in groups, -- that work to operate, in so as to perform one specific given arbitrary function. What I have just mentioned, may be thought of as being, what I term of as being called an "orbifold eigenset." Both the multiplicit orbifold eigenset and its correlative discrete quanta of energy, that work to comprise such a said eigenset, will tend to work to bear the same direction of holomorphic tendency, -- yet, -- since the innate direction that the said orbifold eigenset tends to "want" to move in, takes precedence, -- those earlier mentioned discrete quanta of energy that work to comprise such a said eigenset, will consequently tend to ensue, in so as to invariantly work to bear distortions in motion, from what would otherwise be their innate directional motion -- due to the Ward-Cauchy-related condition, that not all of the given arbitrary individually taken discrete quanta of energy, that work to comprise such a said orbifold eigenset, will thence be able to bear a completely hermtian motion in their holomorphic direction, -- since such said quanta of energy are here to tend to be situated at the outer shell of such an inferred overall "group" of discrete energy, that are here to bear one net overall function. Such said distortions in the innate motion of those discrete quanta of energy, that work to comprise what I term of as being an orbifold eigneset, -- due to the physical condition, that the innate direction of motion of such an eigenset is here to take precedence over the innate direction of motion of its composite stringular-related eigenstates, is my perception as to what Chern-Simons Invariants are thence to be. Consequently; if one is to know the net distributional characteristics of the Chern-Simons Invariants, that are here to be directly related to the motion of any one given arbitrary orbifold eigenset, then, one may consequently have a higher probability of knowing the ensuing delineation of the directly corresponding orbifold eigenset.
Here is a way of looking at this situation, in one general type of a case (if the motion of the set of discrete quanta of energy, is here to be completely hermitian), in more "watered-down, simple terms" :
If you know: 1) That you are dealing with an orbifold eigenset, that is here to work to bear a viable tense of intrinsic Chern-Simons Invariants.
2) What type of "field" that you are dealing with. (Whether it is an f-field, a d-field, etc. ...)
3) What the path-related tendency is here to be. (So one may determine its path integral.)
4) What its angular momentum is here to be, in all of its directorals.
5) That what you are to be dealing with here, is to be an example of a homeomorphic field.
And 6) That such an inferred orbifold eigenset, is here to be acting, via a De Rham cohomology.
Then; you can consequently determine, with a hightened expectation value;
The Delineation-Related "Ratio," as to:
(Its transversal delineation PER
its spin-related delineation in one general axion PER
its spin-related delineation in the correlative general orthogonal axion, etc. ...)
This goes to indicate, that a basic understanding of the distribution of those distortions, that are here to exist in the innate motion of those discrete quanta of energy, that work to form a cohesive set of such said energy, may often work to help one to be able to have a better understanding of the holomorphic transfer of the here implied said orbifold eigenset. Sincerely, Sam Roach.
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