Chern-Simmons singularities are not always existent directly in-between locants in which orbifolds and orbifold eigensets are specifically delineated. Let us first look at what, in general, happens -- when a world-sheet is mapped-out as a tracing as to the exsitence of both what and how a given arbitrary superstring had kinemtatically differentiated over time. We will then consider the just mentioned extrapolation by examining the general cohomology of a specific given arbitrary tracing of a mappable region in which a specific given arbitrary respective superstring had moved kinematically over a correlative sequential series of integrable integrations of group instanton. The so-eluded-to cohomology that we are here considering initially exists as a given arbitrary Rham-based cohomology. This, as an ansantx, means that the initial increment of traceable mapping of the correlative world-sheet, that works to form the here considered ghost-based cohomology, is delineated as a Yau-Exact substringular distribution over time -- to where the directly associated singularities that are thus formed by such a cohomology are then here of a Yau-Exact nature. This also means that the so-eluded-to cohomology is on the relative Real Reimmanian Plane -- over the correlative duration in which such an eluded-to ghost-based integration of indices is being formed, as a physical memory as to both the existence of what and where and how the directly affileated correlative group of one or more superstrings -- that here operate in so as to perform a given arbitrary specific function in the substringular, over a correlative given arbitrary group covariant action, over time. The given ghost-based cohomology, that is here a mappable tracing of a world-sheet -- that works to indicate both the how, what, and where the so-stated set of superstrings of a common functional operation -- will, in the situation in which I am here addressing, conjoin with another respective given arbitrary world-sheet-based tracing, at an orphoganal-based manner, that will then elemetarily bind at a given arbitrary 90 degree-based differential-geometric-based webbing. This will thus happen as a relatively local binding cite, that acts as an addition to the initially mentioned cohomology that I had mentioned at the beginning of this post. Since the topological-based directoral-sway of such a spike in the substringular would thus form a change in derivatives, that is higher in Hodge-based index than the number of physical spatial dimensions that the general mappable tracing is being delineated through -- over the binary-based Lagrangian format, that would here involve the Laplacian-based exrapolation of the tracing of the overall cohomological pattern, of this given arbitrary case, over time, then, the just described general cohomology that is thus formed will bear at least some Lagrangian-based Chern-Simmons singularities. This will then happen, even though the individual initially-mentioned "mers" of such a cohomology may be smooth enough in topological sway, on their own, in such a manner in so that the two eluded-to segments of such a cohomology may be of a Rham-based cohomology in and of themselves. (This is before the covariant-based conjoining is here to be considered, for the overall mappable tracing, that is to then involve both of the eluded-to segments.) This would then work to form an overall mappable tracing that would then be of a Doubolt nature, when the overall tracing is to be extrapolated, as an integration of both of the so-stated segments -- over the mapped-out Lagrangian that is to here involve both of the eluded-to respective segments that I have here described, in general. This would then make the so-eluded-to overall just mentioned cohomological pattern of a manner that is thus not Yau-Exact.
I will continue with the suspense later! To Be Continued!!! Sincerely, Sam Roach.
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