Tuesday, January 22, 2019

Fundamentals As To Why Chern-Simons Invariants Are Always Of A Minimum Of A Cotangent Bundle Of R3

Whenever one is to have a given arbitrary Lagrangian-based Trace, that is here to be curving in such a respective manner, to where it is to bear both one or more transversal-based components -- as well as to here be bearing one or more radial-based components in time and space, -- it will always be translated through the general said time and space -- via a dimensionality that is here to work to bear a minimum of two spatial dimensions plus time.  A Lagrangian-Based Chern-Simons singularity will always be able to be mapped-out through a Laplacian-related locus, at which the directly corresponding phenomenon -- that is here to be acting in so as to be in the process of working to bear such a said Lagrangian-Based Chern-Simons singularity -- will be changing in one or  more derivatives of motion, beyond what the number of spatial dimensions that are here to be pertinent to the translation of the motion of this said phenomenology, that is here to be acting in so as to work to form the earlier inferred mappable trace.  Consequently, -- this general situation of tendency will then work to infer -- that certainly if one were to be consistently to be mapping-out any given arbitrary region, over the course of a so-eluded-to Fourier Transform, in which there is to be any translation of mappable-tracing that is to be present, as taken from the initial side of such an earlier inferred trace -- that is to exist in going from Before the presence of such a general Lagrangian-based Chern-Simons singularity to After the presence of the self-same Lagrangian-based Chern-Simons singularity, -- one will deductively need to have the proximal local presence of a dimensional field, that is here to require the existence of the eminent presence of At Least Three spatial dimensions plus time.  Any respective general locus of a cotangent bundle, is here to work to mean and/or to infer, the presence of a convergent region of discrete energy-related phenomenology.  Therefore -- in any situation in which there is to exist the presence of Chern-Simons Invariants, there will always be the presence of a situation in which there is a minimum case of a Cotangent Bundle of at least R3.  Plain and simple.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.

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