Let us consider, as to how one is to work to determine what the Chern-Simons Invariants are to be, -- for a superstring, that is here to be of a cotangent bundle in R3:
Let us consider the Lagrangian-based motion of a superstring of discrete energy permittivity, as it is to moving through a Hamiltonian operand in space-time-fabric over time. Such a superstring, in this particular given arbitrary case, is theoretically to be traveling in only three spatial dimensions, over the course of the dimension of time. (Time here, -- is to considered as the duration of the directly corresponding sequential series of group-related instantons, that are here to be most correlative to this so-stated superstring of discrete energy permittivity, that is of such a respective given arbitrary theoretical case scenario.) In the process of doing such, this said string is here to form a cohomological mappable-tracing. Such a so-stated cohomological mappable-tracing, is here to form a Lagrangian-based trace. Such a said "trace," is here to be the product of the unitary trajectory of the directly corresponding superstring -- as it is here to be traveling through its correlative Lagrangian, With the length of its core-field-density. Next -- consider the sum of the following: The directly corresponding Anti-De-Sitter/De-Sitter equation, plus the integral of the directly corresponding Anti-De-Sitter/De-Sitter equation, plus the double-integral of the directly corresponding Anti-De-Sitter/De-Sitter equation. This will then work to help to indicate the matter-based nature of the spurious flow of phenomenology, in three spatial dimensions. Now, take the directly correlative said Lagrangian-based trace, multiply this by the overall sum of the said directly corresponding -- Anti-De-Sitter/De-Sitter equation Plus the integral of the Anti-De-Sitter/De-Sitter equation Plus the double-integral of the Anti-De-Sitter/De-Sitter equation -- while then multiplying this whole thing by 2/3 (This is the spatial dimensionality of the correlative Lagrangian-based trace, when this is divided by the number of spatial dimensions that the said superstring is here to be traveling through, in this particular respective case), While Then Dividing This Whole Thing By 4PI (The overall number of degrees that any one given three-dimensional phenomenon is to bear a direct Cauchy relationship with, is 720 degrees. (There are 4PI degrees of freedom in three spatial dimensions.)). -- This will then work to help to determine a pattern, in which such a said theoretical superstring that is here to be traveling along the so-inferred path, will then tend to bear a general spurious flow of a disturbance of space, in its correlative variation of parameters -- when this is taken along the path of its directly corresponding Lagrangian-based trace, -- to where this will then help one to know what the directly correlative Chern-Simons Invariants will then tend to be, in such a theoretical case of such a said superstring, -- that is here to be of a cotangent bundle of R3 (as such a said string is here to be converging upon a path, that is of three spatial dimensions plus time.) Sam Roach.
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