A cohomology that is considered to be of a Doubolt genus is one that starts out at a relatively reverse-holomorphic end of the traceable mapping of the trajectory of its projection, in a relatively hermitian manner, prior to the existence of those one or more Chern-Simmons singularities that work to make the eluded to cohomology Doubolt instead of Rham. So, as one traces the delineation of the eluded to cohomology from the relatively reverse-holomorphic end of its distribution to the relatively forward-holomorphic end of its distribution, that is, from the initial delineation of its general Lagrangian path, toward the continuation of the ensuing path of its general Lagrangian, this eluded to tracing happens in a manner that tends to sway homotopically in a propagation that may be traced by static ghost anomaly indices -- that may be mapped-out in a non-time-oriented manner. This happens in a format of smooth-curvedness, afterwhich, following a traceable mapping of one or more points of singularity, in the here discussed given arbitrary scenario, the initial contour of the mapped-out tracing of the Lagrangian of any of such initally Rham cohomologies will then here becomes a Doubolt cohomology. This works to proceed to bear a trajectory of the eluded to projection that is affiliated with either a Lagrangian-based, and/or a metrical-based spike, that works to form both a codifferentiable and a codetermineable genus of Chern-Simmons spuriousness. This acitivity operates to form the basis as to why the overall here considered cohomology acts as a Doubolt-based cohomology, instead of a Rham-based cohomology. This is the case here, as the said tracing of the projection of the eluded to Lagrangian -- that the eluded to Yakawa-based interconnection of ghost-anomaly-based indices is translated through space, in what is here to be considered as the relatively forward-holomorphic directoral sway. This is what is considered as a tracing of a cohomology that has a directoral-based bearing that moves in an arbitrarily relatively forward-holomorphic general direction. Whatever the general direction that a given arbitrary cohomology tends to apply its sway of permittivity towards, as the said cohomology propagates through a given arbitrary Hamiltonian-based operand, is here to be considered as the forward-holomorphic directoral topological sway of the said cohomology. So, the distinguishment that may work to determine as to whether or not a said cohomology is a Yakawa-based interconnection of ghost-based indices that is Rham -- to where, there are here to be no extrapolation-based Chern-Simmons singularities in the path of the projection of neither the Lagrangian-based genus nor the metrical-based genus of the said cohomology, or, if a given cohomology may be, instead, of a Doubolt nature -- to where this is to bear one or more extrapolation-based Chern-Simmons singularities in the path of the projection of either the Lagrangian-based genus or the metrical-based genus of the said cohomology -- often is related to the scope of the Sterling-based approximation, that may work to determine what the endpoint-based loci are (yet, in terms of the determination of the Ward-Caucy bounds of a substringular neighborhood, instead of in terms of the determination of the Ward-Caucy bounds of a singular substringular eigenfield), that would here work to define as to where the extrapolated cohomology is to begin, and, as to where the extrapolated cohomology is to end. So, whether a cohomology bears any Chern-Simmons and/or Njenhuis-based singularities or not is related to what region works to define what is here to be the considered neighborhood of projection that is being mapped-out.
To Be Continued. Sincerely, Samuel David Roach.
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