The Fourth Part of the Fifth Session of Course 17 About the Ricci Scalar

Let us say that a given arbitrary orbifold or orbifold eigenset -- in this case -- is of a harmonic-based Lagrangian nature, over a discrete group oriented metric.  Let us say that all of the Lagrangian-based singularities that are formed by the said orbifold or orbifold eigenset here are of a Real Reimmanian-based nature.  Let us now say that all of these just mentioned singularities are hermitian.  Then, all of the ghost-based indices that are here formed will be of a Rham-based cohomoligical-based nature, over time.  Now, let us say, instead, that all of the Lagrangian-based singularities of the otherwise same said orbifold or orbifold eigenset are of a Chern-Simmons-based nature.  Then, all of the directly corresponding ghost-based indices that are here formed will be of a Doubolt cohomological-based nature here.  Let us now say that the eluded-to said orbifold or orbifold eigenset bears hermitian-based Lagangian singularities that are not of a Real Reimmanian-based nature.  Such singularities would then here be of a Njenhuis-based nature.  Then, the ghost-based indices that are thus formed here will be of a Doubolt cohomological-based nature, in spite of the so-eluded-to hermicity that would here be involved.  Let us say that there is -- in this case -- an orbifold or an orbifold eigenset that bears both hermitian and Chern-Simmons Lagrangian-based singularities, over time.  Or, if the orbifold has both Real Reimmanian and/or Njenhuis-based singularities, or, if there is a combination of the last two scenarios.  Then, the ghost-based indices that would then here be formed by the said orbifold will bear both Rham and Doubolt cohomologies.  Now, imagine an orbifold or an orbifold eigenset that is just as I have here mentioned, except, that the so-eluded-to orbifold or orbifold eigenset is of an annharmonic based nature.  Then, the ghost-based indices would be similar in cohomological index, yet, these ghosts would would bear a different delineatory-based index of distribution.  I will continue with the suspense later!  To Be Continued!!! Sincerely, Sam Roach.