Cohomology-Related Eigenstates Of Opposite Parity

Two different sets of cohomology-related eigenstates are of opposite parity -- when one of these two mentioned sets of cohomological eigenstates is to bear an order of grouping, that is asymmetrically isometric to the order of grouping, -- that the other respective set of cohomological eigenstates is to bear.  I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.