Harmonically Gauged/Anharmonic Gauged Hamiltonian Operator

 A harmonically gauged mass-bearing Hamiltonian Operator, often tends to be typically heuristically affiliated, with the eminent Ward-Cauchy-Related presence, of a directly associated co-tangential bundle. Whereas; An anharmonic gauged mass-bearing Hamiltonian Operator, often tends to be typically heuristically affiliated, with the eminent Ward-Cauchy-Related presence, of a directly associated tangential bundle. I WILL CONTINUE WITH THE SUSPENSE LATER! SINCERELY, SAM ROACH.

A Superstring-Related Stricken Balance Between Convergence And Divergence

 Ward-Cauchy-Related phenomenology, that is of a heuristic Noether-Based nature, that is here to strike an evenly-smooth balance, amongst the covariant dual conditions, that are here to be of the convergence and divergence, that is here to be directed respectively either towards upon or directed away from a superstring-related topological manifold, are here to thereby consequently have a general tendency, of neither being overtly tugged towards the general covariant direction of the delineation of the so inferred cotangent bundle, that is of such an earlier stated superstring-related topological manifold, nor would such an earlier initially stated Ward-Cauchy-Related phenomenology, have a general tendency of being spontaneously tugged, in any viable degree of measure, towards the directly corresponding inferred tangential bundle, (to where, such a inferred "tangential bundle," is here to be directed, relatively "away from" the proximal local covariant delineation, that is of the earlier stated "cotangent bundle"), that is of a respective covariant tense of delineation, as this is here to be considered, in terms of such an earlier stated superstring-related topological manifold. I WILL CONTINUE WITH THE SUSPENSE LATER! SAM ROACH.

More As To Tangential Bundle

 The general multiplicity of the tangential bundle (as opposed to the "cotangent bundle"),  may often appertain to a cohesive set of index-like eigenstates, that are here to be diverging away from the phenomenology, of a cohesive set of discrete energy quanta. To Be Continued! Sincerely, SAM ROACH.

Compounded Homotopic Residue — Asymptotic Divergence

 The more that the homotopic residue of an escalating Lagrangian, that is here to be of a Euclidean expansion, is to be compounded, over a given arbitrary proscribed duration, that is here to be of a sequential series of group-related instantons, the more that the corresponding pertinent Euclidean tangential bundle(s) directly involved, will consequently result, in tending to diverge in more of an asymptotic manner. The more that the homotopic residue of an escalating Lagrangian, that is here to be of a Clifford expansion, is to be compounded, over a given arbitrary proscribed duration, that is of a sequential series of group-related instantons, the more that the corresponding pertinent hyperbolic tangential bundle(s) directly involved, will consequently result, in tending to diverge in more of an asymptotic manner. I will continue with the suspense later! Sincerely, SAM ROACH. (1989).