Solutions To the First Question of the Last Test of Course 11

1)  The angular momentum eigenstates that appertain to the vibratorial indices that are expended from Planck-like phenomena that are adjacent, and, are from the same universe, are normal or orphoganal -- with a covariant, codifferentiable, and codeterminable relativistic wobble that bears a back-and-forth vibratorial oscillation of ~1.104735878*10^(-81)I degrees.  In such a case, the different PLP -- that are here each from the same universe, are norm to each other -- when mapped-out physically in a Laplacian-based manner.  This is while also bearing the mentioned relativistic wobble. This is because all touch is based on normalcy or tangency, and, norm-conditions are based on conditions of orphoganation.  Since here, the directly corresponding various PLP (Planck-related phenomena) are of the same universe, and are adjacent here too, these must be oriented at 90 degrees relative to one another during the BRST portion of instanton.  This is what causes the mentioned wobbling to here be normal with the same back-and-forth angle of relativistic vibratorial oscillation that I have mentioned.  This determination as to orphoganation works to readjust by 90 degrees for each proceeding layer of adjacency that goes outward from the most adjacent layer -- as is according to the right-hand-rule for up to 32 spatial dimensions -- while also allowing for an orphoganal condition that starts over at a 0 degree relational basis 64 layers of adjacency out from the initial layer of adjacency.  So, at 65 layers of adjacency from the most adjacent PLP from a PLP that is of a same universe fromt the first stated one of this sentence, the two PLP are oriented at 90 degrees -- with an angular momentum index that works to meet at an orientation of 90 degrees, due to how the corresponding vibratorial oscillations of the mini-string segments that are expended outward from the said covariant angular momentum eigenstates are directly kinematically associated over a given arbitrary iteration of BRST during a group instanton.  The said levels of adjacency just mentioned here are not specifically bearing on the conditions of relativistic proximity.  I will continue with the suspense of the test solution to the second test question of what I asked on Friday later! 
Sincerely,
Samuel David Roach.