A Change In The Second Derivative

First of all -- what a "change in the second derivative" is, is when a curvature is to, at that point in space and/or in time, to either go from concave-up to concave-down, or, instead, to go form concave- down to concave-up.  Right where there is here to be any such change in the concavity of a curve and/or of a wave-like pattern, -- there is then, right at that spot at which such a said change is then to occur, what is known of as a change in the second derivative.  Let's take this now one step further.  Let us then initially consider an orbifold eigenset, that is here to be propagated along a sinusoidal path -- as such an eigenset is to be in the process of working to bear a relatively continuous transversal delineation-related mode, over an evenly-gauged Hamiltonian eigenmetric -- as the said orbifold eigenset, is here to be tranferred into the relative forward-holomorphic direction.  Consequently, one may here be able to arbitrarily consider that, as such a set of one or more discrete quanta of energy, that are here to be translated in both a transversal and in a spin-orbital manner, are here to be moving into this said forward-holomorphic path -- to where then, the wave that is thence most directly appertaining to the transfer of the said eigenset -- will then act, in so as to simultaneously, via an extrapolation, that is here to be relative to the vantage-point of a central conipoint in time and space, to go from arcing into the relative norm-to-forward-holomorphic direction,  into then relatively changing in the second derivative, -- to then be acting, in so as to be arcing into the relative norm-to-reverse-holomorphic direction, and so on; -- in so long as such a said wave-like pattern, that is of the said orbifold eigenset, is to continue to bear a sinusoidal translation as such, into the relatively forward-holomorphic direction.  Yet, if at some point in duration, such a wave-like tendency is then to be perturbated into a relatively continuous transversal delineation-related mode, that is here to still be resulting in an overall transfer into the holomorphic direction, over an evenly-gauged Hamiltonian eigenmetric -- to where it is then to work to bear a simultaneous, (via the vantage-point of a central conipoint), a spin-orbital translation, that is here to go from arcing into the relative Nijenhuis-norm-to-reverse-holomorphic direction, into then to be changing in the second derivative, to where such a wave is then to be arcing into the relative Nijenhuis-norm-to-forward-holomorphic diretion, -- and so-on, once again, as such a said orbifold eigenset, is to work to bear an overall transfer into the relative forward-holomorphic direction, -- to where this will then happen, in so as to work to form a wave-like pattern, that is to alter in the manner of its forward-holomorphic translation, by a scalar attribute, that is here to bear its resultant spin-orbital change of venue, by a multiple, that is here to be tantamount to being of the scalar amplitude, that is tantamount to being of (-i).  This, then, works to help at explaining that Ward-Cauchy-related condition, that is to generally exist from among a stated condition of a unitary Lagrangian-related operation -- as to the general relationship, that is here to exist from between any one given arbitrary Hamiltonian Operator and its correlative Lagrangian, that is here to most directly appertain to the comparison -- that is here to exist, in so as to describe, in a manner that is relatively more pictorial, -- the difference that is to be exhibited -- between the descriptive energy of any one given arbitrary respective Hamiltonian Operator, & its directly associated Lagrangian.
I will continue with the suspense later!  To Be Continued!  Sincerely, Samuel David Roach.