Part Two of the Solutions To The First Test Of Course 13

5)  An abelian geometry is the Laplacian-based differential framework of substringular phenomena that bears a wave-tug and/or a wave-pull that has a Hamiltonian operational-basis that is directly effectual when in terms of the Yakawa-based flow of mapped-out delineation of one local tense of partial differential framework relative to another local tense of partial differential framework.  The sequenial series of such a basis may often be applicable to a kinematic fluidity of motion that may be described by a Fourier Transformation.  In other situations, the kinematic fluidity of motion of what was initially a Laplacian-based mapping-out of a covariant, codifferentiable, and codeterminable condition of an abelian-based geometric scenario may be applicable to a duration that happens either within the overall metric of a given arbitrary group instanton, or, in other cases, one may consider at times the abelian-geometric conditions of either a snapshot as to what happens in-between individual durations of instanton, or, at times, instead, one may consider the abelian-geometric conditions of a kinematic flow of topological-based substringular substrate that occurs during the generally unnoticed portion of Ultimon Flow.

6)  A non-abelian geometry is a geomtric condition that differs from an abelian geometry on account of the wave-tug and/or the wave-pull that is here pertainant having here a Hamiltonian operational-basis that is directly non-effectual in terms of one substringular substrate towards another -- when under the conditions of the Yakawa-based flow of the mapped-out delineation of one local tense of partial differential framework relative to another local tense of partial differential framework.

7)  Both momentum and inertia are quantified by the basis of discrete Hamiltonian-based operations, discrete Hamiltonian-based operators, thru given arbitrary Lagrangians that here exists as discrete Hamiltonian-based operands.  A given arbitrary  discrete quantum of momentum specifically is quantified by the basis of a discrete Hamiltonian operation, while a given arbitrary discrete quantum  of inertia specifically is quantified by the basis of a discrete Hamiltonian operator.  The given arbitrary region in which the said Hamiltonian operation of momentum is pulled or tugged into -- as a holonomic substrate that exists as an entity that acts as a Hamiltonian operation of inertia -- is what I have termed of as the said discrete Hamiltonian-based operand