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In a previous paper, we developed a table of components of algebraicsolutions of a system of equations generated by an inhomogeneous proper-valueequation involving K\"ahler's total angular momentum. This table looks as if itwere a representation of real life quarks. We did not consider all options forsolutions of the system of equations that gave rise to it. We shall not,therefore, claim that the present distribution of those components as a wellordered table has strict physical relevance. It, however, is of great interestfor the purpose of developing methodology, which may then be used for othersolutions. We insert into our present table concepts that parallel those of thephenomenology of HEP: generations, color, flavor, isospin, etc. Breaking thenloose from that distribution, we consider simpler alternatives for algebraic"quarks" of primary color (The mathematics speaks of each generation having itsown primary color). We use them to show how stoichiometric argument allows oneto reach what appear to be esthetically appealing idempotent representation ofparticles for other than electrons and positrons (K\"ahler already providedthese half a century ago with idempotents similar to our hypothetical quarks).We then use neutron decay to obtain formulas for also hypothetical algebraicneutrinos and the $Z_{0}$, and use pair annihilation to obtain formulas forgamma particles. We go back to the system of equations and develop analternative option. We solve the system but stop short of studying it along thepresent line. This will thus be an easy entry point to this theory by HEPphysicists, who will be able to go aster and further.

Algebraic Quarks from the Tangent Bundle: Methodology