Rearranging constituents of composite structures to find the minimum energy configuration of each could be a nightmare without some disciplinary constraints. The forces of each charged particle on every other all mushed into one number is mind numbing. So… rather than that we take advantage of each of the two denominations of quarks being identical in kind and so each must experience the same forces as its peers. Thus, we impose a separate geometric symmetry on the ups and downs in the composite such that each and every quark of the given type will experience identical forces. We assign a single dimensional parameter to that relationship. We place the two up and down structures in a symmetric relationship whose dimension is determined by one of the separate dimensional parameters.
The individual geometric structural assignments are the following:
Two like quarks lineal geometry
Three like quarks equilateral triangular geometry
Four like quarks square geometry.
Viability demands that the two separate structures share the same center. As for example two downs on opposite sides of an up, or the other way around. Two ups on a line through a square with downs on its corners, etc. An up and down in a u-d structure are precluded from symmetric convergence by the repulsive force encountered at the crossover separation distance.
A net structural energy determination is made primarily from the electrostatic Poisson interaction energies, with gravitational corrections becoming significant only when quarks approach their crossover separation distance.
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